Struct truck_geometry::nurbs::BSplineSurface
source · pub struct BSplineSurface<P> { /* private fields */ }
Expand description
B-spline surface
Examples
use truck_geometry::*;
const N : usize = 100; // sample size in test
// the knot vectors
let knot_vec0 = KnotVec::bezier_knot(3);
let knot_vec1 = KnotVec::from(
vec![0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5, 1.0, 1.0, 1.0, 1.0]
);
let knot_vecs = (knot_vec0, knot_vec1);
// the control points
let mut v = vec![vec![Vector4::zero(); 7]; 4];
v[0][0] = Vector4::new(0.0, 0.0, 1.0, 1.0);
v[0][1] = &v[0][0] / 3.0;
v[0][2] = v[0][1].clone();
v[0][3] = v[0][0].clone();
v[0][4] = v[0][1].clone();
v[0][5] = v[0][1].clone();
v[0][6] = v[0][0].clone();
v[1][0] = Vector4::new(2.0, 0.0, 1.0, 1.0) / 3.0;
v[1][1] = Vector4::new(2.0, 4.0, 1.0, 1.0) / 9.0;
v[1][2] = Vector4::new(-2.0, 4.0, 1.0, 1.0) / 9.0;
v[1][3] = Vector4::new(-2.0, 0.0, 1.0, 1.0) / 3.0;
v[1][4] = Vector4::new(-2.0, -4.0, 1.0, 1.0) / 9.0;
v[1][5] = Vector4::new(2.0, -4.0, 1.0, 1.0) / 9.0;
v[1][6] = Vector4::new(2.0, 0.0, 1.0, 1.0) / 3.0;
v[2][0] = Vector4::new(2.0, 0.0, -1.0, 1.0) / 3.0;
v[2][1] = Vector4::new(2.0, 4.0, -1.0, 1.0) / 9.0;
v[2][2] = Vector4::new(-2.0, 4.0, -1.0, 1.0) / 9.0;
v[2][3] = Vector4::new(-2.0, 0.0, -1.0, 1.0) / 3.0;
v[2][4] = Vector4::new(-2.0, -4.0, -1.0, 1.0) / 9.0;
v[2][5] = Vector4::new(2.0, -4.0, -1.0, 1.0) / 9.0;
v[2][6] = Vector4::new(2.0, 0.0, -1.0, 1.0) / 3.0;
v[3][0] = Vector4::new(0.0, 0.0, -1.0, 1.0);
v[3][1] = &v[3][0] / 3.0;
v[3][2] = v[3][1].clone();
v[3][3] = v[3][0].clone();
v[3][4] = v[3][1].clone();
v[3][5] = v[3][1].clone();
v[3][6] = v[3][0].clone();
// cunstruct the B-spline curve
let bspline = BSplineSurface::new(knot_vecs, v);
// This B-spline curve is a nurbs representation of the unit sphere.
for i in 0..N {
for j in 0..N {
let u = 1.0 / (N as f64) * (i as f64);
let v = 1.0 / (N as f64) * (j as f64);
let v = bspline.subs(u, v); // We can use the instances as a function.
let c = (v[0] / v[3]).powi(2) + (v[1] / v[3]).powi(2) + (v[2] / v[3]).powi(2);
assert_near2!(c, 1.0);
}
}
Implementations§
source§impl<P> BSplineSurface<P>
impl<P> BSplineSurface<P>
sourcepub fn new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> BSplineSurface<P>
pub fn new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> BSplineSurface<P>
constructor.
Arguments
knot_vecs
- the knot vectorscontrol_points
- the vector of the control points
Panics
There are 3 rules for construct B-spline curve.
- The number of knots is more than the one of control points.
- There exist at least two different knots.
- There are at least one control point.
Examples found in repository?
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pub fn debug_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
) -> BSplineSurface<P> {
match cfg!(debug_assertions) {
true => Self::new(knot_vecs, control_points),
false => Self::new_unchecked(knot_vecs, control_points),
}
}
/// Returns the reference of the knot vectors
#[inline(always)]
pub const fn knot_vecs(&self) -> &(KnotVec, KnotVec) { &self.knot_vecs }
/// Returns the u knot vector.
#[inline(always)]
pub const fn uknot_vec(&self) -> &KnotVec { &self.knot_vecs.0 }
/// Returns the v knot vector.
#[inline(always)]
pub const fn vknot_vec(&self) -> &KnotVec { &self.knot_vecs.1 }
/// Returns the `idx`th u knot.
#[inline(always)]
pub fn uknot(&self, idx: usize) -> f64 { self.knot_vecs.0[idx] }
/// returns the `idx`th v knot.
#[inline(always)]
pub fn vknot(&self, idx: usize) -> f64 { self.knot_vecs.1[idx] }
/// Returns the reference of the vector of the control points
#[inline(always)]
pub const fn control_points(&self) -> &Vec<Vec<P>> { &self.control_points }
/// Returns the reference of the control point corresponding to the index `(idx0, idx1)`.
#[inline(always)]
pub fn control_point(&self, idx0: usize, idx1: usize) -> &P { &self.control_points[idx0][idx1] }
/// Apply the given transformation to all control points.
#[inline(always)]
pub fn transform_control_points<F: FnMut(&mut P)>(&mut self, f: F) {
self.control_points.iter_mut().flatten().for_each(f)
}
/// Returns the iterator over the control points in the `column_idx`th row.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut iter = bspsurface.ctrl_pts_row_iter(1);
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 0.0, 1.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
/// assert_eq!(iter.next(), None);
/// ```
#[inline(always)]
pub fn ctrl_pts_row_iter(
&self,
column_idx: usize,
) -> impl ExactSizeIterator<Item = &P> + FusedIterator<Item = &P> {
self.control_points.iter().map(move |vec| &vec[column_idx])
}
/// Returns the iterator over the control points in the `row_idx`th row.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut iter = bspsurface.ctrl_pts_column_iter(1);
/// assert_eq!(iter.next(), Some(&Vector3::new(0.0, 1.0, 0.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(2.0, 1.0, 2.0)));
/// assert_eq!(iter.next(), None);
/// ```
#[inline(always)]
pub fn ctrl_pts_column_iter(&self, row_idx: usize) -> std::slice::Iter<'_, P> {
self.control_points[row_idx].iter()
}
/// Returns the mutable reference of the control point corresponding to index `(idx0, idx1)`.
#[inline(always)]
pub fn control_point_mut(&mut self, idx0: usize, idx1: usize) -> &mut P {
&mut self.control_points[idx0][idx1]
}
/// Returns the iterator on all control points
#[inline(always)]
pub fn control_points_mut(&mut self) -> impl Iterator<Item = &mut P> {
self.control_points.iter_mut().flatten()
}
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.udegree(), 1);
/// ```
#[inline(always)]
pub fn udegree(&self) -> usize { self.knot_vecs.0.len() - self.control_points.len() - 1 }
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.vdegree(), 2);
/// ```
#[inline(always)]
pub fn vdegree(&self) -> usize { self.knot_vecs.1.len() - self.control_points[0].len() - 1 }
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.degrees(), (1, 2));
/// ```
#[inline(always)]
pub fn degrees(&self) -> (usize, usize) { (self.udegree(), self.vdegree()) }
/// Returns whether the knot vectors are clamped or not.
#[inline(always)]
pub fn is_clamped(&self) -> bool {
self.knot_vecs.0.is_clamped(self.udegree()) && self.knot_vecs.1.is_clamped(self.vdegree())
}
/// Swaps two parameters.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs0 = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts0 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface0 = BSplineSurface::new(knot_vecs0, ctrl_pts0);
///
/// let knot_vecs1 = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(1));
/// let ctrl_pts1 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 2.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface1 = BSplineSurface::new(knot_vecs1, ctrl_pts1);
/// assert_eq!(bspsurface0.swap_axes(), &bspsurface1);
/// ```
pub fn swap_axes(&mut self) -> &mut Self
where P: Clone {
let knot_vec = self.knot_vecs.0.clone();
self.knot_vecs.0 = self.knot_vecs.1.clone();
self.knot_vecs.1 = knot_vec;
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let mut new_points = vec![Vec::with_capacity(n0); n1];
for pts in &self.control_points {
for (vec0, pt) in new_points.iter_mut().zip(pts) {
vec0.push(pt.clone());
}
}
self.control_points = new_points;
self
}
/// The range of the parameter of the surface.
#[inline(always)]
pub fn parameter_range(&self) -> ((f64, f64), (f64, f64)) {
(
(
self.knot_vecs.0[0],
self.knot_vecs.0[self.knot_vecs.0.len() - 1],
),
(
self.knot_vecs.1[0],
self.knot_vecs.1[self.knot_vecs.1.len() - 1],
),
)
}
/// Creates the curve whose control points are the `idx`th column control points of `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.column_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(2));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// );
/// ```
pub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.vknot_vec().clone();
let ctrl_pts = self.control_points[row_idx].clone();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
/// Creates the column sectional curve.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.row_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(1));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(1.0, 0.0, 1.0), Vector3::new(1.0, 1.0, 1.0)],
/// );
/// ```
pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
/// Creates a surface by its boundary.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
/// assert_eq!(
/// surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// ],
/// );
/// ```
/// # Remarks
/// If the end points of curves are not connected, `curve1` and `curve3` take precedence. i.e.
/// `curve1` and `curve3` are contained in the boundary of the surface and `curve0` and
/// `curve2` are not contained.
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(
/// curve0.clone(),
/// curve1.clone(),
/// curve2.clone(),
/// curve3.clone()
/// );
/// assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
/// assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
/// ```
pub fn by_boundary(
mut curve0: BSplineCurve<P>,
mut curve1: BSplineCurve<P>,
mut curve2: BSplineCurve<P>,
mut curve3: BSplineCurve<P>,
) -> BSplineSurface<P> {
curve2.invert();
curve3.invert();
curve0.syncro_degree(&mut curve2);
curve0.optimize();
curve2.optimize();
curve0.syncro_knots(&mut curve2);
curve1.syncro_degree(&mut curve3);
curve1.optimize();
curve3.optimize();
curve1.syncro_knots(&mut curve3);
let knot_vecs = (curve0.knot_vec().clone(), curve3.knot_vec().clone());
let mut control_points = vec![curve3.control_points().clone()];
let n = curve0.control_points().len();
let m = curve3.control_points().len();
for i in 1..(n - 1) {
let u = (i as f64) / (n as f64);
let pt0 = curve2.control_points[i]
+ (curve0.control_points[i] - curve2.control_points[i]) * u;
let mut new_row = vec![*curve0.control_point(i)];
for j in 1..(m - 1) {
let v = (j as f64) / (m as f64);
let pt1 = curve1.control_points[j]
+ (curve3.control_points[j] - curve1.control_points[j]) * v;
new_row.push(pt0 + (pt1 - pt0) / 2.0);
}
new_row.push(*curve2.control_point(i));
control_points.push(new_row);
}
control_points.push(curve1.control_points().clone());
BSplineSurface::new(knot_vecs, control_points)
}
sourcepub fn try_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> Result<BSplineSurface<P>>
pub fn try_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> Result<BSplineSurface<P>>
constructor.
Arguments
knot_vecs
- the knot vectorscontrol_points
- the vector of the control points
Failures
There are 3 rules for construct B-spline curve.
- The number of knots is more than the one of control points.
- There exist at least two different knots.
- There are at least one control point.
Examples found in repository?
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pub fn new(knot_vecs: (KnotVec, KnotVec), control_points: Vec<Vec<P>>) -> BSplineSurface<P> {
BSplineSurface::try_new(knot_vecs, control_points).unwrap_or_else(|e| panic!("{}", e))
}
/// constructor.
/// # Arguments
/// * `knot_vecs` - the knot vectors
/// * `control_points` - the vector of the control points
/// # Failures
/// There are 3 rules for construct B-spline curve.
/// * The number of knots is more than the one of control points.
/// * There exist at least two different knots.
/// * There are at least one control point.
#[inline(always)]
pub fn try_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
) -> Result<BSplineSurface<P>> {
if control_points.is_empty() || control_points[0].is_empty() {
Err(Error::EmptyControlPoints)
} else if knot_vecs.0.len() <= control_points.len() {
Err(Error::TooShortKnotVector(
knot_vecs.0.len(),
control_points.len(),
))
} else if knot_vecs.1.len() <= control_points[0].len() {
Err(Error::TooShortKnotVector(
knot_vecs.1.len(),
control_points[0].len(),
))
} else if knot_vecs.0.range_length().so_small() || knot_vecs.1.range_length().so_small() {
Err(Error::ZeroRange)
} else {
let len = control_points[0].len();
if control_points.iter().any(|vec| vec.len() != len) {
Err(Error::IrregularControlPoints)
} else {
Ok(BSplineSurface::new_unchecked(knot_vecs, control_points))
}
}
}
/// constructor.
/// # Arguments
/// * `knot_vecs` - the knot vectors
/// * `control_points` - the vector of the control points
/// # Failures
/// This method is prepared only for performance-critical development and is not recommended.
/// This method does NOT check the 3 rules for constructing B-spline surface.
/// The programmer must guarantee these conditions before using this method.
#[inline(always)]
pub const fn new_unchecked(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
) -> BSplineSurface<P> {
BSplineSurface {
knot_vecs,
control_points,
}
}
/// constructor.
/// # Arguments
/// * `knot_vecs` - the knot vectors
/// * `control_points` - the vector of the control points
/// # Failures
/// This method checks the 3 rules for constructing B-spline surface in the debug mode.
/// The programmer must guarantee these conditions before using this method.
#[inline(always)]
pub fn debug_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
) -> BSplineSurface<P> {
match cfg!(debug_assertions) {
true => Self::new(knot_vecs, control_points),
false => Self::new_unchecked(knot_vecs, control_points),
}
}
/// Returns the reference of the knot vectors
#[inline(always)]
pub const fn knot_vecs(&self) -> &(KnotVec, KnotVec) { &self.knot_vecs }
/// Returns the u knot vector.
#[inline(always)]
pub const fn uknot_vec(&self) -> &KnotVec { &self.knot_vecs.0 }
/// Returns the v knot vector.
#[inline(always)]
pub const fn vknot_vec(&self) -> &KnotVec { &self.knot_vecs.1 }
/// Returns the `idx`th u knot.
#[inline(always)]
pub fn uknot(&self, idx: usize) -> f64 { self.knot_vecs.0[idx] }
/// returns the `idx`th v knot.
#[inline(always)]
pub fn vknot(&self, idx: usize) -> f64 { self.knot_vecs.1[idx] }
/// Returns the reference of the vector of the control points
#[inline(always)]
pub const fn control_points(&self) -> &Vec<Vec<P>> { &self.control_points }
/// Returns the reference of the control point corresponding to the index `(idx0, idx1)`.
#[inline(always)]
pub fn control_point(&self, idx0: usize, idx1: usize) -> &P { &self.control_points[idx0][idx1] }
/// Apply the given transformation to all control points.
#[inline(always)]
pub fn transform_control_points<F: FnMut(&mut P)>(&mut self, f: F) {
self.control_points.iter_mut().flatten().for_each(f)
}
/// Returns the iterator over the control points in the `column_idx`th row.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut iter = bspsurface.ctrl_pts_row_iter(1);
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 0.0, 1.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
/// assert_eq!(iter.next(), None);
/// ```
#[inline(always)]
pub fn ctrl_pts_row_iter(
&self,
column_idx: usize,
) -> impl ExactSizeIterator<Item = &P> + FusedIterator<Item = &P> {
self.control_points.iter().map(move |vec| &vec[column_idx])
}
/// Returns the iterator over the control points in the `row_idx`th row.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut iter = bspsurface.ctrl_pts_column_iter(1);
/// assert_eq!(iter.next(), Some(&Vector3::new(0.0, 1.0, 0.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(2.0, 1.0, 2.0)));
/// assert_eq!(iter.next(), None);
/// ```
#[inline(always)]
pub fn ctrl_pts_column_iter(&self, row_idx: usize) -> std::slice::Iter<'_, P> {
self.control_points[row_idx].iter()
}
/// Returns the mutable reference of the control point corresponding to index `(idx0, idx1)`.
#[inline(always)]
pub fn control_point_mut(&mut self, idx0: usize, idx1: usize) -> &mut P {
&mut self.control_points[idx0][idx1]
}
/// Returns the iterator on all control points
#[inline(always)]
pub fn control_points_mut(&mut self) -> impl Iterator<Item = &mut P> {
self.control_points.iter_mut().flatten()
}
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.udegree(), 1);
/// ```
#[inline(always)]
pub fn udegree(&self) -> usize { self.knot_vecs.0.len() - self.control_points.len() - 1 }
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.vdegree(), 2);
/// ```
#[inline(always)]
pub fn vdegree(&self) -> usize { self.knot_vecs.1.len() - self.control_points[0].len() - 1 }
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.degrees(), (1, 2));
/// ```
#[inline(always)]
pub fn degrees(&self) -> (usize, usize) { (self.udegree(), self.vdegree()) }
/// Returns whether the knot vectors are clamped or not.
