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use crate::utils::inv_or_zero;
use crate::Float;
use approx::ulps_eq;
#[derive(Clone, PartialEq, Debug)]
pub struct KnotVector(pub Vec<Float>);
impl KnotVector {
pub fn new(knots: Vec<Float>) -> KnotVector {
KnotVector(knots)
}
pub fn from_values_and_multiplicities(
values: Vec<Float>,
multiplicities: Vec<usize>,
) -> KnotVector {
let mut knots = Vec::with_capacity(multiplicities.iter().sum());
for (value, multiplicity) in values.into_iter().zip(multiplicities.into_iter()) {
knots.extend(std::iter::repeat(value).take(multiplicity));
}
KnotVector(knots)
}
pub fn normalize(&self) -> KnotVector {
let start = self[0];
let length = self[self.len() - 1] - self[0];
self.iter()
.map(|value| (value - start) / length)
.collect::<Vec<_>>()
.into()
}
pub fn multiplicity(&self, i: usize) -> usize {
self.iter().filter(|u| ulps_eq!(self[i], u)).count()
}
pub fn shrink(&self) -> KnotVector {
KnotVector(self[1..self.len() - 1].to_vec())
}
pub fn spans(&self, degree: usize) -> Vec<Float> {
self.windows(degree + 1)
.map(|span| span[degree] - span[0])
.collect()
}
pub fn span_index(&self, u: Float) -> usize {
if let Some(index) = self.iter().rposition(|t| *t <= u) {
if index == self.len() - 1 {
index - self.multiplicity(index)
} else {
index
}
} else {
self.multiplicity(0)
}
}
pub fn bspline_basis(&self, degree: usize, u: Float) -> Vec<Float> {
let n = self.len() - 1;
let index = self.span_index(u);
let mut values = vec![0.0; n];
values[index] = 1.0;
for k in 1..=degree {
let base = if index < k { 0 } else { index - k };
let delta = self[base + k] - self[base];
let max = if index + k < n { index } else { n - k - 1 };
let mut a = inv_or_zero(delta) * (u - self[base]);
for i in base..=max {
let delta = self[i + k + 1] - self[i + 1];
let b = inv_or_zero(delta) * (self[i + k + 1] - u);
values[i] = a * values[i] + b * values[i + 1];
a = 1.0 - b;
}
}
values.truncate(n - degree);
values
}
pub fn bezier_knot(degree: usize) -> KnotVector {
let mut knots = Vec::with_capacity(degree * 2 + 2);
knots.extend(std::iter::repeat(0.0).take(degree + 1));
knots.extend(std::iter::repeat(1.0).take(degree + 1));
KnotVector(knots)
}
pub fn uniform_knot(degree: usize, division: usize) -> KnotVector {
let step = 1.0 / division as Float;
let mut knots = Vec::with_capacity(degree * 2 + 2);
knots.extend(std::iter::repeat(0.0).take(degree + 1));
knots.extend((1..division).map(|i| (i as Float) * step));
knots.extend(std::iter::repeat(1.0).take(degree + 1));
KnotVector(knots)
}
pub fn add_knot(&mut self, knot: f64) -> usize {
match self.iter().rposition(|t| *t <= knot) {
Some(index) => {
self.0.insert(index + 1, knot);
index + 1
}
None => {
self.0.insert(0, knot);
0
}
}
}
#[inline]
pub fn sub_vec<I: std::slice::SliceIndex<[f64], Output = [f64]>>(
&self,
range: I,
) -> KnotVector {
KnotVector(Vec::from(&self.0[range]))
}
}
impl From<Vec<Float>> for KnotVector {
fn from(vec: Vec<Float>) -> KnotVector {
KnotVector(vec)
}
}
impl std::iter::FromIterator<Float> for KnotVector {
#[inline(always)]
fn from_iter<I: IntoIterator<Item = Float>>(iter: I) -> KnotVector {
KnotVector::new(iter.into_iter().collect::<Vec<_>>())
}
}
impl<'a> IntoIterator for &'a KnotVector {
type Item = &'a Float;
type IntoIter = std::slice::Iter<'a, Float>;
#[inline(always)]
fn into_iter(self) -> Self::IntoIter {
self.0.iter()
}
}
impl std::ops::Deref for KnotVector {
type Target = Vec<Float>;
#[inline(always)]
fn deref(&self) -> &Vec<Float> {
&self.0
}
}
impl AsRef<[Float]> for KnotVector {
#[inline(always)]
fn as_ref(&self) -> &[Float] {
&self.0
}
}
#[test]
fn test_bspline_basis() {
let knots = KnotVector::bezier_knot(3);
assert_eq!(knots.bspline_basis(3, 0.0), vec![1.0, 0.0, 0.0, 0.0]);
assert_eq!(
knots.bspline_basis(3, 0.5),
vec![0.125, 0.375, 0.375, 0.125]
);
assert_eq!(knots.bspline_basis(3, 1.0), vec![0.0, 0.0, 0.0, 1.0]);
assert_eq!(
*KnotVector::uniform_knot(2, 2),
vec![0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0],
);
}