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use super::PlineVertex;
use crate::core::{
math::{
angle, angle_is_within_sweep, bulge_from_angle, delta_angle, delta_angle_signed,
dist_squared, line_seg_closest_point, midpoint, min_max, point_on_circle,
point_within_arc_sweep, Vector2,
},
traits::Real,
};
use static_aabb2d_index::AABB;
/// Get the arc radius and center of an arc polyline segment defined by `v1` to `v2`.
/// Behavior undefined (may panic or return without error) if v1.bulge is zero.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::traits::*;
/// # use cavalier_contours::core::math::*;
/// // arc half circle arc segment going from (0, 0) to (1, 0) counter clockwise
/// let v1 = PlineVertex::new(0.0, 0.0, 1.0);
/// let v2 = PlineVertex::new(1.0, 0.0, 0.0);
/// let (arc_radius, arc_center) = seg_arc_radius_and_center(v1, v2);
/// assert!(arc_radius.fuzzy_eq(0.5));
/// assert!(arc_center.fuzzy_eq(Vector2::new(0.5, 0.0)));
///```
pub fn seg_arc_radius_and_center<T>(v1: PlineVertex<T>, v2: PlineVertex<T>) -> (T, Vector2<T>)
where
T: Real,
{
debug_assert!(!v1.bulge_is_zero(), "v1 to v2 must be an arc");
debug_assert!(!v1.pos().fuzzy_eq(v2.pos()), "v1 must not be on top of v2");
// compute radius
let abs_bulge = v1.bulge.abs();
let chord_v = v2.pos() - v1.pos();
let chord_len = chord_v.length();
let radius = chord_len * (abs_bulge * abs_bulge + T::one()) / (T::four() * abs_bulge);
// compute center
let s = abs_bulge * chord_len / T::two();
let m = radius - s;
let mut offs_x = -m * chord_v.y / chord_len;
let mut offs_y = m * chord_v.x / chord_len;
if v1.bulge_is_neg() {
offs_x = -offs_x;
offs_y = -offs_y;
}
let center = Vector2::new(
v1.x + chord_v.x / T::two() + offs_x,
v1.y + chord_v.y / T::two() + offs_y,
);
(radius, center)
}
/// Result from splitting a segment using [seg_split_at_point].
#[derive(Debug, Copy, Clone)]
pub struct SplitResult<T = f64>
where
T: Real,
{
/// Updated start vertex (has same position as start of segment but with updated bulge value).
pub updated_start: PlineVertex<T>,
/// Vertex at split point (position is equal to split point, bulge set to maintain same curve to
/// the next vertex).
pub split_vertex: PlineVertex<T>,
}
/// Splits a polyline segment defined by `v1` to `v2` at the `point_on_seg` given. Assumes the `point_on_seg` lies on the segment.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::core::math::*;
/// # use cavalier_contours::polyline::*;
/// // arc half circle arc segment going from (0, 0) to (1, 0) counter clockwise
/// let v1 = PlineVertex::new(0.0, 0.0, 1.0);
/// let v2 = PlineVertex::new(1.0, 0.0, 0.0);
/// let point = Vector2::new(0.5, -0.5);
/// let SplitResult { updated_start, split_vertex } = seg_split_at_point(v1, v2, point, 1e-5);
/// let quarter_circle_bulge = (std::f64::consts::PI / 8.0).tan();
/// assert!(updated_start.fuzzy_eq(PlineVertex::new(v1.x, v1.y, quarter_circle_bulge)));
/// assert!(split_vertex.fuzzy_eq(PlineVertex::new(point.x, point.y, quarter_circle_bulge)));
/// ```
pub fn seg_split_at_point<T>(
v1: PlineVertex<T>,
v2: PlineVertex<T>,
point_on_seg: Vector2<T>,