#[inline(always)]
pub fn is_clamped(&self) -> bool {
self.knot_vecs.0.is_clamped(self.udegree()) && self.knot_vecs.1.is_clamped(self.vdegree())
}
/// Swaps two parameters.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs0 = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts0 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface0 = BSplineSurface::new(knot_vecs0, ctrl_pts0);
///
/// let knot_vecs1 = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(1));
/// let ctrl_pts1 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 2.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface1 = BSplineSurface::new(knot_vecs1, ctrl_pts1);
/// assert_eq!(bspsurface0.swap_axes(), &bspsurface1);
/// ```
pub fn swap_axes(&mut self) -> &mut Self
where P: Clone {
let knot_vec = self.knot_vecs.0.clone();
self.knot_vecs.0 = self.knot_vecs.1.clone();
self.knot_vecs.1 = knot_vec;
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let mut new_points = vec![Vec::with_capacity(n0); n1];
for pts in &self.control_points {
for (vec0, pt) in new_points.iter_mut().zip(pts) {
vec0.push(pt.clone());
}
}
self.control_points = new_points;
self
}
/// The range of the parameter of the surface.
#[inline(always)]
pub fn parameter_range(&self) -> ((f64, f64), (f64, f64)) {
(
(
self.knot_vecs.0[0],
self.knot_vecs.0[self.knot_vecs.0.len() - 1],
),
(
self.knot_vecs.1[0],
self.knot_vecs.1[self.knot_vecs.1.len() - 1],
),
)
}
/// Creates the curve whose control points are the `idx`th column control points of `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.column_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(2));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// );
/// ```
pub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.vknot_vec().clone();
let ctrl_pts = self.control_points[row_idx].clone();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
/// Creates the column sectional curve.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.row_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(1));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(1.0, 0.0, 1.0), Vector3::new(1.0, 1.0, 1.0)],
/// );
/// ```
pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
/// Creates a surface by its boundary.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
/// assert_eq!(
/// surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// ],
/// );
/// ```
/// # Remarks
/// If the end points of curves are not connected, `curve1` and `curve3` take precedence. i.e.
/// `curve1` and `curve3` are contained in the boundary of the surface and `curve0` and
/// `curve2` are not contained.
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(
/// curve0.clone(),
/// curve1.clone(),
/// curve2.clone(),
/// curve3.clone()
/// );
/// assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
/// assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
/// ```
pub fn by_boundary(
mut curve0: BSplineCurve<P>,
mut curve1: BSplineCurve<P>,
mut curve2: BSplineCurve<P>,
mut curve3: BSplineCurve<P>,
) -> BSplineSurface<P> {
curve2.invert();
curve3.invert();
curve0.syncro_degree(&mut curve2);
curve0.optimize();
curve2.optimize();
curve0.syncro_knots(&mut curve2);
curve1.syncro_degree(&mut curve3);
curve1.optimize();
curve3.optimize();
curve1.syncro_knots(&mut curve3);
let knot_vecs = (curve0.knot_vec().clone(), curve3.knot_vec().clone());
let mut control_points = vec![curve3.control_points().clone()];
let n = curve0.control_points().len();
let m = curve3.control_points().len();
for i in 1..(n - 1) {
let u = (i as f64) / (n as f64);
let pt0 = curve2.control_points[i]
+ (curve0.control_points[i] - curve2.control_points[i]) * u;
let mut new_row = vec![*curve0.control_point(i)];
for j in 1..(m - 1) {
let v = (j as f64) / (m as f64);
let pt1 = curve1.control_points[j]
+ (curve3.control_points[j] - curve1.control_points[j]) * v;
new_row.push(pt0 + (pt1 - pt0) / 2.0);
}
new_row.push(*curve2.control_point(i));
control_points.push(new_row);
}
control_points.push(curve1.control_points().clone());
BSplineSurface::new(knot_vecs, control_points)
}
/// Normalizes the knot vectors
#[inline(always)]
pub fn knot_normalize(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
self
}
/// Translates the knot vectors.
#[inline(always)]
pub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self {
self.knot_vecs.0.translate(x);
self.knot_vecs.1.translate(y);
self
}
/// Removes knots in order from the back
pub fn optimize(&mut self) -> &mut Self {
loop {
let (n0, n1) = (self.knot_vecs.0.len(), self.knot_vecs.1.len());
let mut flag = true;
for i in 1..=n0 {
flag = flag && self.try_remove_uknot(n0 - i).is_err();
}
for j in 1..=n1 {
flag = flag && self.try_remove_vknot(n1 - j).is_err();
}
if flag {
break;
}
}
self
}
/// Get the boundary by four splitted curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let curves = bspsurface.splitted_boundary();
/// assert_eq!(
/// curves[0].control_points(),
/// &vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0), Vector2::new(0.0, 2.0), Vector2::new(0.0, 3.0)],
/// );
/// assert_eq!(
/// curves[1].control_points(),
/// &vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// );
/// assert_eq!(
/// curves[2].control_points(),
/// &vec![Vector2::new(1.0, 3.0), Vector2::new(1.0, 2.0), Vector2::new(1.0, 1.0), Vector2::new(1.0, 0.0)],
/// );
/// assert_eq!(
/// curves[3].control_points(),
/// &vec![Vector2::new(1.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(0.0, 0.0)],
/// );
/// ```
pub fn splitted_boundary(&self) -> [BSplineCurve<P>; 4] {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let control_points0 = self.control_points.iter().map(|x| x[0]).collect();
let control_points1 = self.control_points.last().unwrap().clone();
let control_points2 = self
.control_points
.iter()
.map(|x| *x.last().unwrap())
.collect();
let control_points3 = self.control_points[0].clone();
let curve0 = BSplineCurve::new_unchecked(uknot_vec.clone(), control_points0);
let curve1 = BSplineCurve::new_unchecked(vknot_vec.clone(), control_points1);
let mut curve2 = BSplineCurve::new_unchecked(uknot_vec, control_points2);
curve2.invert();
let mut curve3 = BSplineCurve::new_unchecked(vknot_vec, control_points3);
curve3.invert();
[curve0, curve1, curve2, curve3]
}
/// Extracts the boundary of surface
pub fn boundary(&self) -> BSplineCurve<P> {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let (range0, range1) = (uknot_vec.range_length(), vknot_vec.range_length());
let [bspline0, mut bspline1, mut bspline2, mut bspline3] = self.splitted_boundary();
bspline0
.concat(bspline1.knot_translate(range0))
.concat(bspline2.invert().knot_translate(range0 + range1))
.concat(bspline3.invert().knot_translate(range0 * 2.0 + range1))
}
/// Determines whether `self` and `other` is near as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) = Vector2::new(0.4, 1.0);
/// assert!(!bspsurface0.near_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near(y))
}
/// Determines whether `self` and `other` is near in square order as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let eps = TOLERANCE;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) += Vector2::new(eps, eps / 2.0);
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
/// assert!(!bspsurface0.near2_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near2_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near2(y))
}
}
impl<V> BSplineSurface<V>
where V: MetricSpace<Metric = f64> + Index<usize, Output = f64> + Bounded<f64> + Copy
{
/// Returns the bounding box including all control points.
#[inline(always)]
pub fn roughly_bounding_box(&self) -> BoundingBox<V> {
self.control_points.iter().flatten().collect()
}
}
impl<P: ControlPoint<f64>> ParameterDivision2D for BSplineSurface<P>
where P: EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>
+ HashGen<f64>
{
#[inline(always)]
fn parameter_division(
&self,
range: ((f64, f64), (f64, f64)),
tol: f64,
) -> (Vec<f64>, Vec<f64>) {
algo::surface::parameter_division(self, range, tol)
}
}
impl ParametricSurface3D for BSplineSurface<Point3> {}
impl<V> BoundedSurface for BSplineSurface<V>
where BSplineSurface<V>: ParametricSurface
{
#[inline(always)]
fn parameter_range(&self) -> ((f64, f64), (f64, f64)) { self.parameter_range() }
}
impl<V: Clone> Invertible for BSplineSurface<V> {
#[inline(always)]
fn invert(&mut self) { self.swap_axes(); }
}
impl SearchParameter<D2> for BSplineSurface<Point2> {
type Point = Point2;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point2,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter2d(self, point, hint, trials)
}
}
impl SearchParameter<D2> for BSplineSurface<Point3> {
type Point = Point3;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point3,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter3d(self, point, hint, trials)
}
}
impl<P> SearchNearestParameter<D2> for BSplineSurface<P>
where
P: ControlPoint<f64>
+ EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>,
<P as ControlPoint<f64>>::Diff: InnerSpace<Scalar = f64> + Tolerance,
{
type Point = P;
fn search_nearest_parameter<H: Into<SPHint2D>>(
&self,
point: P,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_nearest_parameter(self, point, hint, trials)
}
}
impl IncludeCurve<BSplineCurve<Point2>> for BSplineSurface<Point2> {
fn include(&self, curve: &BSplineCurve<Point2>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<BSplineCurve<Point3>> for BSplineSurface<Point3> {
fn include(&self, curve: &BSplineCurve<Point3>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<NURBSCurve<Vector4>> for BSplineSurface<Point3> {
fn include(&self, curve: &NURBSCurve<Vector4>) -> bool {
let pt = curve.subs(curve.knot_vec()[0]);
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = curve.subs(t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
macro_rules! impl_mat_multi {
($vector: ty, $matrix: ty) => {
impl Mul<BSplineSurface<$vector>> for $matrix {
type Output = BSplineSurface<$vector>;
fn mul(self, mut spline: BSplineSurface<$vector>) -> Self::Output {
spline
.control_points
.iter_mut()
.flat_map(|vec| vec.iter_mut())
.for_each(|vec| *vec = self * *vec);
spline
}
}
impl Mul<&BSplineSurface<$vector>> for $matrix {
type Output = BSplineSurface<$vector>;
fn mul(self, spline: &BSplineSurface<$vector>) -> Self::Output { self * spline.clone() }
}
};
}
macro_rules! impl_scalar_multi {
($vector: ty, $scalar: ty) => {
impl_mat_multi!($vector, $scalar);
impl Mul<$scalar> for &BSplineSurface<$vector> {
type Output = BSplineSurface<$vector>;
fn mul(self, scalar: $scalar) -> Self::Output { scalar * self }
}
impl Mul<$scalar> for BSplineSurface<$vector> {
type Output = BSplineSurface<$vector>;
fn mul(self, scalar: $scalar) -> Self::Output { scalar * self }
}
};
}
impl_mat_multi!(Vector2, Matrix2);
impl_scalar_multi!(Vector2, f64);
impl_mat_multi!(Vector3, Matrix3);
impl_scalar_multi!(Vector3, f64);
impl_mat_multi!(Vector4, Matrix4);
impl_scalar_multi!(Vector4, f64);
impl<M, P: EuclideanSpace<Scalar = f64>> Transformed<M> for BSplineSurface<P>
where M: Transform<P>
{
#[inline(always)]
fn transform_by(&mut self, trans: M) {
self.control_points
.iter_mut()
.flatten()
.for_each(|p| *p = trans.transform_point(*p))
}
}
impl<'de, P> Deserialize<'de> for BSplineSurface<P>
where P: Deserialize<'de>
{
fn deserialize<D>(deserializer: D) -> std::result::Result<Self, D::Error>
where D: serde::Deserializer<'de> {
#[derive(Deserialize)]
struct BSplineSurface_<P> {
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
}
let BSplineSurface_ {
knot_vecs,
control_points,
} = BSplineSurface_::<P>::deserialize(deserializer)?;
Self::try_new(knot_vecs, control_points).map_err(serde::de::Error::custom)
}
sourcepub const fn new_unchecked(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> BSplineSurface<P>
pub const fn new_unchecked(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> BSplineSurface<P>
constructor.
Arguments
knot_vecs
- the knot vectorscontrol_points
- the vector of the control points
Failures
This method is prepared only for performance-critical development and is not recommended.
This method does NOT check the 3 rules for constructing B-spline surface.
The programmer must guarantee these conditions before using this method.
Examples found in repository?
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pub fn try_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
) -> Result<BSplineSurface<P>> {
if control_points.is_empty() || control_points[0].is_empty() {
Err(Error::EmptyControlPoints)
} else if knot_vecs.0.len() <= control_points.len() {
Err(Error::TooShortKnotVector(
knot_vecs.0.len(),
control_points.len(),
))
} else if knot_vecs.1.len() <= control_points[0].len() {
Err(Error::TooShortKnotVector(
knot_vecs.1.len(),
control_points[0].len(),
))
} else if knot_vecs.0.range_length().so_small() || knot_vecs.1.range_length().so_small() {
Err(Error::ZeroRange)
} else {
let len = control_points[0].len();
if control_points.iter().any(|vec| vec.len() != len) {
Err(Error::IrregularControlPoints)
} else {
Ok(BSplineSurface::new_unchecked(knot_vecs, control_points))
}
}
}
/// constructor.
/// # Arguments
/// * `knot_vecs` - the knot vectors
/// * `control_points` - the vector of the control points
/// # Failures
/// This method is prepared only for performance-critical development and is not recommended.
/// This method does NOT check the 3 rules for constructing B-spline surface.
/// The programmer must guarantee these conditions before using this method.
#[inline(always)]
pub const fn new_unchecked(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
) -> BSplineSurface<P> {
BSplineSurface {
knot_vecs,
control_points,
}
}
/// constructor.
/// # Arguments
/// * `knot_vecs` - the knot vectors
/// * `control_points` - the vector of the control points
/// # Failures
/// This method checks the 3 rules for constructing B-spline surface in the debug mode.
/// The programmer must guarantee these conditions before using this method.
#[inline(always)]
pub fn debug_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>,
) -> BSplineSurface<P> {
match cfg!(debug_assertions) {
true => Self::new(knot_vecs, control_points),
false => Self::new_unchecked(knot_vecs, control_points),
}
}
/// Returns the reference of the knot vectors
#[inline(always)]
pub const fn knot_vecs(&self) -> &(KnotVec, KnotVec) { &self.knot_vecs }
/// Returns the u knot vector.
#[inline(always)]
pub const fn uknot_vec(&self) -> &KnotVec { &self.knot_vecs.0 }
/// Returns the v knot vector.
#[inline(always)]
pub const fn vknot_vec(&self) -> &KnotVec { &self.knot_vecs.1 }
/// Returns the `idx`th u knot.
#[inline(always)]
pub fn uknot(&self, idx: usize) -> f64 { self.knot_vecs.0[idx] }
/// returns the `idx`th v knot.
#[inline(always)]
pub fn vknot(&self, idx: usize) -> f64 { self.knot_vecs.1[idx] }
/// Returns the reference of the vector of the control points
#[inline(always)]
pub const fn control_points(&self) -> &Vec<Vec<P>> { &self.control_points }
/// Returns the reference of the control point corresponding to the index `(idx0, idx1)`.
#[inline(always)]
pub fn control_point(&self, idx0: usize, idx1: usize) -> &P { &self.control_points[idx0][idx1] }
/// Apply the given transformation to all control points.
#[inline(always)]
pub fn transform_control_points<F: FnMut(&mut P)>(&mut self, f: F) {
self.control_points.iter_mut().flatten().for_each(f)
}
/// Returns the iterator over the control points in the `column_idx`th row.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut iter = bspsurface.ctrl_pts_row_iter(1);
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 0.0, 1.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
/// assert_eq!(iter.next(), None);
/// ```
#[inline(always)]
pub fn ctrl_pts_row_iter(
&self,
column_idx: usize,
) -> impl ExactSizeIterator<Item = &P> + FusedIterator<Item = &P> {
self.control_points.iter().map(move |vec| &vec[column_idx])
}
/// Returns the iterator over the control points in the `row_idx`th row.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut iter = bspsurface.ctrl_pts_column_iter(1);
/// assert_eq!(iter.next(), Some(&Vector3::new(0.0, 1.0, 0.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
/// assert_eq!(iter.next(), Some(&Vector3::new(2.0, 1.0, 2.0)));
/// assert_eq!(iter.next(), None);
/// ```
#[inline(always)]
pub fn ctrl_pts_column_iter(&self, row_idx: usize) -> std::slice::Iter<'_, P> {
self.control_points[row_idx].iter()
}
/// Returns the mutable reference of the control point corresponding to index `(idx0, idx1)`.
