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Implement closest_point for Segments.

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This commit is contained in:
IQuick143 2025-07-14 13:31:02 +02:00
parent 33bed5dd70
commit 0372a8a734
2 changed files with 159 additions and 0 deletions
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78
crates/bevy_math/src/primitives/dim2.rs
View File

@ -1480,6 +1480,38 @@ impl Segment2d {
self.reverse();
self
}
/// Returns the point on the [`Segment2d`] that is closest to the specified `point`.
#[inline(always)]
pub fn closest_point(&self, point: Vec2) -> Vec2 {
// `point`
// x
// ^|
// / |
//`offset`/ |
// / | `segment_vector`
// x----.-------------->x
// 0 t 1
let segment_vector = self.vertices[1] - self.vertices[0];
let offset = point - self.vertices[0];
// The signed projection of `offset` onto `segment_vector`, scaled by the length of the segment.
let projection_scaled = segment_vector.dot(offset);
// `point` is too far "left" in the picture
if projection_scaled <= 0.0 {
return self.vertices[0];
}
let length_squared = segment_vector.length_squared();
// `point` is too far "right" in the picture
if projection_scaled >= length_squared {
return self.vertices[1];
}
// Point lies somewhere in the middle, we compute the closest point by finding the parameter along the line.
let t = projection_scaled / length_squared;
self.vertices[0] + t * segment_vector
}
}
impl From<[Vec2; 2]> for Segment2d {
@ -2288,6 +2320,52 @@ mod tests {
assert_eq!(rhombus.closest_point(Vec2::new(-0.55, 0.35)), Vec2::ZERO);
}
#[test]
fn segment_closest_point() {
assert_eq!(
Segment2d::new(Vec2::new(0.0, 0.0), Vec2::new(3.0, 0.0))
.closest_point(Vec2::new(1.0, 6.0)),
Vec2::new(1.0, 0.0)
);
let segments = [
Segment2d::new(Vec2::new(0.0, 0.0), Vec2::new(0.0, 0.0)),
Segment2d::new(Vec2::new(0.0, 0.0), Vec2::new(1.0, 0.0)),
Segment2d::new(Vec2::new(1.0, 0.0), Vec2::new(0.0, 1.0)),
Segment2d::new(Vec2::new(1.0, 0.0), Vec2::new(1.0, 5.0 * f32::EPSILON)),
];
let points = [
Vec2::new(0.0, 0.0),
Vec2::new(1.0, 0.0),
Vec2::new(-1.0, 1.0),
Vec2::new(1.0, 1.0),
Vec2::new(-1.0, 0.0),
Vec2::new(5.0, -1.0),
Vec2::new(1.0, f32::EPSILON),
];
for point in points.iter() {
for segment in segments.iter() {
let closest = segment.closest_point(*point);
assert!(
point.distance_squared(closest) <= point.distance_squared(segment.point1()),
"Closest point must always at least as close as either vertex."
);
assert!(
point.distance_squared(closest) <= point.distance_squared(segment.point2()),
"Closest point must always at least as close as either vertex."
);
assert!(
point.distance_squared(closest) <= point.distance_squared(segment.center()),
"Closest point must always at least as close as the center."
);
let closest_to_closest = segment.closest_point(closest);
// Closest point must already be on the segment
assert_relative_eq!(closest_to_closest, closest);
}
}
}
#[test]
fn circle_math() {
let circle = Circle { radius: 3.0 };

81
crates/bevy_math/src/primitives/dim3.rs
View File

@ -548,6 +548,38 @@ impl Segment3d {
self.reverse();
self
}
/// Returns the point on the [`Segment3d`] that is closest to the specified `point`.
#[inline(always)]
pub fn closest_point(&self, point: Vec3) -> Vec3 {
// `point`
// x
// ^|
// / |
//`offset`/ |
// / | `segment_vector`
// x----.-------------->x
// 0 t 1
let segment_vector = self.vertices[1] - self.vertices[0];
let offset = point - self.vertices[0];
// The signed projection of `offset` onto `segment_vector`, scaled by the length of the segment.
let projection_scaled = segment_vector.dot(offset);
// `point` is too far "left" in the picture
if projection_scaled <= 0.0 {
return self.vertices[0];
}
let length_squared = segment_vector.length_squared();
// `point` is too far "right" in the picture
if projection_scaled >= length_squared {
return self.vertices[1];
}
// Point lies somewhere in the middle, we compute the closest point by finding the parameter along the line.
let t = projection_scaled / length_squared;
self.vertices[0] + t * segment_vector
}
}
impl From<[Vec3; 2]> for Segment3d {
@ -1532,6 +1564,55 @@ mod tests {
);
}
#[test]
fn segment_closest_point() {
assert_eq!(
Segment3d::new(Vec3::new(0.0, 0.0, 0.0), Vec3::new(3.0, 0.0, 0.0))
.closest_point(Vec3::new(1.0, 6.0, -2.0)),
Vec3::new(1.0, 0.0, 0.0)
);
let segments = [
Segment3d::new(Vec3::new(0.0, 0.0, 0.0), Vec3::new(0.0, 0.0, 0.0)),
Segment3d::new(Vec3::new(0.0, 0.0, 0.0), Vec3::new(1.0, 0.0, 0.0)),
Segment3d::new(Vec3::new(1.0, 0.0, 2.0), Vec3::new(0.0, 1.0, -2.0)),
Segment3d::new(
Vec3::new(1.0, 0.0, 0.0),
Vec3::new(1.0, 5.0 * f32::EPSILON, 0.0),
),
];
let points = [
Vec3::new(0.0, 0.0, 0.0),
Vec3::new(1.0, 0.0, 0.0),
Vec3::new(-1.0, 1.0, 2.0),
Vec3::new(1.0, 1.0, 1.0),
Vec3::new(-1.0, 0.0, 0.0),
Vec3::new(5.0, -1.0, 0.5),
Vec3::new(1.0, f32::EPSILON, 0.0),
];
for point in points.iter() {
for segment in segments.iter() {
let closest = segment.closest_point(*point);
assert!(
point.distance_squared(closest) <= point.distance_squared(segment.point1()),
"Closest point must always at least as close as either vertex."
);
assert!(
point.distance_squared(closest) <= point.distance_squared(segment.point2()),
"Closest point must always at least as close as either vertex."
);
assert!(
point.distance_squared(closest) <= point.distance_squared(segment.center()),
"Closest point must always at least as close as the center."
);
let closest_to_closest = segment.closest_point(closest);
// Closest point must already be on the segment
assert_relative_eq!(closest_to_closest, closest);
}
}
}
#[test]
fn sphere_math() {
let sphere = Sphere { radius: 4.0 };