pos_equal_eps: T,
) -> SplitResult<T>
where
T: Real,
{
if v1.bulge_is_zero() {
// v1->v2 is a line segment, just use point as end point
let updated_start = v1;
let split_vertex = PlineVertex::new(point_on_seg.x, point_on_seg.y, T::zero());
return SplitResult {
updated_start,
split_vertex,
};
}
if v1.pos().fuzzy_eq_eps(v2.pos(), pos_equal_eps)
|| v1.pos().fuzzy_eq_eps(point_on_seg, pos_equal_eps)
{
// v1 == v2 or v1 == point, updated_start is put on top of split_vertex
let updated_start = PlineVertex::new(point_on_seg.x, point_on_seg.y, T::zero());
let split_vertex = PlineVertex::new(point_on_seg.x, point_on_seg.y, v1.bulge);
return SplitResult {
updated_start,
split_vertex,
};
}
if v2.pos().fuzzy_eq_eps(point_on_seg, pos_equal_eps) {
// point is at end point of segment
let updated_start = v1;
let split_vertex = PlineVertex::new(v2.x, v2.y, T::zero());
return SplitResult {
updated_start,
split_vertex,
};
}
let (_, arc_center) = seg_arc_radius_and_center(v1, v2);
let point_pos_angle = angle(arc_center, point_on_seg);
let arc_start_angle = angle(arc_center, v1.pos());
let theta1 = delta_angle_signed(arc_start_angle, point_pos_angle, v1.bulge_is_neg());
let bulge1 = bulge_from_angle(theta1);
let arc_end_angle = angle(arc_center, v2.pos());
let theta2 = delta_angle_signed(point_pos_angle, arc_end_angle, v1.bulge_is_neg());
let bulge2 = bulge_from_angle(theta2);
let updated_start = PlineVertex::new(v1.x, v1.y, bulge1);
let split_vertex = PlineVertex::new(point_on_seg.x, point_on_seg.y, bulge2);
SplitResult {
updated_start,
split_vertex,
}
}
/// Find the tangent direction vector on a polyline segment defined by `v1` to `v2` at `point_on_seg`.
///
/// Note: The vector returned is just the direction vector, add the `point_on_seg` position to
/// get the actual tangent vector.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::math::*;
/// // counter clockwise half circle arc going from (2, 2) to (2, 4)
/// let v1 = PlineVertex::new(2.0, 2.0, 1.0);
/// let v2 = PlineVertex::new(4.0, 2.0, 0.0);
/// let midpoint = Vector2::new(3.0, 1.0);
/// assert!(seg_tangent_vector(v1, v2, midpoint).normalize().fuzzy_eq(Vector2::new(1.0, 0.0)));
/// assert!(seg_tangent_vector(v1, v2, v1.pos()).normalize().fuzzy_eq(Vector2::new(0.0, -1.0)));
/// assert!(seg_tangent_vector(v1, v2, v2.pos()).normalize().fuzzy_eq(Vector2::new(0.0, 1.0)));
/// ```
pub fn seg_tangent_vector<T>(
v1: PlineVertex<T>,
v2: PlineVertex<T>,
point_on_seg: Vector2<T>,
) -> Vector2<T>
where
T: Real,
{
if v1.bulge_is_zero() {
return v2.pos() - v1.pos();
}
let (_, arc_center) = seg_arc_radius_and_center(v1, v2);
if v1.bulge_is_pos() {
// ccw, rotate vector from center to point_on_seg 90 degrees
return Vector2::new(
-(point_on_seg.y - arc_center.y),
point_on_seg.x - arc_center.x,
);
}
// cw, rotate vector from center to point_on_seg -90 degrees
Vector2::new(
point_on_seg.y - arc_center.y,
-(point_on_seg.x - arc_center.x),
)
}
/// Find the closest point on a polyline segment defined by `v1` to `v2` to `point` given.
/// If there are multiple closest points then one is chosen (which is chosen is not defined).