#[inline(always)]
pub fn control_point_mut(&mut self, idx0: usize, idx1: usize) -> &mut P {
&mut self.control_points[idx0][idx1]
}
/// Returns the iterator on all control points
#[inline(always)]
pub fn control_points_mut(&mut self) -> impl Iterator<Item = &mut P> {
self.control_points.iter_mut().flatten()
}
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.udegree(), 1);
/// ```
#[inline(always)]
pub fn udegree(&self) -> usize { self.knot_vecs.0.len() - self.control_points.len() - 1 }
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.vdegree(), 2);
/// ```
#[inline(always)]
pub fn vdegree(&self) -> usize { self.knot_vecs.1.len() - self.control_points[0].len() - 1 }
/// Returns the degrees of B-spline surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
/// let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// assert_eq!(bspsurface.degrees(), (1, 2));
/// ```
#[inline(always)]
pub fn degrees(&self) -> (usize, usize) { (self.udegree(), self.vdegree()) }
/// Returns whether the knot vectors are clamped or not.
#[inline(always)]
pub fn is_clamped(&self) -> bool {
self.knot_vecs.0.is_clamped(self.udegree()) && self.knot_vecs.1.is_clamped(self.vdegree())
}
/// Swaps two parameters.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs0 = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts0 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface0 = BSplineSurface::new(knot_vecs0, ctrl_pts0);
///
/// let knot_vecs1 = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(1));
/// let ctrl_pts1 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 2.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface1 = BSplineSurface::new(knot_vecs1, ctrl_pts1);
/// assert_eq!(bspsurface0.swap_axes(), &bspsurface1);
/// ```
pub fn swap_axes(&mut self) -> &mut Self
where P: Clone {
let knot_vec = self.knot_vecs.0.clone();
self.knot_vecs.0 = self.knot_vecs.1.clone();
self.knot_vecs.1 = knot_vec;
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let mut new_points = vec![Vec::with_capacity(n0); n1];
for pts in &self.control_points {
for (vec0, pt) in new_points.iter_mut().zip(pts) {
vec0.push(pt.clone());
}
}
self.control_points = new_points;
self
}
/// The range of the parameter of the surface.
#[inline(always)]
pub fn parameter_range(&self) -> ((f64, f64), (f64, f64)) {
(
(
self.knot_vecs.0[0],
self.knot_vecs.0[self.knot_vecs.0.len() - 1],
),
(
self.knot_vecs.1[0],
self.knot_vecs.1[self.knot_vecs.1.len() - 1],
),
)
}
/// Creates the curve whose control points are the `idx`th column control points of `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.column_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(2));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// );
/// ```
pub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.vknot_vec().clone();
let ctrl_pts = self.control_points[row_idx].clone();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
/// Creates the column sectional curve.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.row_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(1));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(1.0, 0.0, 1.0), Vector3::new(1.0, 1.0, 1.0)],
/// );
/// ```
pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
sourcepub fn debug_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> BSplineSurface<P>
pub fn debug_new(
knot_vecs: (KnotVec, KnotVec),
control_points: Vec<Vec<P>>
) -> BSplineSurface<P>
constructor.
Arguments
knot_vecs
- the knot vectorscontrol_points
- the vector of the control points
Failures
This method checks the 3 rules for constructing B-spline surface in the debug mode.
The programmer must guarantee these conditions before using this method.
Examples found in repository?
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pub fn into_bspline(&self) -> BSplineSurface<Point3> {
let o = self.o;
let p = self.p;
let q = self.q;
BSplineSurface::debug_new(
(KnotVec::bezier_knot(1), KnotVec::bezier_knot(1)),
vec![vec![o, q], vec![p, p + (q - o)]],
)
}
/// into NURBS surface
/// # Examples
/// ```
/// use truck_geometry::*;
/// let pt0 = Point3::new(0.0, 1.0, 2.0);
/// let pt1 = Point3::new(1.0, 1.0, 3.0);
/// let pt2 = Point3::new(0.0, 2.0, 3.0);
/// let plane: Plane = Plane::new(pt0, pt1, pt2);
/// let surface: NURBSSurface<Vector4> = plane.into_nurbs();
/// assert_eq!(surface.parameter_range(), ((0.0, 1.0), (0.0, 1.0)));
///
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = i as f64 / N as f64;
/// let v = j as f64 / N as f64;
/// let res = surface.subs(u, v);
/// let ans = plane.subs(u, v);
/// assert_near!(ans, res);
/// }
/// }
/// ```
#[inline(always)]
pub fn into_nurbs(&self) -> NURBSSurface<Vector4> {
let o = self.o.to_homogeneous();
let p = self.p.to_homogeneous();
let q = self.q.to_homogeneous();
NURBSSurface::new(BSplineSurface::debug_new(
(KnotVec::bezier_knot(1), KnotVec::bezier_knot(1)),
vec![vec![o, q], vec![p, p + q - o]],
))
}
sourcepub const fn knot_vecs(&self) -> &(KnotVec, KnotVec)
pub const fn knot_vecs(&self) -> &(KnotVec, KnotVec)
Returns the reference of the knot vectors
Examples found in repository?
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fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
sourcepub const fn uknot_vec(&self) -> &KnotVec
pub const fn uknot_vec(&self) -> &KnotVec
Returns the u knot vector.
Examples found in repository?
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pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
/// Creates a surface by its boundary.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
/// assert_eq!(
/// surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// ],
/// );
/// ```
/// # Remarks
/// If the end points of curves are not connected, `curve1` and `curve3` take precedence. i.e.
/// `curve1` and `curve3` are contained in the boundary of the surface and `curve0` and
/// `curve2` are not contained.
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(
/// curve0.clone(),
/// curve1.clone(),
/// curve2.clone(),
/// curve3.clone()
/// );
/// assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
/// assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
/// ```
pub fn by_boundary(
mut curve0: BSplineCurve<P>,
mut curve1: BSplineCurve<P>,
mut curve2: BSplineCurve<P>,
mut curve3: BSplineCurve<P>,
) -> BSplineSurface<P> {
curve2.invert();
curve3.invert();
curve0.syncro_degree(&mut curve2);
curve0.optimize();
curve2.optimize();
curve0.syncro_knots(&mut curve2);
curve1.syncro_degree(&mut curve3);
curve1.optimize();
curve3.optimize();
curve1.syncro_knots(&mut curve3);
let knot_vecs = (curve0.knot_vec().clone(), curve3.knot_vec().clone());
let mut control_points = vec![curve3.control_points().clone()];
let n = curve0.control_points().len();
let m = curve3.control_points().len();
for i in 1..(n - 1) {
let u = (i as f64) / (n as f64);
let pt0 = curve2.control_points[i]
+ (curve0.control_points[i] - curve2.control_points[i]) * u;
let mut new_row = vec![*curve0.control_point(i)];
for j in 1..(m - 1) {
let v = (j as f64) / (m as f64);
let pt1 = curve1.control_points[j]
+ (curve3.control_points[j] - curve1.control_points[j]) * v;
new_row.push(pt0 + (pt1 - pt0) / 2.0);
}
new_row.push(*curve2.control_point(i));
control_points.push(new_row);
}
control_points.push(curve1.control_points().clone());
BSplineSurface::new(knot_vecs, control_points)
}
/// Normalizes the knot vectors
#[inline(always)]
pub fn knot_normalize(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
self
}
/// Translates the knot vectors.
#[inline(always)]
pub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self {
self.knot_vecs.0.translate(x);
self.knot_vecs.1.translate(y);
self
}
/// Removes knots in order from the back
pub fn optimize(&mut self) -> &mut Self {
loop {
let (n0, n1) = (self.knot_vecs.0.len(), self.knot_vecs.1.len());
let mut flag = true;
for i in 1..=n0 {
flag = flag && self.try_remove_uknot(n0 - i).is_err();
}
for j in 1..=n1 {
flag = flag && self.try_remove_vknot(n1 - j).is_err();
}
if flag {
break;
}
}
self
}
/// Get the boundary by four splitted curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let curves = bspsurface.splitted_boundary();
/// assert_eq!(
/// curves[0].control_points(),
/// &vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0), Vector2::new(0.0, 2.0), Vector2::new(0.0, 3.0)],
/// );
/// assert_eq!(
/// curves[1].control_points(),
/// &vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// );
/// assert_eq!(
/// curves[2].control_points(),
/// &vec![Vector2::new(1.0, 3.0), Vector2::new(1.0, 2.0), Vector2::new(1.0, 1.0), Vector2::new(1.0, 0.0)],
/// );
/// assert_eq!(
/// curves[3].control_points(),
/// &vec![Vector2::new(1.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(0.0, 0.0)],
/// );
/// ```
pub fn splitted_boundary(&self) -> [BSplineCurve<P>; 4] {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let control_points0 = self.control_points.iter().map(|x| x[0]).collect();
let control_points1 = self.control_points.last().unwrap().clone();
let control_points2 = self
.control_points
.iter()
.map(|x| *x.last().unwrap())
.collect();
let control_points3 = self.control_points[0].clone();
let curve0 = BSplineCurve::new_unchecked(uknot_vec.clone(), control_points0);
let curve1 = BSplineCurve::new_unchecked(vknot_vec.clone(), control_points1);
let mut curve2 = BSplineCurve::new_unchecked(uknot_vec, control_points2);
curve2.invert();
let mut curve3 = BSplineCurve::new_unchecked(vknot_vec, control_points3);
curve3.invert();
[curve0, curve1, curve2, curve3]
}
/// Extracts the boundary of surface
pub fn boundary(&self) -> BSplineCurve<P> {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let (range0, range1) = (uknot_vec.range_length(), vknot_vec.range_length());
let [bspline0, mut bspline1, mut bspline2, mut bspline3] = self.splitted_boundary();
bspline0
.concat(bspline1.knot_translate(range0))
.concat(bspline2.invert().knot_translate(range0 + range1))
.concat(bspline3.invert().knot_translate(range0 * 2.0 + range1))
}
/// Determines whether `self` and `other` is near as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) = Vector2::new(0.4, 1.0);
/// assert!(!bspsurface0.near_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near(y))
}
/// Determines whether `self` and `other` is near in square order as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let eps = TOLERANCE;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) += Vector2::new(eps, eps / 2.0);
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
/// assert!(!bspsurface0.near2_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near2_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near2(y))
}
}
impl<V> BSplineSurface<V>
where V: MetricSpace<Metric = f64> + Index<usize, Output = f64> + Bounded<f64> + Copy
{
/// Returns the bounding box including all control points.
#[inline(always)]
pub fn roughly_bounding_box(&self) -> BoundingBox<V> {
self.control_points.iter().flatten().collect()
}
}
impl<P: ControlPoint<f64>> ParameterDivision2D for BSplineSurface<P>
where P: EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>
+ HashGen<f64>
{
#[inline(always)]
fn parameter_division(
&self,
range: ((f64, f64), (f64, f64)),
tol: f64,
) -> (Vec<f64>, Vec<f64>) {
algo::surface::parameter_division(self, range, tol)
}
}
impl ParametricSurface3D for BSplineSurface<Point3> {}
impl<V> BoundedSurface for BSplineSurface<V>
where BSplineSurface<V>: ParametricSurface
{
#[inline(always)]
fn parameter_range(&self) -> ((f64, f64), (f64, f64)) { self.parameter_range() }
}
impl<V: Clone> Invertible for BSplineSurface<V> {
#[inline(always)]
fn invert(&mut self) { self.swap_axes(); }
}
impl SearchParameter<D2> for BSplineSurface<Point2> {
type Point = Point2;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point2,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter2d(self, point, hint, trials)
}
}
impl SearchParameter<D2> for BSplineSurface<Point3> {
type Point = Point3;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point3,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter3d(self, point, hint, trials)
}
}
impl<P> SearchNearestParameter<D2> for BSplineSurface<P>
where
P: ControlPoint<f64>
+ EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>,
<P as ControlPoint<f64>>::Diff: InnerSpace<Scalar = f64> + Tolerance,
{
type Point = P;
fn search_nearest_parameter<H: Into<SPHint2D>>(
&self,
point: P,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_nearest_parameter(self, point, hint, trials)
}
}
impl IncludeCurve<BSplineCurve<Point2>> for BSplineSurface<Point2> {
fn include(&self, curve: &BSplineCurve<Point2>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<BSplineCurve<Point3>> for BSplineSurface<Point3> {
fn include(&self, curve: &BSplineCurve<Point3>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<NURBSCurve<Vector4>> for BSplineSurface<Point3> {
fn include(&self, curve: &NURBSCurve<Vector4>) -> bool {
let pt = curve.subs(curve.knot_vec()[0]);
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = curve.subs(t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
sourcepub const fn vknot_vec(&self) -> &KnotVec
pub const fn vknot_vec(&self) -> &KnotVec
Returns the v knot vector.
Examples found in repository?
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pub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.vknot_vec().clone();
let ctrl_pts = self.control_points[row_idx].clone();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
/// Creates the column sectional curve.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.row_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(1));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(1.0, 0.0, 1.0), Vector3::new(1.0, 1.0, 1.0)],
/// );
/// ```
pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
/// Creates a surface by its boundary.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
/// assert_eq!(
/// surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// ],
/// );
/// ```
/// # Remarks
/// If the end points of curves are not connected, `curve1` and `curve3` take precedence. i.e.
/// `curve1` and `curve3` are contained in the boundary of the surface and `curve0` and
/// `curve2` are not contained.
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(
/// curve0.clone(),
/// curve1.clone(),
/// curve2.clone(),
/// curve3.clone()
/// );
/// assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
/// assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
/// ```
pub fn by_boundary(
mut curve0: BSplineCurve<P>,
mut curve1: BSplineCurve<P>,
mut curve2: BSplineCurve<P>,
mut curve3: BSplineCurve<P>,
) -> BSplineSurface<P> {
curve2.invert();
curve3.invert();
curve0.syncro_degree(&mut curve2);
curve0.optimize();
curve2.optimize();
curve0.syncro_knots(&mut curve2);
curve1.syncro_degree(&mut curve3);
curve1.optimize();
curve3.optimize();
curve1.syncro_knots(&mut curve3);
let knot_vecs = (curve0.knot_vec().clone(), curve3.knot_vec().clone());
let mut control_points = vec![curve3.control_points().clone()];
let n = curve0.control_points().len();
let m = curve3.control_points().len();
for i in 1..(n - 1) {
let u = (i as f64) / (n as f64);
let pt0 = curve2.control_points[i]
+ (curve0.control_points[i] - curve2.control_points[i]) * u;
let mut new_row = vec![*curve0.control_point(i)];
for j in 1..(m - 1) {
let v = (j as f64) / (m as f64);
let pt1 = curve1.control_points[j]
+ (curve3.control_points[j] - curve1.control_points[j]) * v;
new_row.push(pt0 + (pt1 - pt0) / 2.0);
}
new_row.push(*curve2.control_point(i));
control_points.push(new_row);
}
control_points.push(curve1.control_points().clone());
BSplineSurface::new(knot_vecs, control_points)
}
/// Normalizes the knot vectors
#[inline(always)]
pub fn knot_normalize(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
self
}
/// Translates the knot vectors.
