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[Merged by Bors] - Fixed the frustum-sphere collision and added tests #4035

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[Merged by Bors] - Fixed the frustum-sphere collision and added tests #4035

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16bb5b7
Fixed the frustum-sphere collision and added tests
hayashi-stl Feb 25, 2022
881db86
Formatting
hayashi-stl Feb 25, 2022
ce787f6
Added constructor that normalizes normal
hayashi-stl Feb 25, 2022
3507530
Applied suggestions
hayashi-stl Mar 3, 2022
a46ea9f
Inlined constructor of Plane
hayashi-stl Mar 7, 2022
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224 changes: 222 additions & 2 deletions crates/bevy_render/src/primitives/mod.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -74,7 +74,7 @@ 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
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Suggested change
/// Any point p is in the plane if n.p = d
/// 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 then p is on the positive side of the plane.
/// For planes defining half-spaces such as for frusta, if n.p > d then p is on the positive side (inside) of the plane.
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Suggested change
/// For planes defining half-spaces such as for frusta, if n.p > d then p is on the positive side (inside) of the plane.
/// 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,
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Suggested change
pub normal_d: Vec4,
normal_d: Vec4,

And then update other code that uses Plane to use Plane::new for construction.

Expand Down Expand Up @@ -118,7 +118,12 @@ impl Frustum {

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 {
// The formula `normal . center + d + radius <= 0` relies on `normal` being normalized,
// which is not necessarily the case.
let factor = (plane.normal_d.truncate().length_squared()
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Please split up this statement. It's hard to read in it's current state.

/ plane.normal_d.length_squared())
.sqrt();
if plane.normal_d.dot(sphere.center.extend(1.0)) + sphere.radius * factor <= 0.0 {
return false;
}
}
Expand Down Expand Up @@ -159,3 +164,218 @@ impl CubemapFrusta {
self.frusta.iter_mut()
}
}

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

fn big_frustum() -> Frustum {
Frustum {
planes: [
Plane {
normal_d: Vec4::new(-0.2425, -0.0606, -0.0000, 1.9403).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, 0.2500, -0.0000, 1.0000).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.0606, -0.2425, 0.7276).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.2500, -0.0000, 1.0000).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.0606, 0.2425, 0.7276).normalize(),
},
Plane {
normal_d: Vec4::new(0.2425, -0.0606, -0.0000, -0.4851).normalize(),
},
],
}
}

#[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 {
normal_d: Vec4::new(-0.9701, -0.2425, -0.0000, 0.7276).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, 1.0000, -0.0000, 1.0000).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.2425, -0.9701, 0.7276).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -1.0000, -0.0000, 1.0000).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.2425, 0.9701, 0.7276).normalize(),
},
Plane {
normal_d: Vec4::new(0.9701, -0.2425, -0.0000, 0.7276).normalize(),
},
],
}
}

#[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));
}

// These tests are not handled, and it may not be worth handling them.
//#[test]
//fn intersects_sphere_frustum_dodges_2_planes() {
// // Sphere avoids intersecting the frustum by a combination of 2 planes
// let frustum = frustum();
// let sphere = Sphere {
// center: Vec3::new(-1.6048, -1.5564, 0.0000),
// radius: 0.7000,
// };
// assert!(!frustum.intersects_sphere(&sphere));
//}

//#[test]
//fn intersects_sphere_frustum_dodges_3_planes() {
// // Sphere avoids intersecting the frustum by a combination of 3 planes
// let frustum = frustum();
// let sphere = Sphere {
// center: Vec3::new(-1.3059, -1.5564, -1.4264),
// radius: 0.7000,
// };
// assert!(!frustum.intersects_sphere(&sphere));
//}
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// A long frustum.
fn long_frustum() -> Frustum {
Frustum {
planes: [
Plane {
normal_d: Vec4::new(-0.2425, -0.0054, -0.0000, -0.4741).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, 0.0222, -0.0000, 1.0000).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.0054, -0.3202, 0.7276).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.0222, -0.0000, 1.0000).normalize(),
},
Plane {
normal_d: Vec4::new(-0.0000, -0.0054, 0.3202, 0.7276).normalize(),
},
Plane {
normal_d: Vec4::new(0.2425, -0.0054, -0.0000, 1.9293).normalize(),
},
],
}
}

#[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));
}
}