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Fixed the frustum-sphere collision and added tests (bevyengine#4035)
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# Objective

Fixes bevyengine#3744 

## Solution

The old code used the formula `normal . center + d + radius <= 0` to determine if the sphere with center `center` and radius `radius` is outside the plane with normal `normal` and distance from origin `d`. This only works if `normal` is normalized, which is not necessarily the case. Instead, `normal` and `d` are both multiplied by some factor that `radius` isn't multiplied by. So the additional code multiplied `radius` by that factor.
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@hayashi-stl @rparrett
hayashi-stl authored and rparrett committed Mar 9, 2022
1 parent 9b2f9a3 commit 206c423
Showing 1 changed file with 203 additions and 14 deletions.
217 changes: 203 additions & 14 deletions crates/bevy_render/src/primitives/mod.rs
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
use bevy_ecs::{component::Component, reflect::ReflectComponent};
use bevy_math::{Mat4, Vec3, Vec3A, Vec4};
use bevy_math::{Mat4, Vec3, Vec3A, Vec4, Vec4Swizzles};
use bevy_reflect::Reflect;

/// An Axis-Aligned Bounding Box
Expand Down Expand Up @@ -72,12 +72,47 @@ impl Sphere {
}
}

/// A plane defined by a normal and distance value along the normal
/// Any point p is in the plane if n.p = d
/// For planes defining half-spaces such as for frusta, if n.p > d then p is on the positive side of the plane.
/// A plane defined by a unit normal and distance from the origin along the normal
/// Any point p is in the plane if n.p + d = 0
/// For planes defining half-spaces such as for frusta, if n.p + d > 0 then p is on
/// the positive side (inside) of the plane.
#[derive(Clone, Copy, Debug, Default)]
pub struct Plane {
pub normal_d: Vec4,
normal_d: Vec4,
}

impl Plane {
/// Constructs a `Plane` from a 4D vector whose first 3 components
/// are the normal and whose last component is the distance along the normal
/// from the origin.
/// This constructor ensures that the normal is normalized and the distance is
/// scaled accordingly so it represents the signed distance from the origin.
#[inline]
pub fn new(normal_d: Vec4) -> Self {
Self {
normal_d: normal_d * normal_d.xyz().length_recip(),
}
}

/// `Plane` unit normal
#[inline]
pub fn normal(&self) -> Vec3 {
self.normal_d.xyz()
}

/// Signed distance from the origin along the unit normal such that n.p + d = 0 for point p in
/// the `Plane`
#[inline]
pub fn d(&self) -> f32 {
self.normal_d.w
}

/// `Plane` unit normal and signed distance from the origin such that n.p + d = 0 for point p
/// in the `Plane`
#[inline]
pub fn normal_d(&self) -> Vec4 {
self.normal_d
}
}

#[derive(Component, Clone, Copy, Debug, Default, Reflect)]
Expand All @@ -102,23 +137,20 @@ impl Frustum {
let mut planes = [Plane::default(); 6];
for (i, plane) in planes.iter_mut().enumerate().take(5) {
let row = view_projection.row(i / 2);
plane.normal_d = if (i & 1) == 0 && i != 4 {
*plane = Plane::new(if (i & 1) == 0 && i != 4 {
row3 + row
} else {
row3 - row
}
.normalize();
});
}
let far_center = *view_translation - far * *view_backward;
planes[5].normal_d = view_backward
.extend(-view_backward.dot(far_center))
.normalize();
planes[5] = Plane::new(view_backward.extend(-view_backward.dot(far_center)));
Self { planes }
}

pub fn intersects_sphere(&self, sphere: &Sphere) -> bool {
for plane in &self.planes {
if plane.normal_d.dot(sphere.center.extend(1.0)) + sphere.radius <= 0.0 {
if plane.normal_d().dot(sphere.center.extend(1.0)) + sphere.radius <= 0.0 {
return false;
}
}
Expand All @@ -134,9 +166,9 @@ impl Frustum {
];

for plane in &self.planes {
let p_normal = Vec3A::from(plane.normal_d);
let p_normal = Vec3A::from(plane.normal_d());
let relative_radius = aabb.relative_radius(&p_normal, &axes);
if plane.normal_d.dot(aabb_center_world) + relative_radius <= 0.0 {
if plane.normal_d().dot(aabb_center_world) + relative_radius <= 0.0 {
return false;
}
}
Expand All @@ -159,3 +191,160 @@ impl CubemapFrusta {
self.frusta.iter_mut()
}
}

#[cfg(test)]
mod tests {
use super::*;

// A big, offset frustum
fn big_frustum() -> Frustum {
Frustum {
planes: [
Plane::new(Vec4::new(-0.9701, -0.2425, -0.0000, 7.7611)),
Plane::new(Vec4::new(-0.0000, 1.0000, -0.0000, 4.0000)),
Plane::new(Vec4::new(-0.0000, -0.2425, -0.9701, 2.9104)),
Plane::new(Vec4::new(-0.0000, -1.0000, -0.0000, 4.0000)),
Plane::new(Vec4::new(-0.0000, -0.2425, 0.9701, 2.9104)),
Plane::new(Vec4::new(0.9701, -0.2425, -0.0000, -1.9403)),
],
}
}