#[inline(always)]
pub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self {
self.knot_vecs.0.translate(x);
self.knot_vecs.1.translate(y);
self
}
/// Removes knots in order from the back
pub fn optimize(&mut self) -> &mut Self {
loop {
let (n0, n1) = (self.knot_vecs.0.len(), self.knot_vecs.1.len());
let mut flag = true;
for i in 1..=n0 {
flag = flag && self.try_remove_uknot(n0 - i).is_err();
}
for j in 1..=n1 {
flag = flag && self.try_remove_vknot(n1 - j).is_err();
}
if flag {
break;
}
}
self
}
/// Get the boundary by four splitted curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let curves = bspsurface.splitted_boundary();
/// assert_eq!(
/// curves[0].control_points(),
/// &vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0), Vector2::new(0.0, 2.0), Vector2::new(0.0, 3.0)],
/// );
/// assert_eq!(
/// curves[1].control_points(),
/// &vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// );
/// assert_eq!(
/// curves[2].control_points(),
/// &vec![Vector2::new(1.0, 3.0), Vector2::new(1.0, 2.0), Vector2::new(1.0, 1.0), Vector2::new(1.0, 0.0)],
/// );
/// assert_eq!(
/// curves[3].control_points(),
/// &vec![Vector2::new(1.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(0.0, 0.0)],
/// );
/// ```
pub fn splitted_boundary(&self) -> [BSplineCurve<P>; 4] {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let control_points0 = self.control_points.iter().map(|x| x[0]).collect();
let control_points1 = self.control_points.last().unwrap().clone();
let control_points2 = self
.control_points
.iter()
.map(|x| *x.last().unwrap())
.collect();
let control_points3 = self.control_points[0].clone();
let curve0 = BSplineCurve::new_unchecked(uknot_vec.clone(), control_points0);
let curve1 = BSplineCurve::new_unchecked(vknot_vec.clone(), control_points1);
let mut curve2 = BSplineCurve::new_unchecked(uknot_vec, control_points2);
curve2.invert();
let mut curve3 = BSplineCurve::new_unchecked(vknot_vec, control_points3);
curve3.invert();
[curve0, curve1, curve2, curve3]
}
/// Extracts the boundary of surface
pub fn boundary(&self) -> BSplineCurve<P> {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let (range0, range1) = (uknot_vec.range_length(), vknot_vec.range_length());
let [bspline0, mut bspline1, mut bspline2, mut bspline3] = self.splitted_boundary();
bspline0
.concat(bspline1.knot_translate(range0))
.concat(bspline2.invert().knot_translate(range0 + range1))
.concat(bspline3.invert().knot_translate(range0 * 2.0 + range1))
}
/// Determines whether `self` and `other` is near as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) = Vector2::new(0.4, 1.0);
/// assert!(!bspsurface0.near_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near(y))
}
/// Determines whether `self` and `other` is near in square order as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let eps = TOLERANCE;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) += Vector2::new(eps, eps / 2.0);
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
/// assert!(!bspsurface0.near2_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near2_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near2(y))
}
}
impl<V> BSplineSurface<V>
where V: MetricSpace<Metric = f64> + Index<usize, Output = f64> + Bounded<f64> + Copy
{
/// Returns the bounding box including all control points.
#[inline(always)]
pub fn roughly_bounding_box(&self) -> BoundingBox<V> {
self.control_points.iter().flatten().collect()
}
}
impl<P: ControlPoint<f64>> ParameterDivision2D for BSplineSurface<P>
where P: EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>
+ HashGen<f64>
{
#[inline(always)]
fn parameter_division(
&self,
range: ((f64, f64), (f64, f64)),
tol: f64,
) -> (Vec<f64>, Vec<f64>) {
algo::surface::parameter_division(self, range, tol)
}
}
impl ParametricSurface3D for BSplineSurface<Point3> {}
impl<V> BoundedSurface for BSplineSurface<V>
where BSplineSurface<V>: ParametricSurface
{
#[inline(always)]
fn parameter_range(&self) -> ((f64, f64), (f64, f64)) { self.parameter_range() }
}
impl<V: Clone> Invertible for BSplineSurface<V> {
#[inline(always)]
fn invert(&mut self) { self.swap_axes(); }
}
impl SearchParameter<D2> for BSplineSurface<Point2> {
type Point = Point2;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point2,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter2d(self, point, hint, trials)
}
}
impl SearchParameter<D2> for BSplineSurface<Point3> {
type Point = Point3;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point3,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter3d(self, point, hint, trials)
}
}
impl<P> SearchNearestParameter<D2> for BSplineSurface<P>
where
P: ControlPoint<f64>
+ EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>,
<P as ControlPoint<f64>>::Diff: InnerSpace<Scalar = f64> + Tolerance,
{
type Point = P;
fn search_nearest_parameter<H: Into<SPHint2D>>(
&self,
point: P,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_nearest_parameter(self, point, hint, trials)
}
}
impl IncludeCurve<BSplineCurve<Point2>> for BSplineSurface<Point2> {
fn include(&self, curve: &BSplineCurve<Point2>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<BSplineCurve<Point3>> for BSplineSurface<Point3> {
fn include(&self, curve: &BSplineCurve<Point3>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<NURBSCurve<Vector4>> for BSplineSurface<Point3> {
fn include(&self, curve: &NURBSCurve<Vector4>) -> bool {
let pt = curve.subs(curve.knot_vec()[0]);
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = curve.subs(t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
sourcepub fn uknot(&self, idx: usize) -> f64
pub fn uknot(&self, idx: usize) -> f64
Returns the idx
th u knot.
Examples found in repository?
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pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
sourcepub fn vknot(&self, idx: usize) -> f64
pub fn vknot(&self, idx: usize) -> f64
returns the idx
th v knot.
Examples found in repository?
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pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
sourcepub const fn control_points(&self) -> &Vec<Vec<P>> ⓘ
pub const fn control_points(&self) -> &Vec<Vec<P>> ⓘ
Returns the reference of the vector of the control points
sourcepub fn control_point(&self, idx0: usize, idx1: usize) -> &P
pub fn control_point(&self, idx0: usize, idx1: usize) -> &P
Returns the reference of the control point corresponding to the index (idx0, idx1)
.
Examples found in repository?
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fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
sourcepub fn transform_control_points<F: FnMut(&mut P)>(&mut self, f: F)
pub fn transform_control_points<F: FnMut(&mut P)>(&mut self, f: F)
Apply the given transformation to all control points.
sourcepub fn ctrl_pts_row_iter(
&self,
column_idx: usize
) -> impl ExactSizeIterator<Item = &P> + FusedIterator<Item = &P>
pub fn ctrl_pts_row_iter(
&self,
column_idx: usize
) -> impl ExactSizeIterator<Item = &P> + FusedIterator<Item = &P>
Returns the iterator over the control points in the column_idx
th row.
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::bezier_knot(1);
let vknot_vec = KnotVec::bezier_knot(2);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let mut iter = bspsurface.ctrl_pts_row_iter(1);
assert_eq!(iter.next(), Some(&Vector3::new(1.0, 0.0, 1.0)));
assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
assert_eq!(iter.next(), None);
Examples found in repository?
More examples
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pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
sourcepub fn ctrl_pts_column_iter(&self, row_idx: usize) -> Iter<'_, P>
pub fn ctrl_pts_column_iter(&self, row_idx: usize) -> Iter<'_, P>
Returns the iterator over the control points in the row_idx
th row.
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::bezier_knot(1);
let vknot_vec = KnotVec::bezier_knot(2);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let mut iter = bspsurface.ctrl_pts_column_iter(1);
assert_eq!(iter.next(), Some(&Vector3::new(0.0, 1.0, 0.0)));
assert_eq!(iter.next(), Some(&Vector3::new(1.0, 1.0, 1.0)));
assert_eq!(iter.next(), Some(&Vector3::new(2.0, 1.0, 2.0)));
assert_eq!(iter.next(), None);
Examples found in repository?
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pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
sourcepub fn control_point_mut(&mut self, idx0: usize, idx1: usize) -> &mut P
pub fn control_point_mut(&mut self, idx0: usize, idx1: usize) -> &mut P
Returns the mutable reference of the control point corresponding to index (idx0, idx1)
.
sourcepub fn control_points_mut(&mut self) -> impl Iterator<Item = &mut P>
pub fn control_points_mut(&mut self) -> impl Iterator<Item = &mut P>
Returns the iterator on all control points
sourcepub fn udegree(&self) -> usize
pub fn udegree(&self) -> usize
Returns the degrees of B-spline surface
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
assert_eq!(bspsurface.udegree(), 1);
Examples found in repository?
More examples
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pub fn degrees(&self) -> (usize, usize) { (self.udegree(), self.vdegree()) }
/// Returns whether the knot vectors are clamped or not.
#[inline(always)]
pub fn is_clamped(&self) -> bool {
self.knot_vecs.0.is_clamped(self.udegree()) && self.knot_vecs.1.is_clamped(self.vdegree())
}
/// Swaps two parameters.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs0 = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts0 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface0 = BSplineSurface::new(knot_vecs0, ctrl_pts0);
///
/// let knot_vecs1 = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(1));
/// let ctrl_pts1 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 2.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface1 = BSplineSurface::new(knot_vecs1, ctrl_pts1);
/// assert_eq!(bspsurface0.swap_axes(), &bspsurface1);
/// ```
pub fn swap_axes(&mut self) -> &mut Self
where P: Clone {
let knot_vec = self.knot_vecs.0.clone();
self.knot_vecs.0 = self.knot_vecs.1.clone();
self.knot_vecs.1 = knot_vec;
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let mut new_points = vec![Vec::with_capacity(n0); n1];
for pts in &self.control_points {
for (vec0, pt) in new_points.iter_mut().zip(pts) {
vec0.push(pt.clone());
}
}
self.control_points = new_points;
self
}
/// The range of the parameter of the surface.
#[inline(always)]
pub fn parameter_range(&self) -> ((f64, f64), (f64, f64)) {
(
(
self.knot_vecs.0[0],
self.knot_vecs.0[self.knot_vecs.0.len() - 1],
),
(
self.knot_vecs.1[0],
self.knot_vecs.1[self.knot_vecs.1.len() - 1],
),
)
}
/// Creates the curve whose control points are the `idx`th column control points of `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.column_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(2));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// );
/// ```
pub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.vknot_vec().clone();
let ctrl_pts = self.control_points[row_idx].clone();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
/// Creates the column sectional curve.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.row_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(1));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(1.0, 0.0, 1.0), Vector3::new(1.0, 1.0, 1.0)],
/// );
/// ```
pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
sourcepub fn vdegree(&self) -> usize
pub fn vdegree(&self) -> usize
Returns the degrees of B-spline surface
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
assert_eq!(bspsurface.vdegree(), 2);
Examples found in repository?
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pub fn degrees(&self) -> (usize, usize) { (self.udegree(), self.vdegree()) }
/// Returns whether the knot vectors are clamped or not.
#[inline(always)]
pub fn is_clamped(&self) -> bool {
self.knot_vecs.0.is_clamped(self.udegree()) && self.knot_vecs.1.is_clamped(self.vdegree())
}
/// Swaps two parameters.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs0 = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts0 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface0 = BSplineSurface::new(knot_vecs0, ctrl_pts0);
///
/// let knot_vecs1 = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(1));
/// let ctrl_pts1 = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 2.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface1 = BSplineSurface::new(knot_vecs1, ctrl_pts1);
/// assert_eq!(bspsurface0.swap_axes(), &bspsurface1);
/// ```
pub fn swap_axes(&mut self) -> &mut Self
where P: Clone {
let knot_vec = self.knot_vecs.0.clone();
self.knot_vecs.0 = self.knot_vecs.1.clone();
self.knot_vecs.1 = knot_vec;
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let mut new_points = vec![Vec::with_capacity(n0); n1];
for pts in &self.control_points {
for (vec0, pt) in new_points.iter_mut().zip(pts) {
vec0.push(pt.clone());
}
}
self.control_points = new_points;
self
}
/// The range of the parameter of the surface.
#[inline(always)]
pub fn parameter_range(&self) -> ((f64, f64), (f64, f64)) {
(
(
self.knot_vecs.0[0],
self.knot_vecs.0[self.knot_vecs.0.len() - 1],
),
(
self.knot_vecs.1[0],
self.knot_vecs.1[self.knot_vecs.1.len() - 1],
),
)
}
/// Creates the curve whose control points are the `idx`th column control points of `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.column_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(2));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// );
/// ```
pub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.vknot_vec().clone();
let ctrl_pts = self.control_points[row_idx].clone();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
/// Creates the column sectional curve.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let bspcurve = bspsurface.row_curve(1);
///
/// assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(1));
/// assert_eq!(
/// bspcurve.control_points(),
/// &vec![Vector3::new(1.0, 0.0, 1.0), Vector3::new(1.0, 1.0, 1.0)],
/// );
/// ```
pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>
where P: Clone {
let knot_vec = self.uknot_vec().clone();
let ctrl_pts: Vec<_> = self.ctrl_pts_row_iter(column_idx).cloned().collect();
BSplineCurve::new_unchecked(knot_vec, ctrl_pts)
}
}
impl<P: ControlPoint<f64>> BSplineSurface<P> {
/// Returns the closure of substitution.
#[inline(always)]
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_ { move |u, v| self.subs(u, v) }
#[inline(always)]
fn udelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if i == 0 {
self.control_point(i, j).to_vec()
} else if i == self.control_points.len() {
self.control_point(i - 1, j).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i - 1, j)
}
}
#[inline(always)]
fn udelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.udegree();
let knot_vec = self.uknot_vec();
if i == 0 {
let coef = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
self.udelta_control_points(i, j) * coef
} else if i == self.control_points.len() + 1 {
let coef = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i - 1, j) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[i + k] - knot_vec[i]);
let coef1 = inv_or_zero(knot_vec[i - 1 + k] - knot_vec[i - 1]);
self.udelta_control_points(i, j) * coef0 - self.udelta_control_points(i - 1, j) * coef1
}
}
#[inline(always)]
fn vdelta_control_points(&self, i: usize, j: usize) -> P::Diff {
if j == 0 {
self.control_point(i, j).to_vec()
} else if j == self.control_points[0].len() {
self.control_point(i, j - 1).to_vec() * (-1.0)
} else {
*self.control_point(i, j) - *self.control_point(i, j - 1)
}
}
#[inline(always)]
fn vdelta2_control_points(&self, i: usize, j: usize) -> P::Diff {
let k = self.vdegree();
let knot_vec = self.vknot_vec();
if j == 0 {
let coef = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
self.vdelta_control_points(i, j) * coef
} else if j == self.control_points[0].len() + 1 {
let coef = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j - 1) * (-coef)
} else {
let coef0 = inv_or_zero(knot_vec[j + k] - knot_vec[j]);
let coef1 = inv_or_zero(knot_vec[j - 1 + k] - knot_vec[j - 1]);
self.vdelta_control_points(i, j) * coef0 - self.vdelta_control_points(i, j - 1) * coef1
}
}
/// Calculate derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let uderivation = bspsurface.uderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 1..N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// uderivation.subs(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
sourcepub fn degrees(&self) -> (usize, usize)
pub fn degrees(&self) -> (usize, usize)
Returns the degrees of B-spline surface
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0]);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
assert_eq!(bspsurface.degrees(), (1, 2));
Examples found in repository?
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pub fn uderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (k, _) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
(0..=n0)
.map(|i| {
let delta = uknot_vec[i + k] - uknot_vec[i];
let coef = (k as f64) * inv_or_zero(delta);
(0..n1)
.map(|j| self.udelta_control_points(i, j) * coef)
.collect()
})
.collect()
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
/// Calculate derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let vderivation = bspsurface.vderivation();
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// vderivation.subs(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
pub fn vderivation(&self) -> BSplineSurface<P::Diff> {
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let (_, k) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let new_points = if k > 0 {
let mut new_points = vec![Vec::with_capacity(n1 + 1); n0];
for j in 0..=n1 {
let delta = vknot_vec[j + k] - vknot_vec[j];
let coef = (k as f64) * inv_or_zero(delta);
for (i, vec) in new_points.iter_mut().enumerate() {
vec.push(self.vdelta_control_points(i, j) * coef)
}
}
new_points
} else {
vec![vec![P::Diff::zero(); n1]; n0]
};
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), new_points)
}
pub(super) fn sub_near_as_surface<F: Fn(&P, &P) -> bool>(
&self,
other: &BSplineSurface<P>,
div_coef: usize,
ord: F,
) -> bool {
if !self.knot_vecs.0.same_range(&other.knot_vecs.0) {
return false;
}
if !self.knot_vecs.1.same_range(&other.knot_vecs.1) {
return false;
}
let (self_degree0, self_degree1) = self.degrees();
let (other_degree0, other_degree1) = other.degrees();
let division0 = std::cmp::max(self_degree0, other_degree0) * div_coef;
let division1 = std::cmp::max(self_degree1, other_degree1) * div_coef;
for i0 in 1..self.knot_vecs.0.len() {
let delta0 = self.knot_vecs.0[i0] - self.knot_vecs.0[i0 - 1];
if delta0.so_small() {
continue;
}
for j0 in 0..division0 {
let u = self.knot_vecs.0[i0 - 1] + delta0 * (j0 as f64) / (division0 as f64);
for i1 in 1..self.knot_vecs.1.len() {
let delta1 = self.knot_vecs.1[i1] - self.knot_vecs.1[i1 - 1];
if delta1.so_small() {
continue;
}
for j1 in 0..division1 {
let v =
self.knot_vecs.1[i1 - 1] + delta1 * (j1 as f64) / (division1 as f64);
if !ord(&self.subs(u, v), &other.subs(u, v)) {
return false;
}
}
}
}
}
true
}
}
impl<V: Homogeneous<f64>> BSplineSurface<V> {
/// lift up control points to homogeneous coordinate.