///
/// `epsilon` is used for fuzzy float comparisons.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::core::math::*;
/// # use cavalier_contours::polyline::*;
/// // counter clockwise half circle arc going from (2, 2) to (2, 4)
/// let v1 = PlineVertex::new(2.0, 2.0, 1.0);
/// let v2 = PlineVertex::new(4.0, 2.0, 0.0);
/// assert!(
/// seg_closest_point(v1, v2, Vector2::new(3.0, 0.0), 1e-5).fuzzy_eq(Vector2::new(3.0, 1.0))
/// );
/// assert!(
/// seg_closest_point(v1, v2, Vector2::new(3.0, 1.2), 1e-5).fuzzy_eq(Vector2::new(3.0, 1.0))
/// );
/// assert!(seg_closest_point(v1, v2, v1.pos(), 1e-5).fuzzy_eq(v1.pos()));
/// assert!(seg_closest_point(v1, v2, v2.pos(), 1e-5).fuzzy_eq(v2.pos()));
/// ```
pub fn seg_closest_point<T>(
v1: PlineVertex<T>,
v2: PlineVertex<T>,
point: Vector2<T>,
epsilon: T,
) -> Vector2<T>
where
T: Real,
{
if v1.bulge_is_zero() {
return line_seg_closest_point(v1.pos(), v2.pos(), point);
}
let (arc_radius, arc_center) = seg_arc_radius_and_center(v1, v2);
if point.fuzzy_eq_eps(arc_center, epsilon) {
// avoid normalizing zero length vector (point is at center, just return start point)
return v1.pos();
}
if point_within_arc_sweep(
arc_center,
v1.pos(),
v2.pos(),
v1.bulge_is_neg(),
point,
epsilon,
) {
// closest point is on the arc
let v_to_point = (point - arc_center).normalize();
return v_to_point.scale(arc_radius) + arc_center;
}
// closest point is one of the ends
let dist1 = dist_squared(v1.pos(), point);
let dist2 = dist_squared(v2.pos(), point);
if dist1 < dist2 {
return v1.pos();
}
v2.pos()
}
/// Computes a fast approximate axis aligned bounding box of a polyline segment defined by `v1` to `v2`.
///
/// The bounding box may be larger than the true bounding box for the segment (but is never smaller).
/// For the true axis aligned bounding box use [seg_bounding_box] but this function is faster for arc
/// segments.
pub fn seg_fast_approx_bounding_box<T>(v1: PlineVertex<T>, v2: PlineVertex<T>) -> AABB<T>
where
T: Real,
{
if v1.bulge_is_zero() {
// line segment
let (min_x, max_x) = min_max(v1.x, v2.x);
let (min_y, max_y) = min_max(v1.y, v2.y);
return AABB::new(min_x, min_y, max_x, max_y);
}
// For arcs we don't compute the actual extents which is slower, instead we create an approximate
// bounding box from the rectangle formed by extending the chord by the sagitta, note this
// approximate bounding box is always equal to or bigger than the true bounding box
let b = v1.bulge;
let offs_x = b * (v2.y - v1.y) / T::two();
let offs_y = -b * (v2.x - v1.x) / T::two();
let (pt_x_min, pt_x_max) = min_max(v1.x + offs_x, v2.x + offs_x);
let (pt_y_min, pt_y_max) = min_max(v1.y + offs_y, v2.y + offs_y);
let (end_point_x_min, end_point_x_max) = min_max(v1.x, v2.x);
let (end_point_y_min, end_point_y_max) = min_max(v1.y, v2.y);
let min_x = num_traits::real::Real::min(end_point_x_min, pt_x_min);
let min_y = num_traits::real::Real::min(end_point_y_min, pt_y_min);
let max_x = num_traits::real::Real::max(end_point_x_max, pt_x_max);
let max_y = num_traits::real::Real::max(end_point_y_max, pt_y_max);
AABB::new(min_x, min_y, max_x, max_y)
}
/// Returns the arc segment bounding box. Assumes `v1` to `v2` is an arc.
pub(crate) fn arc_seg_bounding_box<T>(v1: PlineVertex<T>, v2: PlineVertex<T>) -> AABB<T>
where
T: Real,
{
debug_assert!(!v1.bulge_is_zero(), "expected arc");
if v1.pos().fuzzy_eq(v2.pos()) {
return AABB::new(v1.x, v1.y, v1.x, v1.y);
}
let (arc_radius, arc_center) = seg_arc_radius_and_center(v1, v2);
let start_angle = angle(arc_center, v1.pos());
let end_angle = angle(arc_center, v2.pos());
let sweep_angle = delta_angle_signed(start_angle, end_angle, v1.bulge_is_neg());
let crosses_angle = |angle| angle_is_within_sweep(angle, start_angle, sweep_angle);
let min_x = if crosses_angle(T::pi()) {
// crosses PI
arc_center.x - arc_radius
} else {
num_traits::real::Real::min(v1.x, v2.x)
};
let min_y = if crosses_angle(T::from(1.5).unwrap() * T::pi()) {
// crosses 3PI/2
arc_center.y - arc_radius
} else {
num_traits::real::Real::min(v1.y, v2.y)
};
let max_x = if crosses_angle(T::zero()) {
// crosses 2PI
arc_center.x + arc_radius
} else {
num_traits::real::Real::max(v1.x, v2.x)
};
let max_y = if crosses_angle(T::from(0.5).unwrap() * T::pi()) {
// crosses PI/2
arc_center.y + arc_radius
} else {
num_traits::real::Real::max(v1.y, v2.y)
};
AABB::new(min_x, min_y, max_x, max_y)
}
/// Computes the axis aligned bounding box of a polyline segment defined by `v1` to `v2`.