#[test]
fn intersects_sphere_big_frustum_outside() {
// Sphere outside frustum
let frustum = big_frustum();
let sphere = Sphere {
center: Vec3::new(0.9167, 0.0000, 0.0000),
radius: 0.7500,
};
assert!(!frustum.intersects_sphere(&sphere));
}

#[test]
fn intersects_sphere_big_frustum_intersect() {
// Sphere intersects frustum boundary
let frustum = big_frustum();
let sphere = Sphere {
center: Vec3::new(7.9288, 0.0000, 2.9728),
radius: 2.0000,
};
assert!(frustum.intersects_sphere(&sphere));
}

// A frustum
fn frustum() -> Frustum {
Frustum {
planes: [
Plane::new(Vec4::new(-0.9701, -0.2425, -0.0000, 0.7276)),
Plane::new(Vec4::new(-0.0000, 1.0000, -0.0000, 1.0000)),
Plane::new(Vec4::new(-0.0000, -0.2425, -0.9701, 0.7276)),
Plane::new(Vec4::new(-0.0000, -1.0000, -0.0000, 1.0000)),
Plane::new(Vec4::new(-0.0000, -0.2425, 0.9701, 0.7276)),
Plane::new(Vec4::new(0.9701, -0.2425, -0.0000, 0.7276)),
],
}
}

#[test]
fn intersects_sphere_frustum_surrounding() {
// Sphere surrounds frustum
let frustum = frustum();
let sphere = Sphere {
center: Vec3::new(0.0000, 0.0000, 0.0000),
radius: 3.0000,
};
assert!(frustum.intersects_sphere(&sphere));
}

#[test]
fn intersects_sphere_frustum_contained() {
// Sphere is contained in frustum
let frustum = frustum();
let sphere = Sphere {
center: Vec3::new(0.0000, 0.0000, 0.0000),
radius: 0.7000,
};
assert!(frustum.intersects_sphere(&sphere));
}

#[test]
fn intersects_sphere_frustum_intersects_plane() {
// Sphere intersects a plane
let frustum = frustum();
let sphere = Sphere {
center: Vec3::new(0.0000, 0.0000, 0.9695),
radius: 0.7000,
};
assert!(frustum.intersects_sphere(&sphere));
}

#[test]
fn intersects_sphere_frustum_intersects_2_planes() {
// Sphere intersects 2 planes
let frustum = frustum();
let sphere = Sphere {
center: Vec3::new(1.2037, 0.0000, 0.9695),
radius: 0.7000,
};
assert!(frustum.intersects_sphere(&sphere));
}

#[test]
fn intersects_sphere_frustum_intersects_3_planes() {
// Sphere intersects 3 planes
let frustum = frustum();
let sphere = Sphere {
center: Vec3::new(1.2037, -1.0988, 0.9695),
radius: 0.7000,
};
assert!(frustum.intersects_sphere(&sphere));
}

#[test]
fn intersects_sphere_frustum_dodges_1_plane() {
// Sphere avoids intersecting the frustum by 1 plane
let frustum = frustum();
let sphere = Sphere {
center: Vec3::new(-1.7020, 0.0000, 0.0000),
radius: 0.7000,
};
assert!(!frustum.intersects_sphere(&sphere));
}

// A long frustum.
fn long_frustum() -> Frustum {
Frustum {
planes: [
Plane::new(Vec4::new(-0.9998, -0.0222, -0.0000, -1.9543)),
Plane::new(Vec4::new(-0.0000, 1.0000, -0.0000, 45.1249)),
Plane::new(Vec4::new(-0.0000, -0.0168, -0.9999, 2.2718)),
Plane::new(Vec4::new(-0.0000, -1.0000, -0.0000, 45.1249)),
Plane::new(Vec4::new(-0.0000, -0.0168, 0.9999, 2.2718)),
Plane::new(Vec4::new(0.9998, -0.0222, -0.0000, 7.9528)),
],
}
}

#[test]
fn intersects_sphere_long_frustum_outside() {
// Sphere outside frustum
let frustum = long_frustum();
let sphere = Sphere {
center: Vec3::new(-4.4889, 46.9021, 0.0000),
radius: 0.7500,
};
assert!(!frustum.intersects_sphere(&sphere));
}

#[test]
fn intersects_sphere_long_frustum_intersect() {
// Sphere intersects frustum boundary
let frustum = long_frustum();
let sphere = Sphere {
center: Vec3::new(-4.9957, 0.0000, -0.7396),
radius: 4.4094,
};
assert!(frustum.intersects_sphere(&sphere));
}
}

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