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self {
let control_points = surface
.control_points
.into_iter()
.map(|vec| vec.into_iter().map(V::from_point).collect())
.collect();
BSplineSurface::new_unchecked(surface.knot_vecs, control_points)
}
}
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P> {
type Point = P;
type Vector = P::Diff;
/// Substitutes to a B-spline surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.subs(u, v),
/// Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn subs(&self, u: f64, v: f64) -> P {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P, (vec, b0): (&Vec<P>, f64)| {
let closure = move |sum: P, (pt, b1): (&P, &f64)| sum + pt.to_vec() * (b0 * b1);
vec.iter().zip(&basis1).fold(sum, closure)
};
control_points.iter().zip(basis0).fold(P::origin(), closure)
}
/// Substitutes derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uder(u, v),
/// Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes derived B-spline surface by the first parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vder(u, v),
/// Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[i + degree1] - vknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.vdelta_control_points(j, i) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the first parameter `u`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uuder: (0, 4v(v - 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uuder(u, v),
/// Vector2::new(0.0, 4.0 * v * (v - 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uuder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree0 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 2, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1, v);
let closure = move |sum: P::Diff, (i, b0): (usize, f64)| {
let coef = inv_or_zero(uknot_vec[i + degree0 - 1] - uknot_vec[i]);
let closure = |sum: P::Diff, (j, b1): (usize, &f64)| {
sum + self.udelta2_control_points(i, j) * coef * b0 * *b1
};
basis1.iter().enumerate().fold(sum, closure)
};
basis0
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the second parameter `v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // vvder: (0, 4(u^2 - 3u + 1))
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.vvder(u, v),
/// Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn vvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
if degree1 < 2 {
return P::Diff::zero();
}
let (uknot_vec, vknot_vec) = self.knot_vecs();
let basis0 = uknot_vec.bspline_basis_functions(degree0, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 2, v);
let closure = move |sum: P::Diff, (j, b0): (usize, f64)| {
let coef = inv_or_zero(vknot_vec[j + degree1 - 1] - vknot_vec[j]);
let closure = |sum: P::Diff, (i, b1): (usize, &f64)| {
sum + self.vdelta2_control_points(i, j) * coef * b0 * *b1
};
basis0.iter().enumerate().fold(sum, closure)
};
basis1
.into_iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree1 as f64
}
/// Substitutes 2nd-ord derived B-spline surface by the both parameters `u, v`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
/// // uvder: (0, 8uv - 4u - 12v + 6)
/// const N: usize = 100; // sample size
/// for i in 0..=N {
/// let u = (i as f64) / (N as f64);
/// for j in 0..=N {
/// let v = (j as f64) / (N as f64);
/// assert_near2!(
/// bspsurface.uvder(u, v),
/// Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
/// );
/// }
/// }
/// ```
#[inline(always)]
fn uvder(&self, u: f64, v: f64) -> P::Diff {
let (degree0, degree1) = self.degrees();
let BSplineSurface {
knot_vecs: (ref uknot_vec, ref vknot_vec),
ref control_points,
} = self;
let basis0 = uknot_vec.bspline_basis_functions(degree0 - 1, u);
let basis1 = vknot_vec.bspline_basis_functions(degree1 - 1, v);
let closure = |sum: P::Diff, (i, vec): (usize, &Vec<P>)| {
let coef0 = inv_or_zero(uknot_vec[i + degree0] - uknot_vec[i]);
let coef1 = inv_or_zero(uknot_vec[i + degree0 + 1] - uknot_vec[i + 1]);
let b0 = basis0[i] * coef0 - basis0[i + 1] * coef1;
let closure = |sum: P::Diff, (j, pt): (usize, &P)| {
let coef0 = inv_or_zero(vknot_vec[j + degree1] - vknot_vec[j]);
let coef1 = inv_or_zero(vknot_vec[j + degree1 + 1] - vknot_vec[j + 1]);
sum + pt.to_vec() * (basis1[j] * coef0 - basis1[j + 1] * coef1) * b0
};
vec.iter().enumerate().fold(sum, closure)
};
control_points
.iter()
.enumerate()
.fold(P::Diff::zero(), closure)
* degree0 as f64
* degree1 as f64
}
}
impl<V: Tolerance> BSplineSurface<V> {
/// Returns whether all control points are same or not.
/// If the knot vector is clamped, it means whether the curve is constant or not.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
/// assert!(bspsurface.is_const());
///
/// *bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
/// assert!(!bspsurface.is_const());
/// ```
/// # Remarks
/// If the knot vector is not clamped and the BSpline basis function is not partition of unity,
/// then perhaps returns true even if the surface is not constant.
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 5);
/// let vknot_vec = KnotVec::uniform_knot(1, 5);
/// let pt = Vector2::new(1.0, 2.0);
/// let ctrl_pts = vec![
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// vec![pt.clone(), pt.clone(), pt.clone()],
/// ];
/// let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
///
/// // bspsurface is not constant.
/// assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
/// assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
///
/// // bspsurface.is_const() is true.
/// assert!(bspsurface.is_const());
/// ```
#[inline(always)]
pub fn is_const(&self) -> bool {
for vec in self.control_points.iter().flat_map(|pts| pts.iter()) {
if !vec.near(&self.control_points[0][0]) {
return false;
}
}
true
}
}
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P> {
/// Adds a knot `x` of the first parameter `u`, and do not change `self` as a surface.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
/// ```
pub fn add_uknot(&mut self, x: f64) -> &mut Self {
let k = self.udegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let uknot_vec = &mut self.knot_vecs.0;
let control_points = &mut self.control_points;
if x < uknot_vec[0] {
uknot_vec.add_knot(x);
control_points.insert(0, vec![P::origin(); n1]);
return self;
}
let idx = uknot_vec.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n0 {
control_points.push(vec![P::origin(); n1]);
n0 + 1
} else {
control_points.insert(idx - 1, control_points[idx - 1].clone());
idx
};
for i in start..end {
let i0 = end + start - i - 1;
let delta = self.uknot(i0 + k + 1) - self.uknot(i0);
let a = inv_or_zero(delta) * (self.uknot(idx) - self.uknot(i0));
for j in 0..n1 {
let p = self.udelta_control_points(i0, j) * (1.0 - a);
self.control_points[i0][j] -= p;
}
}
self
}
/// add a knot `x` for the second parameter, and do not change `self` as a surface.
/// Return `false` if cannot add the knot, i.e.
/// * the index of `x` will be lower than the degree, or
/// * the index of `x` will be higher than the number of control points.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
/// bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
/// ```
pub fn add_vknot(&mut self, x: f64) -> &mut Self {
if x < self.knot_vecs.1[0] {
self.knot_vecs.1.add_knot(x);
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(0, P::origin()));
return self;
}
let k = self.vdegree();
let n0 = self.control_points.len();
let n1 = self.control_points[0].len();
let idx = self.knot_vecs.1.add_knot(x);
let start = if idx > k { idx - k } else { 0 };
let end = if idx > n1 {
self.control_points
.iter_mut()
.for_each(|vec| vec.push(P::origin()));
n1 + 1
} else {
self.control_points
.iter_mut()
.for_each(|vec| vec.insert(idx - 1, vec[idx - 1]));
idx
};
for j in start..end {
let j0 = end + start - j - 1;
let delta = self.knot_vecs.1[j0 + k + 1] - self.knot_vecs.1[j0];
let a = inv_or_zero(delta) * (self.knot_vecs.1[idx] - self.knot_vecs.1[j0]);
for i in 0..n0 {
let p = self.vdelta_control_points(i, j0) * (1.0 - a);
self.control_points[i][j0] -= p;
}
}
self
}
/// Removes the uknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
///
/// assert!(bspsurface.try_remove_uknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self> {
let k = self.udegree();
let knot_vec = self.uknot_vec();
let n = self.control_points.len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_column_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_column_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self
.ctrl_pts_column_iter(idx)
.zip(new_points.last().unwrap())
{
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
self.control_points[idx - k + i] = vec;
}
self.control_points.remove(idx);
self.knot_vecs.0.remove(idx);
Ok(self)
}
/// Removes the uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_uknot(0.3).add_uknot(0.5);
/// bspsurface.remove_uknot(3).remove_uknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
sourcepub fn is_clamped(&self) -> bool
pub fn is_clamped(&self) -> bool
Returns whether the knot vectors are clamped or not.
sourcepub fn swap_axes(&mut self) -> &mut Selfwhere
P: Clone,
pub fn swap_axes(&mut self) -> &mut Selfwhere
P: Clone,
Swaps two parameters.
Examples
use truck_geometry::*;
let knot_vecs0 = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts0 = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let mut bspsurface0 = BSplineSurface::new(knot_vecs0, ctrl_pts0);
let knot_vecs1 = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(1));
let ctrl_pts1 = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0)],
vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 2.0)],
vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 1.0)],
];
let mut bspsurface1 = BSplineSurface::new(knot_vecs1, ctrl_pts1);
assert_eq!(bspsurface0.swap_axes(), &bspsurface1);
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pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
/// Creates a surface by its boundary.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
/// assert_eq!(
/// surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// ],
/// );
/// ```
/// # Remarks
/// If the end points of curves are not connected, `curve1` and `curve3` take precedence. i.e.
/// `curve1` and `curve3` are contained in the boundary of the surface and `curve0` and
/// `curve2` are not contained.
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(
/// curve0.clone(),
/// curve1.clone(),
/// curve2.clone(),
/// curve3.clone()
/// );
/// assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
/// assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
/// ```
pub fn by_boundary(
mut curve0: BSplineCurve<P>,
mut curve1: BSplineCurve<P>,
mut curve2: BSplineCurve<P>,
mut curve3: BSplineCurve<P>,
) -> BSplineSurface<P> {
curve2.invert();
curve3.invert();
curve0.syncro_degree(&mut curve2);
curve0.optimize();
curve2.optimize();
curve0.syncro_knots(&mut curve2);
curve1.syncro_degree(&mut curve3);
curve1.optimize();
curve3.optimize();
curve1.syncro_knots(&mut curve3);
let knot_vecs = (curve0.knot_vec().clone(), curve3.knot_vec().clone());
let mut control_points = vec![curve3.control_points().clone()];
let n = curve0.control_points().len();
let m = curve3.control_points().len();
for i in 1..(n - 1) {
let u = (i as f64) / (n as f64);
let pt0 = curve2.control_points[i]
+ (curve0.control_points[i] - curve2.control_points[i]) * u;
let mut new_row = vec![*curve0.control_point(i)];
for j in 1..(m - 1) {
let v = (j as f64) / (m as f64);
let pt1 = curve1.control_points[j]
+ (curve3.control_points[j] - curve1.control_points[j]) * v;
new_row.push(pt0 + (pt1 - pt0) / 2.0);
}
new_row.push(*curve2.control_point(i));
control_points.push(new_row);
}
control_points.push(curve1.control_points().clone());
BSplineSurface::new(knot_vecs, control_points)
}
/// Normalizes the knot vectors
#[inline(always)]
pub fn knot_normalize(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
self
}
/// Translates the knot vectors.
#[inline(always)]
pub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self {
self.knot_vecs.0.translate(x);
self.knot_vecs.1.translate(y);
self
}
/// Removes knots in order from the back
pub fn optimize(&mut self) -> &mut Self {
loop {
let (n0, n1) = (self.knot_vecs.0.len(), self.knot_vecs.1.len());
let mut flag = true;
for i in 1..=n0 {
flag = flag && self.try_remove_uknot(n0 - i).is_err();
}
for j in 1..=n1 {
flag = flag && self.try_remove_vknot(n1 - j).is_err();
}
if flag {
break;
}
}
self
}
/// Get the boundary by four splitted curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let curves = bspsurface.splitted_boundary();
/// assert_eq!(
/// curves[0].control_points(),
/// &vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0), Vector2::new(0.0, 2.0), Vector2::new(0.0, 3.0)],
/// );
/// assert_eq!(
/// curves[1].control_points(),
/// &vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// );
/// assert_eq!(
/// curves[2].control_points(),
/// &vec![Vector2::new(1.0, 3.0), Vector2::new(1.0, 2.0), Vector2::new(1.0, 1.0), Vector2::new(1.0, 0.0)],
/// );
/// assert_eq!(
/// curves[3].control_points(),
/// &vec![Vector2::new(1.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(0.0, 0.0)],
/// );
/// ```
pub fn splitted_boundary(&self) -> [BSplineCurve<P>; 4] {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let control_points0 = self.control_points.iter().map(|x| x[0]).collect();
let control_points1 = self.control_points.last().unwrap().clone();
let control_points2 = self
.control_points
.iter()
.map(|x| *x.last().unwrap())
.collect();
let control_points3 = self.control_points[0].clone();
let curve0 = BSplineCurve::new_unchecked(uknot_vec.clone(), control_points0);
let curve1 = BSplineCurve::new_unchecked(vknot_vec.clone(), control_points1);
let mut curve2 = BSplineCurve::new_unchecked(uknot_vec, control_points2);
curve2.invert();
let mut curve3 = BSplineCurve::new_unchecked(vknot_vec, control_points3);
curve3.invert();
[curve0, curve1, curve2, curve3]
}
/// Extracts the boundary of surface
pub fn boundary(&self) -> BSplineCurve<P> {
let (uknot_vec, vknot_vec) = self.knot_vecs.clone();
let (range0, range1) = (uknot_vec.range_length(), vknot_vec.range_length());
let [bspline0, mut bspline1, mut bspline2, mut bspline3] = self.splitted_boundary();
bspline0
.concat(bspline1.knot_translate(range0))
.concat(bspline2.invert().knot_translate(range0 + range1))
.concat(bspline3.invert().knot_translate(range0 * 2.0 + range1))
}
/// Determines whether `self` and `other` is near as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) = Vector2::new(0.4, 1.0);
/// assert!(!bspsurface0.near_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near(y))
}
/// Determines whether `self` and `other` is near in square order as the B-spline surfaces or not.
///
/// Divides each knot domain into the number of degree equal parts,
/// and check `|self(u, v) - other(u, v)| < TOLERANCE` for each end points `(u, v)`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let eps = TOLERANCE;
/// let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
/// vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
/// ];
/// let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let mut bspsurface1 = bspsurface0.clone();
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
///
/// *bspsurface1.control_point_mut(1, 1) += Vector2::new(eps, eps / 2.0);
/// assert!(bspsurface0.near_as_surface(&bspsurface1));
/// assert!(!bspsurface0.near2_as_surface(&bspsurface1));
/// ```
#[inline(always)]
pub fn near2_as_surface(&self, other: &BSplineSurface<P>) -> bool {
self.sub_near_as_surface(other, 1, |x, y| x.near2(y))
}
}
impl<V> BSplineSurface<V>
where V: MetricSpace<Metric = f64> + Index<usize, Output = f64> + Bounded<f64> + Copy
{
/// Returns the bounding box including all control points.
#[inline(always)]
pub fn roughly_bounding_box(&self) -> BoundingBox<V> {
self.control_points.iter().flatten().collect()
}
}
impl<P: ControlPoint<f64>> ParameterDivision2D for BSplineSurface<P>
where P: EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>
+ HashGen<f64>
{
#[inline(always)]
fn parameter_division(
&self,
range: ((f64, f64), (f64, f64)),
tol: f64,
) -> (Vec<f64>, Vec<f64>) {
algo::surface::parameter_division(self, range, tol)
}
}
impl ParametricSurface3D for BSplineSurface<Point3> {}
impl<V> BoundedSurface for BSplineSurface<V>
where BSplineSurface<V>: ParametricSurface
{
#[inline(always)]
fn parameter_range(&self) -> ((f64, f64), (f64, f64)) { self.parameter_range() }
}
impl<V: Clone> Invertible for BSplineSurface<V> {
#[inline(always)]
fn invert(&mut self) { self.swap_axes(); }
sourcepub fn parameter_range(&self) -> ((f64, f64), (f64, f64))
pub fn parameter_range(&self) -> ((f64, f64), (f64, f64))
The range of the parameter of the surface.
Examples found in repository?