///
/// This function is quite a bit slower than [seg_fast_approx_bounding_box] when given an arc.
pub fn seg_bounding_box<T>(v1: PlineVertex<T>, v2: PlineVertex<T>) -> AABB<T>
where
T: Real,
{
if v1.bulge_is_zero() {
// line segment
let (min_x, max_x) = min_max(v1.x, v2.x);
let (min_y, max_y) = min_max(v1.y, v2.y);
AABB::new(min_x, min_y, max_x, max_y)
} else {
arc_seg_bounding_box(v1, v2)
}
}
/// Calculate the path length of the polyline segment defined by `v1` to `v2`.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::traits::*;
/// // counter clockwise half circle arc going from (2, 2) to (2, 4)
/// // arc radius = 1 so length should be PI
/// let v1 = PlineVertex::new(2.0, 2.0, 1.0);
/// let v2 = PlineVertex::new(4.0, 2.0, 0.0);
/// assert!(seg_length(v1, v2).fuzzy_eq(std::f64::consts::PI));
/// ```
///
/// Also works with line segments.
///
/// ```
/// # use cavalier_contours::core::traits::*;
/// # use cavalier_contours::core::math::*;
/// # use cavalier_contours::polyline::*;
/// // line segment going from (2, 2) to (4, 4)
/// let v1 = PlineVertex::new(2.0, 2.0, 0.0);
/// let v2 = PlineVertex::new(4.0, 4.0, 0.0);
/// assert!(seg_length(v1, v2).fuzzy_eq(2.0 * 2.0f64.sqrt()));
/// ```
pub fn seg_length<T>(v1: PlineVertex<T>, v2: PlineVertex<T>) -> T
where
T: Real,
{
if v1.fuzzy_eq(v2) {
return T::zero();
}
if v1.bulge_is_zero() {
return dist_squared(v1.pos(), v2.pos()).sqrt();
}
let (arc_radius, arc_center) = seg_arc_radius_and_center(v1, v2);
let start_angle = angle(arc_center, v1.pos());
let end_angle = angle(arc_center, v2.pos());
arc_radius * delta_angle(start_angle, end_angle).abs()
}
/// Find the midpoint for the polyline segment defined by `v1` to `v2`.
///
/// # Examples
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::math::*;
/// // counter clockwise half circle arc going from (2, 2) to (2, 4)
/// let v1 = PlineVertex::new(2.0, 2.0, 1.0);
/// let v2 = PlineVertex::new(4.0, 2.0, 0.0);
/// assert!(seg_midpoint(v1, v2).fuzzy_eq(Vector2::new(3.0, 1.0)));
/// ```
///
/// Also works with line segments.
///
/// ```
/// # use cavalier_contours::polyline::*;
/// # use cavalier_contours::core::math::*;
/// // line segment going from (2, 2) to (4, 4)
/// let v1 = PlineVertex::new(2.0, 2.0, 0.0);
/// let v2 = PlineVertex::new(4.0, 4.0, 0.0);
/// assert!(seg_midpoint(v1, v2).fuzzy_eq(Vector2::new(3.0, 3.0)));
/// ```
pub fn seg_midpoint<T>(v1: PlineVertex<T>, v2: PlineVertex<T>) -> Vector2<T>
where
T: Real,
{
if v1.bulge_is_zero() {
return midpoint(v1.pos(), v2.pos());
}
let (arc_radius, arc_center) = seg_arc_radius_and_center(v1, v2);
let angle1 = angle(arc_center, v1.pos());
let angle2 = angle(arc_center, v2.pos());
let angle_offset = delta_angle_signed(angle1, angle2, v1.bulge_is_neg()) / T::two();
let mid_angle = angle1 + angle_offset;
point_on_circle(arc_radius, arc_center, mid_angle)
}