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fn parameter_range(&self) -> ((f64, f64), (f64, f64)) { self.parameter_range() }
}
impl<V: Clone> Invertible for BSplineSurface<V> {
#[inline(always)]
fn invert(&mut self) { self.swap_axes(); }
}
impl SearchParameter<D2> for BSplineSurface<Point2> {
type Point = Point2;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point2,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter2d(self, point, hint, trials)
}
}
impl SearchParameter<D2> for BSplineSurface<Point3> {
type Point = Point3;
fn search_parameter<H: Into<SPHint2D>>(
&self,
point: Point3,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_parameter3d(self, point, hint, trials)
}
}
impl<P> SearchNearestParameter<D2> for BSplineSurface<P>
where
P: ControlPoint<f64>
+ EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff>
+ MetricSpace<Metric = f64>,
<P as ControlPoint<f64>>::Diff: InnerSpace<Scalar = f64> + Tolerance,
{
type Point = P;
fn search_nearest_parameter<H: Into<SPHint2D>>(
&self,
point: P,
hint: H,
trials: usize,
) -> Option<(f64, f64)> {
let hint = match hint.into() {
SPHint2D::Parameter(x, y) => (x, y),
SPHint2D::Range(range0, range1) => {
algo::surface::presearch(self, point, (range0, range1), PRESEARCH_DIVISION)
}
SPHint2D::None => {
algo::surface::presearch(self, point, self.parameter_range(), PRESEARCH_DIVISION)
}
};
algo::surface::search_nearest_parameter(self, point, hint, trials)
}
}
impl IncludeCurve<BSplineCurve<Point2>> for BSplineSurface<Point2> {
fn include(&self, curve: &BSplineCurve<Point2>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter2d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<BSplineCurve<Point3>> for BSplineSurface<Point3> {
fn include(&self, curve: &BSplineCurve<Point3>) -> bool {
let pt = curve.front();
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = ParametricCurve::subs(curve, t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
}
impl IncludeCurve<NURBSCurve<Vector4>> for BSplineSurface<Point3> {
fn include(&self, curve: &NURBSCurve<Vector4>) -> bool {
let pt = curve.subs(curve.knot_vec()[0]);
let mut hint =
algo::surface::presearch(self, pt, self.parameter_range(), PRESEARCH_DIVISION);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS) {
Some(got) => got,
None => return false,
};
let uknot_vec = self.uknot_vec();
let vknot_vec = self.vknot_vec();
let degree = curve.degree() * 6;
let (knots, _) = curve.knot_vec().to_single_multi();
for i in 1..knots.len() {
for j in 1..=degree {
let p = j as f64 / degree as f64;
let t = knots[i - 1] * (1.0 - p) + knots[i] * p;
let pt = curve.subs(t);
hint = match algo::surface::search_parameter3d(self, pt, hint, INCLUDE_CURVE_TRIALS)
{
Some(got) => got,
None => return false,
};
if !ParametricSurface::subs(self, hint.0, hint.1).near(&pt)
|| hint.0 < uknot_vec[0] - TOLERANCE
|| hint.0 - uknot_vec[0] > uknot_vec.range_length() + TOLERANCE
|| hint.1 < vknot_vec[0] - TOLERANCE
|| hint.1 - vknot_vec[0] > vknot_vec.range_length() + TOLERANCE
{
return false;
}
}
}
true
}
More examples
sourcepub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>where
P: Clone,
pub fn column_curve(&self, row_idx: usize) -> BSplineCurve<P>where
P: Clone,
Creates the curve whose control points are the idx
th column control points of self
.
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::bezier_knot(1);
let vknot_vec = KnotVec::bezier_knot(2);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let bspcurve = bspsurface.column_curve(1);
assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(2));
assert_eq!(
bspcurve.control_points(),
&vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
);
sourcepub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>where
P: Clone,
pub fn row_curve(&self, column_idx: usize) -> BSplineCurve<P>where
P: Clone,
Creates the column sectional curve.
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::bezier_knot(1);
let vknot_vec = KnotVec::bezier_knot(2);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let bspcurve = bspsurface.row_curve(1);
assert_eq!(bspcurve.knot_vec(), &KnotVec::bezier_knot(1));
assert_eq!(
bspcurve.control_points(),
&vec![Vector3::new(1.0, 0.0, 1.0), Vector3::new(1.0, 1.0, 1.0)],
);
source§impl<P: ControlPoint<f64>> BSplineSurface<P>
impl<P: ControlPoint<f64>> BSplineSurface<P>
sourcepub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_
pub fn get_closure(&self) -> impl Fn(f64, f64) -> P + '_
Returns the closure of substitution.
sourcepub fn uderivation(&self) -> BSplineSurface<P::Diff>
pub fn uderivation(&self) -> BSplineSurface<P::Diff>
Calculate derived B-spline surface by the first parameter u
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let uderivation = bspsurface.uderivation();
// bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
const N: usize = 100; // sample size
for i in 1..N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
uderivation.subs(u, v),
Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
);
}
}
sourcepub fn vderivation(&self) -> BSplineSurface<P::Diff>
pub fn vderivation(&self) -> BSplineSurface<P::Diff>
Calculate derived B-spline surface by the second parameter v
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let vderivation = bspsurface.vderivation();
// bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
const N: usize = 100; // sample size
for i in 0..=N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
vderivation.subs(u, v),
Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
);
}
}
source§impl<V: Homogeneous<f64>> BSplineSurface<V>
impl<V: Homogeneous<f64>> BSplineSurface<V>
sourcepub fn lift_up(surface: BSplineSurface<V::Point>) -> Self
pub fn lift_up(surface: BSplineSurface<V::Point>) -> Self
lift up control points to homogeneous coordinate.
source§impl<V: Tolerance> BSplineSurface<V>
impl<V: Tolerance> BSplineSurface<V>
sourcepub fn is_const(&self) -> bool
pub fn is_const(&self) -> bool
Returns whether all control points are same or not. If the knot vector is clamped, it means whether the curve is constant or not.
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::bezier_knot(1);
let vknot_vec = KnotVec::bezier_knot(2);
let pt = Vector2::new(1.0, 2.0);
let ctrl_pts = vec![
vec![pt.clone(), pt.clone(), pt.clone()],
vec![pt.clone(), pt.clone(), pt.clone()],
];
let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
assert!(bspsurface.is_const());
*bspsurface.control_point_mut(1, 2) = Vector2::new(2.0, 3.0);
assert!(!bspsurface.is_const());
Remarks
If the knot vector is not clamped and the BSpline basis function is not partition of unity, then perhaps returns true even if the surface is not constant.
use truck_geometry::*;
let uknot_vec = KnotVec::uniform_knot(1, 5);
let vknot_vec = KnotVec::uniform_knot(1, 5);
let pt = Vector2::new(1.0, 2.0);
let ctrl_pts = vec![
vec![pt.clone(), pt.clone(), pt.clone()],
vec![pt.clone(), pt.clone(), pt.clone()],
];
let mut bspsurface = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
// bspsurface is not constant.
assert_eq!(bspsurface.subs(0.0, 0.0), Vector2::new(0.0, 0.0));
assert_ne!(bspsurface.subs(0.5, 0.5), Vector2::new(0.0, 0.0));
// bspsurface.is_const() is true.
assert!(bspsurface.is_const());
source§impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P>
impl<P: ControlPoint<f64> + Tolerance> BSplineSurface<P>
sourcepub fn add_uknot(&mut self, x: f64) -> &mut Self
pub fn add_uknot(&mut self, x: f64) -> &mut Self
Adds a knot x
of the first parameter u
, and do not change self
as a surface.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.add_uknot(0.0).add_uknot(0.3).add_uknot(0.5).add_uknot(1.0);
assert!(bspsurface.near2_as_surface(&org_surface));
assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 4);
Examples found in repository?
More examples
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pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
sourcepub fn add_vknot(&mut self, x: f64) -> &mut Self
pub fn add_vknot(&mut self, x: f64) -> &mut Self
add a knot x
for the second parameter, and do not change self
as a surface.
Return false
if cannot add the knot, i.e.
- the index of
x
will be lower than the degree, or - the index of
x
will be higher than the number of control points.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.add_vknot(0.0).add_vknot(0.3).add_vknot(0.5).add_vknot(1.0);
assert!(bspsurface.near2_as_surface(&org_surface));
assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 4);
Examples found in repository?
More examples
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pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
sourcepub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self>
pub fn try_remove_uknot(&mut self, idx: usize) -> Result<&mut Self>
Removes the uknot corresponding to the indice idx
, and do not change self
as a curve.
If the knot cannot be removed, returns
Error::CannotRemoveKnot
.
Examples
use truck_geometry::*;
use errors::Error;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.add_uknot(0.3).add_uknot(0.5);
assert!(bspsurface.try_remove_uknot(3).is_ok());
assert_eq!(bspsurface.try_remove_uknot(2), Err(Error::CannotRemoveKnot(2)));
assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len() + 1);
assert!(bspsurface.near2_as_surface(&org_surface));
Examples found in repository?
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pub fn remove_uknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_uknot(idx);
self
}
/// Removes a vknot corresponding to the indice `idx`, and do not change `self` as a curve.
/// If the knot cannot be removed, returns
/// [`Error::CannotRemoveKnot`](./errors/enum.Error.html#variant.CannotRemoveKnot).
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// assert!(bspsurface.try_remove_vknot(3).is_ok());
/// assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
/// ```
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self> {
let (_, k) = self.degrees();
let knot_vec = self.vknot_vec();
let n = self.control_points[0].len();
if idx < k + 1 || idx >= n {
return Err(Error::CannotRemoveKnot(idx));
}
let mut new_points = Vec::with_capacity(k + 1);
let first_vec = self
.ctrl_pts_row_iter(idx - k - 1)
.cloned()
.collect::<Vec<_>>();
new_points.push(first_vec);
for i in (idx - k)..idx {
let delta = knot_vec[i + k + 1] - knot_vec[i];
let a = inv_or_zero(delta) * (knot_vec[idx] - knot_vec[i]);
if a.so_small() {
break;
} else {
let vec = self
.ctrl_pts_row_iter(i)
.zip(new_points.last().unwrap())
.map(|(pt0, pt1)| *pt1 + (*pt0 - *pt1) / a)
.collect();
new_points.push(vec);
}
}
for (pt0, pt1) in self.ctrl_pts_row_iter(idx).zip(new_points.last().unwrap()) {
if !pt0.near(pt1) {
return Err(Error::CannotRemoveKnot(idx));
}
}
for (i, vec) in new_points.into_iter().skip(1).enumerate() {
for (j, pt) in vec.into_iter().enumerate() {
self.control_points[j][idx - k + i] = pt;
}
}
for vec in &mut self.control_points {
vec.remove(idx);
}
self.knot_vecs.1.remove(idx);
Ok(self)
}
/// Removes a uknot corresponding to the indices `idx`, and do not change `self` as a curve.
/// If cannot remove the knot, do not change `self` and return `self`.
/// # Examples
/// ```
/// use truck_geometry::*;
/// use errors::Error;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.add_vknot(0.3).add_vknot(0.5);
/// bspsurface.remove_vknot(3).remove_vknot(3);
///
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
/// ```
#[inline(always)]
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
/// Creates a surface by its boundary.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
/// assert_eq!(
/// surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// ],
/// );
/// ```
/// # Remarks
/// If the end points of curves are not connected, `curve1` and `curve3` take precedence. i.e.
/// `curve1` and `curve3` are contained in the boundary of the surface and `curve0` and
/// `curve2` are not contained.
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(
/// curve0.clone(),
/// curve1.clone(),
/// curve2.clone(),
/// curve3.clone()
/// );
/// assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
/// assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
/// ```
pub fn by_boundary(
mut curve0: BSplineCurve<P>,
mut curve1: BSplineCurve<P>,
mut curve2: BSplineCurve<P>,
mut curve3: BSplineCurve<P>,
) -> BSplineSurface<P> {
curve2.invert();
curve3.invert();
curve0.syncro_degree(&mut curve2);
curve0.optimize();
curve2.optimize();
curve0.syncro_knots(&mut curve2);
curve1.syncro_degree(&mut curve3);
curve1.optimize();
curve3.optimize();
curve1.syncro_knots(&mut curve3);
let knot_vecs = (curve0.knot_vec().clone(), curve3.knot_vec().clone());
let mut control_points = vec![curve3.control_points().clone()];
let n = curve0.control_points().len();
let m = curve3.control_points().len();
for i in 1..(n - 1) {
let u = (i as f64) / (n as f64);
let pt0 = curve2.control_points[i]
+ (curve0.control_points[i] - curve2.control_points[i]) * u;
let mut new_row = vec![*curve0.control_point(i)];
for j in 1..(m - 1) {
let v = (j as f64) / (m as f64);
let pt1 = curve1.control_points[j]
+ (curve3.control_points[j] - curve1.control_points[j]) * v;
new_row.push(pt0 + (pt1 - pt0) / 2.0);
}
new_row.push(*curve2.control_point(i));
control_points.push(new_row);
}
control_points.push(curve1.control_points().clone());
BSplineSurface::new(knot_vecs, control_points)
}
/// Normalizes the knot vectors
#[inline(always)]
pub fn knot_normalize(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
self
}
/// Translates the knot vectors.
#[inline(always)]
pub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self {
self.knot_vecs.0.translate(x);
self.knot_vecs.1.translate(y);
self
}
/// Removes knots in order from the back
pub fn optimize(&mut self) -> &mut Self {
loop {
let (n0, n1) = (self.knot_vecs.0.len(), self.knot_vecs.1.len());
let mut flag = true;
for i in 1..=n0 {
flag = flag && self.try_remove_uknot(n0 - i).is_err();
}
for j in 1..=n1 {
flag = flag && self.try_remove_vknot(n1 - j).is_err();
}
if flag {
break;
}
}
self
}
More examples
sourcepub fn remove_uknot(&mut self, idx: usize) -> &mut Self
pub fn remove_uknot(&mut self, idx: usize) -> &mut Self
Removes the uknot corresponding to the indices idx
, and do not change self
as a curve.
If cannot remove the knot, do not change self
and return self
.
Examples
use truck_geometry::*;
use errors::Error;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.add_uknot(0.3).add_uknot(0.5);
bspsurface.remove_uknot(3).remove_uknot(3);
assert!(bspsurface.near2_as_surface(&org_surface));
assert_eq!(bspsurface.uknot_vec().len(), org_surface.uknot_vec().len())
sourcepub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self>
pub fn try_remove_vknot(&mut self, idx: usize) -> Result<&mut Self>
Removes a vknot corresponding to the indice idx
, and do not change self
as a curve.
If the knot cannot be removed, returns
Error::CannotRemoveKnot
.
Examples
use truck_geometry::*;
use errors::Error;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.add_vknot(0.3).add_vknot(0.5);
assert!(bspsurface.try_remove_vknot(3).is_ok());
assert_eq!(bspsurface.try_remove_vknot(2), Err(Error::CannotRemoveKnot(2)));
assert!(bspsurface.near2_as_surface(&org_surface));
assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len() + 1);
Examples found in repository?
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pub fn remove_vknot(&mut self, idx: usize) -> &mut Self {
let _ = self.try_remove_vknot(idx);
self
}
/// Elevates the vdegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_vdegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree());
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_vdegree(&mut self) -> &mut Self {
let mut new_knot_vec = KnotVec::new();
for (i, vec) in self.control_points.iter_mut().enumerate() {
let knot_vec = self.knot_vecs.1.clone();
let ctrl_pts = vec.clone();
let mut curve = BSplineCurve::new(knot_vec, ctrl_pts);
curve.elevate_degree();
if i == 0 {
new_knot_vec = curve.knot_vec().clone();
}
*vec = curve.control_points;
}
self.knot_vecs.1 = new_knot_vec;
self
}
/// Elevates the udegree.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
/// vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
/// vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// bspsurface.elevate_udegree();
///
/// assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
/// assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
/// Makes the uknot vector and the vknot vector the same knot vector.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::uniform_knot(1, 2);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// bspsurface.syncro_uvknots();
/// assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvknots(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
let mut i = 0;
let mut j = 0;
while !self.uknot(i).near2(&1.0) || !self.vknot(j).near2(&1.0) {
if self.uknot(i) - self.vknot(j) > TOLERANCE {
self.add_uknot(self.vknot(j));
} else if self.vknot(j) - self.uknot(i) > TOLERANCE {
self.add_vknot(self.uknot(i));
}
i += 1;
j += 1;
}
let ulen = self.uknot_vec().len();
let vlen = self.vknot_vec().len();
use std::cmp::Ordering;
match usize::cmp(&ulen, &vlen) {
Ordering::Less => {
for _ in 0..vlen - ulen {
self.add_uknot(1.0);
}
}
Ordering::Greater => {
for _ in 0..ulen - vlen {
self.add_vknot(1.0);
}
}
_ => {}
}
self
}
/// Cuts the surface into two surfaces at the parameter `u`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.ucut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 0.68 + 0.32 * (i as f64) / (N as f64);
/// let v = 1.0 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn ucut(&mut self, mut u: f64) -> BSplineSurface<P> {
let degree = self.udegree();
let idx = match self.uknot_vec().floor(u) {
Some(idx) => idx,
None => {
let bspline = self.clone();
let uknot_vec = KnotVec::from(vec![u, self.vknot_vec()[0]]);
let vknot_vec = self.vknot_vec().clone();
let ctrl_pts = vec![vec![P::origin(); vknot_vec.len()]];
*self = BSplineSurface::new((uknot_vec, vknot_vec), ctrl_pts);
return bspline;
}
};
let s = if u.near(&self.uknot_vec()[idx]) {
u = self.uknot_vec()[idx];
self.uknot_vec().multiplicity(idx)
} else {
0
};
for _ in s..=degree {
self.add_uknot(u);
}
let vknot_vec = self.vknot_vec().clone();
let k = self.uknot_vec().floor(u).unwrap();
let m = self.uknot_vec().len();
let n = self.control_points.len();
let knot_vec0 = self.uknot_vec().sub_vec(0..=k);
let knot_vec1 = self.uknot_vec().sub_vec((k - degree)..m);
let control_points0 = Vec::from(&self.control_points[0..(k - degree)]);
let control_points1 = Vec::from(&self.control_points[(k - degree)..n]);
*self = BSplineSurface::new((knot_vec0, vknot_vec.clone()), control_points0);
BSplineSurface::new((knot_vec1, vknot_vec), control_points1)
}
/// Cuts the curve to two curves at the parameter `t`
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// let knot_vec0 = KnotVec::uniform_knot(2, 2);
/// let knot_vec1 = KnotVec::uniform_knot(2, 2);
/// let ctrl_pts0 = vec![
/// Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
/// ];
/// let ctrl_pts1 = vec![
/// Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
/// ];
/// let ctrl_pts2 = vec![
/// Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
/// ];
/// let ctrl_pts3 = vec![
/// Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
/// ];
/// let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
/// let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
///
/// let mut part0 = bspsurface.clone();
/// let part1 = part0.vcut(0.68);
/// const N: usize = 100;
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
/// }
/// }
/// for i in 0..=N {
/// for j in 0..=N {
/// let u = 1.0 * (i as f64) / (N as f64);
/// let v = 0.68 + 0.32 * (j as f64) / (N as f64);
/// assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
/// }
/// }
/// ```
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
/// Creates a surface with normailized knot vectors connecting two curves.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let knot_vec0 = KnotVec::bezier_knot(2);
/// let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
/// let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
///
/// let knot_vec1 = KnotVec::bezier_knot(2);
/// let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
/// let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
///
/// let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
/// assert_eq!(
/// homotopy_surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
/// vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
/// ],
/// );
/// ```
pub fn homotopy(
mut bspcurve0: BSplineCurve<P>,
mut bspcurve1: BSplineCurve<P>,
) -> BSplineSurface<P> {
bspcurve0.syncro_degree(&mut bspcurve1);
//bspcurve0.optimize();
//bspcurve1.optimize();
bspcurve0.syncro_knots(&mut bspcurve1);
let uknot_vec = bspcurve0.knot_vec().clone();
let vknot_vec = KnotVec::from(vec![0.0, 0.0, 1.0, 1.0]);
let mut control_points = Vec::new();
for i in 0..bspcurve0.control_points().len() {
control_points.push(Vec::new());
control_points[i].push(*bspcurve0.control_point(i));
control_points[i].push(*bspcurve1.control_point(i));
}
BSplineSurface::new_unchecked((uknot_vec, vknot_vec), control_points)
}
/// Creates a surface by its boundary.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
/// assert_eq!(
/// surface.control_points(),
/// &vec![
/// vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
/// vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
/// ],
/// );
/// ```
/// # Remarks
/// If the end points of curves are not connected, `curve1` and `curve3` take precedence. i.e.
/// `curve1` and `curve3` are contained in the boundary of the surface and `curve0` and
/// `curve2` are not contained.
/// ```
/// use truck_geometry::*;
/// let curve0 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
/// );
/// let curve1 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
/// );
/// let curve2 = BSplineCurve::new(
/// KnotVec::bezier_knot(1),
/// vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
/// );
/// let curve3 = BSplineCurve::new(
/// KnotVec::bezier_knot(2),
/// vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
/// );
/// let surface = BSplineSurface::by_boundary(
/// curve0.clone(),
/// curve1.clone(),
/// curve2.clone(),
/// curve3.clone()
/// );
/// assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
/// assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
/// ```
pub fn by_boundary(
mut curve0: BSplineCurve<P>,
mut curve1: BSplineCurve<P>,
mut curve2: BSplineCurve<P>,
mut curve3: BSplineCurve<P>,
) -> BSplineSurface<P> {
curve2.invert();
curve3.invert();
curve0.syncro_degree(&mut curve2);
curve0.optimize();
curve2.optimize();
curve0.syncro_knots(&mut curve2);
curve1.syncro_degree(&mut curve3);
curve1.optimize();
curve3.optimize();
curve1.syncro_knots(&mut curve3);
let knot_vecs = (curve0.knot_vec().clone(), curve3.knot_vec().clone());
let mut control_points = vec![curve3.control_points().clone()];
let n = curve0.control_points().len();
let m = curve3.control_points().len();
for i in 1..(n - 1) {
let u = (i as f64) / (n as f64);
let pt0 = curve2.control_points[i]
+ (curve0.control_points[i] - curve2.control_points[i]) * u;
let mut new_row = vec![*curve0.control_point(i)];
for j in 1..(m - 1) {
let v = (j as f64) / (m as f64);
let pt1 = curve1.control_points[j]
+ (curve3.control_points[j] - curve1.control_points[j]) * v;
new_row.push(pt0 + (pt1 - pt0) / 2.0);
}
new_row.push(*curve2.control_point(i));
control_points.push(new_row);
}
control_points.push(curve1.control_points().clone());
BSplineSurface::new(knot_vecs, control_points)
}
/// Normalizes the knot vectors
#[inline(always)]
pub fn knot_normalize(&mut self) -> &mut Self {
self.knot_vecs.0.normalize();
self.knot_vecs.1.normalize();
self
}
/// Translates the knot vectors.
#[inline(always)]
pub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self {
self.knot_vecs.0.translate(x);
self.knot_vecs.1.translate(y);
self
}
/// Removes knots in order from the back
pub fn optimize(&mut self) -> &mut Self {
loop {
let (n0, n1) = (self.knot_vecs.0.len(), self.knot_vecs.1.len());
let mut flag = true;
for i in 1..=n0 {
flag = flag && self.try_remove_uknot(n0 - i).is_err();
}
for j in 1..=n1 {
flag = flag && self.try_remove_vknot(n1 - j).is_err();
}
if flag {
break;
}
}
self
}
More examples
sourcepub fn remove_vknot(&mut self, idx: usize) -> &mut Self
pub fn remove_vknot(&mut self, idx: usize) -> &mut Self
Removes a uknot corresponding to the indices idx
, and do not change self
as a curve.
If cannot remove the knot, do not change self
and return self
.
Examples
use truck_geometry::*;
use errors::Error;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.add_vknot(0.3).add_vknot(0.5);
bspsurface.remove_vknot(3).remove_vknot(3);
assert!(bspsurface.near2_as_surface(&org_surface));
assert_eq!(bspsurface.vknot_vec().len(), org_surface.vknot_vec().len())
sourcepub fn elevate_vdegree(&mut self) -> &mut Self
pub fn elevate_vdegree(&mut self) -> &mut Self
Elevates the vdegree.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.elevate_vdegree();
assert_eq!(bspsurface.udegree(), org_surface.udegree());
assert_eq!(bspsurface.vdegree(), org_surface.vdegree() + 1);
assert!(bspsurface.near2_as_surface(&org_surface));
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pub fn elevate_udegree(&mut self) -> &mut Self {
self.swap_axes();
self.elevate_vdegree();
self.swap_axes();
self
}
/// Aligns the udegree with the same degrees.
/// # Examples
/// ```
/// use truck_geometry::*;
/// let uknot_vec = KnotVec::bezier_knot(1);
/// let vknot_vec = KnotVec::bezier_knot(2);
/// let knot_vecs = (uknot_vec, vknot_vec);
/// let ctrl_pts = vec![
/// vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
/// vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
/// let org_surface = bspsurface.clone();
///
/// assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
/// bspsurface.syncro_uvdegrees();
/// assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
/// assert!(bspsurface.near2_as_surface(&org_surface));
/// ```
pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
sourcepub fn elevate_udegree(&mut self) -> &mut Self
pub fn elevate_udegree(&mut self) -> &mut Self
Elevates the udegree.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
bspsurface.elevate_udegree();
assert_eq!(bspsurface.udegree(), org_surface.udegree() + 1);
assert_eq!(bspsurface.vdegree(), org_surface.vdegree());
assert!(bspsurface.near2_as_surface(&org_surface));
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pub fn syncro_uvdegrees(&mut self) -> &mut Self {
if self.udegree() > self.vdegree() {
for _ in 0..(self.udegree() - self.vdegree()) {
self.elevate_vdegree();
}
}
if self.vdegree() > self.udegree() {
for _ in 0..(self.vdegree() - self.udegree()) {
self.elevate_udegree();
}
}
self
}
sourcepub fn syncro_uvdegrees(&mut self) -> &mut Self
pub fn syncro_uvdegrees(&mut self) -> &mut Self
Aligns the udegree with the same degrees.
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::bezier_knot(1);
let vknot_vec = KnotVec::bezier_knot(2);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
assert_ne!(bspsurface.udegree(), bspsurface.vdegree());
bspsurface.syncro_uvdegrees();
assert_eq!(bspsurface.udegree(), bspsurface.vdegree());
assert!(bspsurface.near2_as_surface(&org_surface));
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pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
sourcepub fn syncro_uvknots(&mut self) -> &mut Self
pub fn syncro_uvknots(&mut self) -> &mut Self
Makes the uknot vector and the vknot vector the same knot vector.
Examples
use truck_geometry::*;
let uknot_vec = KnotVec::uniform_knot(1, 2);
let vknot_vec = KnotVec::bezier_knot(2);
let knot_vecs = (uknot_vec, vknot_vec);
let ctrl_pts = vec![
vec![Vector3::new(0.0, 0.0, 0.0), Vector3::new(1.0, 0.0, 1.0), Vector3::new(2.0, 0.0, 2.0)],
vec![Vector3::new(0.0, 1.0, 0.0), Vector3::new(1.0, 1.0, 1.0), Vector3::new(2.0, 1.0, 2.0)],
vec![Vector3::new(0.0, 2.0, 0.0), Vector3::new(1.0, 2.0, 1.0), Vector3::new(2.0, 2.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let org_surface = bspsurface.clone();
assert_ne!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
bspsurface.syncro_uvknots();
assert_eq!(bspsurface.uknot_vec(), bspsurface.vknot_vec());
assert!(bspsurface.near2_as_surface(&org_surface));
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pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
sourcepub fn ucut(&mut self, u: f64) -> BSplineSurface<P>
pub fn ucut(&mut self, u: f64) -> BSplineSurface<P>
Cuts the surface into two surfaces at the parameter u
Examples
use truck_geometry::*;
let knot_vec0 = KnotVec::uniform_knot(2, 2);
let knot_vec1 = KnotVec::uniform_knot(2, 2);
let ctrl_pts0 = vec![
Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
];
let ctrl_pts1 = vec![
Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
];
let ctrl_pts2 = vec![
Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
];
let ctrl_pts3 = vec![
Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
];
let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
let mut part0 = bspsurface.clone();
let part1 = part0.ucut(0.68);
const N: usize = 100;
for i in 0..=N {
for j in 0..=N {
let u = 0.68 * (i as f64) / (N as f64);
let v = 1.0 * (j as f64) / (N as f64);
assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
}
}
for i in 0..=N {
for j in 0..=N {
let u = 0.68 + 0.32 * (i as f64) / (N as f64);
let v = 1.0 * (j as f64) / (N as f64);
assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
}
}
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pub fn vcut(&mut self, v: f64) -> BSplineSurface<P> {
self.swap_axes();
let mut res = self.ucut(v);
self.swap_axes();
res.swap_axes();
res
}
/// Creates a sectional curve with normalized knot vector from the parameter `p` to the parameter `q`.
/// # Examples
/// ```
/// use truck_geometry::*;
///
/// // a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
/// let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
/// let ctrl_pts = vec![
/// vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
/// vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
/// vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
/// ];
/// let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
///
/// // add some knots for the test!
/// bspsurface.add_uknot(0.26);
/// # bspsurface.add_uknot(0.64);
/// bspsurface.add_vknot(0.23);
/// # bspsurface.add_vknot(0.82);
///
/// let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
/// let curve = bspsurface.sectional_curve(bnd_box);
/// const N: usize = 100;
/// assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
/// assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
/// for i in 0..=N {
/// let t = i as f64 / N as f64;
/// let pt = curve.subs(t);
/// assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
/// assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
/// }
/// ```
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
sourcepub fn vcut(&mut self, v: f64) -> BSplineSurface<P>
pub fn vcut(&mut self, v: f64) -> BSplineSurface<P>
Cuts the curve to two curves at the parameter t
Examples
use truck_geometry::*;
let knot_vec0 = KnotVec::uniform_knot(2, 2);
let knot_vec1 = KnotVec::uniform_knot(2, 2);
let ctrl_pts0 = vec![
Vector2::new(0.0, 0.0), Vector2::new(0.5, 0.0), Vector2::new(2.0, 0.0), Vector2::new(2.5, 0.0),
];
let ctrl_pts1 = vec![
Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(2.0, 1.0), Vector2::new(2.5, 1.0),
];
let ctrl_pts2 = vec![
Vector2::new(0.0, 1.5), Vector2::new(0.5, 1.5), Vector2::new(2.0, 1.5), Vector2::new(2.5, 1.5),
];
let ctrl_pts3 = vec![
Vector2::new(0.0, 2.5), Vector2::new(0.5, 2.5), Vector2::new(2.0, 2.5), Vector2::new(2.5, 2.5),
];
let ctrl_pts = vec![ctrl_pts0, ctrl_pts1, ctrl_pts2, ctrl_pts3];
let bspsurface = BSplineSurface::new((knot_vec0, knot_vec1), ctrl_pts);
let mut part0 = bspsurface.clone();
let part1 = part0.vcut(0.68);
const N: usize = 100;
for i in 0..=N {
for j in 0..=N {
let u = 1.0 * (i as f64) / (N as f64);
let v = 0.68 * (j as f64) / (N as f64);
assert_near2!(bspsurface.subs(u, v), part0.subs(u, v));
}
}
for i in 0..=N {
for j in 0..=N {
let u = 1.0 * (i as f64) / (N as f64);
let v = 0.68 + 0.32 * (j as f64) / (N as f64);
assert_near2!(bspsurface.subs(u, v), part1.subs(u, v));
}
}
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pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P> {
let p = bnd_box.min();
let q = bnd_box.max();
let mut bspsurface = self.clone();
if !p[0].near(&bspsurface.uknot(0)) {
bspsurface = bspsurface.ucut(p[0]);
}
if !q[0].near(&bspsurface.uknot(bspsurface.uknot_vec().len() - 1)) {
bspsurface.ucut(q[0]);
}
if !p[0].near(&bspsurface.vknot(0)) {
bspsurface = bspsurface.vcut(p[1]);
}
if !q[0].near(&bspsurface.vknot(bspsurface.vknot_vec().len() - 1)) {
bspsurface.vcut(q[1]);
}
bspsurface.syncro_uvdegrees();
bspsurface.syncro_uvknots();
let degree = bspsurface.udegree();
let comb = combinatorial(degree);
let comb2 = combinatorial(degree * 2);
let (knots, _) = bspsurface.uknot_vec().to_single_multi();
let mut cc = CurveCollector::Singleton;
for p in 1..knots.len() {
let mut backup = None;
if p + 1 != knots.len() {
backup = Some(bspsurface.ucut(knots[p]));
bspsurface.vcut(knots[p]);
}
let mut knot_vec = KnotVec::bezier_knot(degree * 2);
knot_vec.translate(p as f64 - 1.0);
let ctrl_pts: Vec<_> = (0..=degree * 2)
.map(|k| {
(0..=k).fold(P::origin(), |sum, i| {
if i <= degree && k - i <= degree {
let coef = (comb[i] * comb[k - i]) as f64 / comb2[k] as f64;
sum + bspsurface.control_points[i][k - i].to_vec() * coef
} else {
sum
}
})
})
.collect();
cc.concat(&BSplineCurve::new(knot_vec, ctrl_pts));
if p + 1 != knots.len() {
bspsurface = backup.unwrap().vcut(knots[p]);
}
}
let mut curve: BSplineCurve<P> = cc.unwrap();
curve.knot_normalize();
curve
}
sourcepub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P>
pub fn sectional_curve(&self, bnd_box: BoundingBox<Vector2>) -> BSplineCurve<P>
Creates a sectional curve with normalized knot vector from the parameter p
to the parameter q
.
Examples
use truck_geometry::*;
// a parabola surface: x = 2u - 1, y = 2v - 1, z = x^2 + y^z
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector3::new(-1.0, -1.0, 2.0), Vector3::new(-1.0, 0.0, 0.0), Vector3::new(-1.0, 1.0, 2.0)],
vec![Vector3::new(0.0, -1.0, 0.0), Vector3::new(0.0, 0.0, -2.0), Vector3::new(0.0, 1.0, 0.0)],
vec![Vector3::new(1.0, -1.0, 2.0), Vector3::new(1.0, 0.0, 0.0), Vector3::new(1.0, 1.0, 2.0)],
];
let mut bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
// add some knots for the test!
bspsurface.add_uknot(0.26);
bspsurface.add_vknot(0.23);
let bnd_box = BoundingBox::from_iter(&[Vector2::new(0.2, 0.3), Vector2::new(0.8, 0.6)]);
let curve = bspsurface.sectional_curve(bnd_box);
const N: usize = 100;
assert_near2!(curve.subs(0.0), bspsurface.subs(0.2, 0.3));
assert_near2!(curve.subs(1.0), bspsurface.subs(0.8, 0.6));
for i in 0..=N {
let t = i as f64 / N as f64;
let pt = curve.subs(t);
assert_near2!(pt[1], pt[0] * 0.5 - 0.1);
assert_near2!(pt[2], pt[0] * pt[0] + pt[1] * pt[1]);
}
sourcepub fn homotopy(
bspcurve0: BSplineCurve<P>,
bspcurve1: BSplineCurve<P>
) -> BSplineSurface<P>
pub fn homotopy(
bspcurve0: BSplineCurve<P>,
bspcurve1: BSplineCurve<P>
) -> BSplineSurface<P>
Creates a surface with normailized knot vectors connecting two curves.
Examples
use truck_geometry::*;
let knot_vec0 = KnotVec::bezier_knot(2);
let ctrl_pts0 = vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)];
let bspcurve0 = BSplineCurve::new(knot_vec0, ctrl_pts0);
let knot_vec1 = KnotVec::bezier_knot(2);
let ctrl_pts1 = vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 2.0)];
let bspcurve1 = BSplineCurve::new(knot_vec1, ctrl_pts1);
let homotopy_surface = BSplineSurface::homotopy(bspcurve0, bspcurve1);
assert_eq!(
homotopy_surface.control_points(),
&vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 2.0)],
vec![Vector2::new(0.5, -1.0), Vector2::new(0.5, 1.0)],
vec![Vector2::new(1.0, 0.0), Vector2::new(1.0, 2.0)],
],
);
sourcepub fn by_boundary(
curve0: BSplineCurve<P>,
curve1: BSplineCurve<P>,
curve2: BSplineCurve<P>,
curve3: BSplineCurve<P>
) -> BSplineSurface<P>
pub fn by_boundary(
curve0: BSplineCurve<P>,
curve1: BSplineCurve<P>,
curve2: BSplineCurve<P>,
curve3: BSplineCurve<P>
) -> BSplineSurface<P>
Creates a surface by its boundary.
Examples
use truck_geometry::*;
let curve0 = BSplineCurve::new(
KnotVec::bezier_knot(1),
vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
);
let curve1 = BSplineCurve::new(
KnotVec::bezier_knot(2),
vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
);
let curve2 = BSplineCurve::new(
KnotVec::bezier_knot(1),
vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
);
let curve3 = BSplineCurve::new(
KnotVec::bezier_knot(2),
vec![Vector2::new(0.0, 1.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 0.0)],
);
let surface = BSplineSurface::by_boundary(curve0, curve1, curve2, curve3);
assert_eq!(
surface.control_points(),
&vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(-1.0, 0.5), Vector2::new(0.0, 1.0)],
vec![Vector2::new(1.0, 0.0), Vector2::new(2.0, 0.5), Vector2::new(1.0, 1.0)],
],
);
Remarks
If the end points of curves are not connected, curve1
and curve3
take precedence. i.e.
curve1
and curve3
are contained in the boundary of the surface and curve0
and
curve2
are not contained.
use truck_geometry::*;
let curve0 = BSplineCurve::new(
KnotVec::bezier_knot(1),
vec![Vector2::new(0.0, 0.0), Vector2::new(1.0, 0.0)],
);
let curve1 = BSplineCurve::new(
KnotVec::bezier_knot(2),
vec![Vector2::new(2.0, 0.0), Vector2::new(3.0, 0.5), Vector2::new(2.0, 1.0)],
);
let curve2 = BSplineCurve::new(
KnotVec::bezier_knot(1),
vec![Vector2::new(1.0, 1.0), Vector2::new(0.0, 1.0)],
);
let curve3 = BSplineCurve::new(
KnotVec::bezier_knot(2),
vec![Vector2::new(-1.0, 1.0), Vector2::new(-2.0, 0.5), Vector2::new(-1.0, 0.0)],
);
let surface = BSplineSurface::by_boundary(
curve0.clone(),
curve1.clone(),
curve2.clone(),
curve3.clone()
);
assert_ne!(surface.subs(0.0, 0.0), curve0.subs(0.0));
assert_eq!(surface.subs(0.0, 0.0), curve3.subs(1.0));
sourcepub fn knot_normalize(&mut self) -> &mut Self
pub fn knot_normalize(&mut self) -> &mut Self
Normalizes the knot vectors
sourcepub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self
pub fn knot_translate(&mut self, x: f64, y: f64) -> &mut Self
Translates the knot vectors.
sourcepub fn splitted_boundary(&self) -> [BSplineCurve<P>; 4]
pub fn splitted_boundary(&self) -> [BSplineCurve<P>; 4]
Get the boundary by four splitted curves.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
let curves = bspsurface.splitted_boundary();
assert_eq!(
curves[0].control_points(),
&vec![Vector2::new(0.0, 0.0), Vector2::new(0.0, 1.0), Vector2::new(0.0, 2.0), Vector2::new(0.0, 3.0)],
);
assert_eq!(
curves[1].control_points(),
&vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
);
assert_eq!(
curves[2].control_points(),
&vec![Vector2::new(1.0, 3.0), Vector2::new(1.0, 2.0), Vector2::new(1.0, 1.0), Vector2::new(1.0, 0.0)],
);
assert_eq!(
curves[3].control_points(),
&vec![Vector2::new(1.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(0.0, 0.0)],
);
Examples found in repository?
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sourcepub fn boundary(&self) -> BSplineCurve<P>
pub fn boundary(&self) -> BSplineCurve<P>
Extracts the boundary of surface
sourcepub fn near_as_surface(&self, other: &BSplineSurface<P>) -> bool
pub fn near_as_surface(&self, other: &BSplineSurface<P>) -> bool
Determines whether self
and other
is near as the B-spline surfaces or not.
Divides each knot domain into the number of degree equal parts,
and check |self(u, v) - other(u, v)| < TOLERANCE
for each end points (u, v)
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
];
let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
let mut bspsurface1 = bspsurface0.clone();
assert!(bspsurface0.near_as_surface(&bspsurface1));
*bspsurface1.control_point_mut(1, 1) = Vector2::new(0.4, 1.0);
assert!(!bspsurface0.near_as_surface(&bspsurface1));
sourcepub fn near2_as_surface(&self, other: &BSplineSurface<P>) -> bool
pub fn near2_as_surface(&self, other: &BSplineSurface<P>) -> bool
Determines whether self
and other
is near in square order as the B-spline surfaces or not.
Divides each knot domain into the number of degree equal parts,
and check |self(u, v) - other(u, v)| < TOLERANCE
for each end points (u, v)
.
Examples
use truck_geometry::*;
let eps = TOLERANCE;
let knot_vecs = (KnotVec::bezier_knot(3), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 1.0), Vector2::new(1.0, 1.0)],
vec![Vector2::new(0.0, 2.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 2.0)],
vec![Vector2::new(0.0, 3.0), Vector2::new(0.5, 3.5), Vector2::new(1.0, 3.0)],
];
let bspsurface0 = BSplineSurface::new(knot_vecs, ctrl_pts);
let mut bspsurface1 = bspsurface0.clone();
assert!(bspsurface0.near_as_surface(&bspsurface1));
*bspsurface1.control_point_mut(1, 1) += Vector2::new(eps, eps / 2.0);
assert!(bspsurface0.near_as_surface(&bspsurface1));
assert!(!bspsurface0.near2_as_surface(&bspsurface1));
source§impl<V> BSplineSurface<V>where
V: MetricSpace<Metric = f64> + Index<usize, Output = f64> + Bounded<f64> + Copy,
impl<V> BSplineSurface<V>where
V: MetricSpace<Metric = f64> + Index<usize, Output = f64> + Bounded<f64> + Copy,
sourcepub fn roughly_bounding_box(&self) -> BoundingBox<V>
pub fn roughly_bounding_box(&self) -> BoundingBox<V>
Returns the bounding box including all control points.
Trait Implementations§
source§impl<V> BoundedSurface for BSplineSurface<V>where
BSplineSurface<V>: ParametricSurface,
impl<V> BoundedSurface for BSplineSurface<V>where
BSplineSurface<V>: ParametricSurface,
source§impl<P: Clone> Clone for BSplineSurface<P>
impl<P: Clone> Clone for BSplineSurface<P>
source§fn clone(&self) -> BSplineSurface<P>
fn clone(&self) -> BSplineSurface<P>
1.0.0 · source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moresource§impl<P: Debug> Debug for BSplineSurface<P>
impl<P: Debug> Debug for BSplineSurface<P>
source§impl<'de, P> Deserialize<'de> for BSplineSurface<P>where
P: Deserialize<'de>,
impl<'de, P> Deserialize<'de> for BSplineSurface<P>where
P: Deserialize<'de>,
source§fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
source§impl IncludeCurve<BSplineCurve<Point2<f64>>> for BSplineSurface<Point2>
impl IncludeCurve<BSplineCurve<Point2<f64>>> for BSplineSurface<Point2>
source§impl IncludeCurve<BSplineCurve<Point3<f64>>> for BSplineSurface<Point3>
impl IncludeCurve<BSplineCurve<Point3<f64>>> for BSplineSurface<Point3>
source§impl IncludeCurve<NURBSCurve<Vector4<f64>>> for BSplineSurface<Point3>
impl IncludeCurve<NURBSCurve<Vector4<f64>>> for BSplineSurface<Point3>
source§impl<V: Clone> Invertible for BSplineSurface<V>
impl<V: Clone> Invertible for BSplineSurface<V>
source§impl<P> ParameterDivision2D for BSplineSurface<P>where
P: EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff> + MetricSpace<Metric = f64> + HashGen<f64> + ControlPoint<f64>,
impl<P> ParameterDivision2D for BSplineSurface<P>where
P: EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff> + MetricSpace<Metric = f64> + HashGen<f64> + ControlPoint<f64>,
source§impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P>
impl<P: ControlPoint<f64>> ParametricSurface for BSplineSurface<P>
source§fn subs(&self, u: f64, v: f64) -> P
fn subs(&self, u: f64, v: f64) -> P
Substitutes to a B-spline surface.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
// bspsurface: (v, 2v(1 - v)(2u - 1) + u)
const N: usize = 100; // sample size
for i in 0..=N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
bspsurface.subs(u, v),
Vector2::new(v, 2.0 * v * (1.0 - v) * (2.0 * u - 1.0) + u),
);
}
}
source§fn uder(&self, u: f64, v: f64) -> P::Diff
fn uder(&self, u: f64, v: f64) -> P::Diff
Substitutes derived B-spline surface by the first parameter u
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
// bspsurface: (v, 2v(1 - v)(2u - 1) + u), uderivation: (0.0, 4v(1 - v) + 1)
const N: usize = 100; // sample size
for i in 0..=N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
bspsurface.uder(u, v),
Vector2::new(0.0, 4.0 * v * (1.0 - v) + 1.0),
);
}
}
source§fn vder(&self, u: f64, v: f64) -> P::Diff
fn vder(&self, u: f64, v: f64) -> P::Diff
Substitutes derived B-spline surface by the first parameter v
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(1), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
// bspsurface: (v, 2v(1 - v)(2u - 1) + u), vderivation: (1, -2(2u - 1)(2v - 1))
const N: usize = 100; // sample size
for i in 0..=N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
bspsurface.vder(u, v),
Vector2::new(1.0, -2.0 * (2.0 * u - 1.0) * (2.0 * v - 1.0)),
);
}
}
source§fn uuder(&self, u: f64, v: f64) -> P::Diff
fn uuder(&self, u: f64, v: f64) -> P::Diff
Substitutes 2nd-ord derived B-spline surface by the first parameter u
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
// bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
// uuder: (0, 4v(v - 1))
const N: usize = 100; // sample size
for i in 0..=N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
bspsurface.uuder(u, v),
Vector2::new(0.0, 4.0 * v * (v - 1.0)),
);
}
}
source§fn vvder(&self, u: f64, v: f64) -> P::Diff
fn vvder(&self, u: f64, v: f64) -> P::Diff
Substitutes 2nd-ord derived B-spline surface by the second parameter v
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
// bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
// vvder: (0, 4(u^2 - 3u + 1))
const N: usize = 100; // sample size
for i in 0..=N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
bspsurface.vvder(u, v),
Vector2::new(0.0, 4.0 * (u * u - 3.0 * u + 1.0)),
);
}
}
source§fn uvder(&self, u: f64, v: f64) -> P::Diff
fn uvder(&self, u: f64, v: f64) -> P::Diff
Substitutes 2nd-ord derived B-spline surface by the both parameters u, v
.
Examples
use truck_geometry::*;
let knot_vecs = (KnotVec::bezier_knot(2), KnotVec::bezier_knot(2));
let ctrl_pts = vec![
vec![Vector2::new(0.0, 0.0), Vector2::new(0.5, -1.0), Vector2::new(1.0, 0.0)],
vec![Vector2::new(0.0, 0.5), Vector2::new(0.5, 1.0), Vector2::new(1.0, 0.5)],
vec![Vector2::new(0.0, 1.0), Vector2::new(0.5, 2.0), Vector2::new(1.0, 1.0)],
];
let bspsurface = BSplineSurface::new(knot_vecs, ctrl_pts);
// bspsurface: (v, 2 u^2 v^2 - 2 u^2 v - 6 u v^2 + 6uv + 2v^2 + u - 2v)
// uvder: (0, 8uv - 4u - 12v + 6)
const N: usize = 100; // sample size
for i in 0..=N {
let u = (i as f64) / (N as f64);
for j in 0..=N {
let v = (j as f64) / (N as f64);
assert_near2!(
bspsurface.uvder(u, v),
Vector2::new(0.0, 8.0 * u * v - 4.0 * u - 12.0 * v + 6.0),
);
}
}
§type Vector = <P as ControlPoint<f64>>::Diff
type Vector = <P as ControlPoint<f64>>::Diff
source§impl ParametricSurface3D for BSplineSurface<Point3>
impl ParametricSurface3D for BSplineSurface<Point3>
source§impl<P: PartialEq> PartialEq<BSplineSurface<P>> for BSplineSurface<P>
impl<P: PartialEq> PartialEq<BSplineSurface<P>> for BSplineSurface<P>
source§fn eq(&self, other: &BSplineSurface<P>) -> bool
fn eq(&self, other: &BSplineSurface<P>) -> bool
self
and other
values to be equal, and is used
by ==
.source§impl<P> SearchNearestParameter<D2> for BSplineSurface<P>where
P: ControlPoint<f64> + EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff> + MetricSpace<Metric = f64>,
<P as ControlPoint<f64>>::Diff: InnerSpace<Scalar = f64> + Tolerance,
impl<P> SearchNearestParameter<D2> for BSplineSurface<P>where
P: ControlPoint<f64> + EuclideanSpace<Scalar = f64, Diff = <P as ControlPoint<f64>>::Diff> + MetricSpace<Metric = f64>,
<P as ControlPoint<f64>>::Diff: InnerSpace<Scalar = f64> + Tolerance,
source§impl SearchParameter<D2> for BSplineSurface<Point2>
impl SearchParameter<D2> for BSplineSurface<Point2>
source§impl SearchParameter<D2> for BSplineSurface<Point3>
impl SearchParameter<D2> for BSplineSurface<Point3>
source§impl<P> Serialize for BSplineSurface<P>where
P: Serialize,
impl<P> Serialize for BSplineSurface<P>where
P: Serialize,
source§impl<M, P: EuclideanSpace<Scalar = f64>> Transformed<M> for BSplineSurface<P>where
M: Transform<P>,
impl<M, P: EuclideanSpace<Scalar = f64>> Transformed<M> for BSplineSurface<P>where
M: Transform<P>,
source§fn transform_by(&mut self, trans: M)
fn transform_by(&mut self, trans: M)
trans
.source§fn transformed(&self, trans: T) -> Self
fn transformed(&self, trans: T) -> Self
trans
.