Add triangle_math tests and fix Triangle3d::bounding_sphere bug (#13467)

# Objective

Adopted #12659.

Resolved the merge conflicts on #12659;

* I merged the `triangle_tests` added by this PR and by #13020.
* I moved the [commented out
code](https://github.com/bevyengine/bevy/pull/12659#discussion_r1536640427)
from the original PR into a separate test with `#[should_panic]`.

---------

Co-authored-by: Vitor Falcao <vitorfhc@protonmail.com>
Co-authored-by: Ben Harper <ben@tukom.org>

crates/bevy_math/src/bounding/bounded3d/primitive_impls.rs

@@ -323,29 +323,15 @@ impl Bounded3d for Triangle3d {
     /// The [`Triangle3d`] implements the minimal bounding sphere calculation. For acute triangles, the circumcenter is used as
     /// the center of the sphere. For the others, the bounding sphere is the minimal sphere
     /// that contains the largest side of the triangle.
-    fn bounding_sphere(&self, translation: Vec3, rotation: Quat) -> BoundingSphere {
-        if self.is_degenerate() {
+    fn bounding_sphere(&self, translation: Vec3, _rotation: Quat) -> BoundingSphere {
+        if self.is_degenerate() || self.is_obtuse() {
             let (p1, p2) = self.largest_side();
-            let (segment, _) = Segment3d::from_points(p1, p2);
-            return segment.bounding_sphere(translation, rotation);
-        }
-
-        let [a, b, c] = self.vertices;
-
-        let side_opposite_to_non_acute = if (b - a).dot(c - a) <= 0.0 {
-            Some((b, c))
-        } else if (c - b).dot(a - b) <= 0.0 {
-            Some((c, a))
-        } else if (a - c).dot(b - c) <= 0.0 {
-            Some((a, b))
+            let mid_point = (p1 + p2) / 2.0;
+            let radius = mid_point.distance(p1);
+            BoundingSphere::new(mid_point + translation, radius)
         } else {
-            None
-        };
+            let [a, _, _] = self.vertices;
 
-        if let Some((p1, p2)) = side_opposite_to_non_acute {
-            let (segment, _) = Segment3d::from_points(p1, p2);
-            segment.bounding_sphere(translation, rotation)
-        } else {
             let circumcenter = self.circumcenter();
             let radius = circumcenter.distance(a);
             BoundingSphere::new(circumcenter + translation, radius)
@@ -355,13 +341,14 @@ impl Bounded3d for Triangle3d {
 
 #[cfg(test)]
 mod tests {
+    use crate::bounding::BoundingVolume;
     use glam::{Quat, Vec3, Vec3A};
 
     use crate::{
         bounding::Bounded3d,
         primitives::{
             Capsule3d, Cone, ConicalFrustum, Cuboid, Cylinder, InfinitePlane3d, Line3d, Polyline3d,
-            Segment3d, Sphere, Torus,
+            Segment3d, Sphere, Torus, Triangle3d,
         },
         Dir3,
     };
@@ -607,4 +594,69 @@ mod tests {
         assert_eq!(bounding_sphere.center, translation.into());
         assert_eq!(bounding_sphere.radius(), 1.5);
     }
+
+    #[test]
+    fn triangle3d() {
+        let zero_degenerate_triangle = Triangle3d::new(Vec3::ZERO, Vec3::ZERO, Vec3::ZERO);
+
+        let br = zero_degenerate_triangle.aabb_3d(Vec3::ZERO, Quat::IDENTITY);
+        assert_eq!(
+            br.center(),
+            Vec3::ZERO.into(),
+            "incorrect bounding box center"
+        );
+        assert_eq!(
+            br.half_size(),
+            Vec3::ZERO.into(),
+            "incorrect bounding box half extents"
+        );
+
+        let bs = zero_degenerate_triangle.bounding_sphere(Vec3::ZERO, Quat::IDENTITY);
+        assert_eq!(
+            bs.center,
+            Vec3::ZERO.into(),
+            "incorrect bounding sphere center"
+        );
+        assert_eq!(bs.sphere.radius, 0.0, "incorrect bounding sphere radius");
+
+        let dup_degenerate_triangle = Triangle3d::new(Vec3::ZERO, Vec3::X, Vec3::X);
+        let bs = dup_degenerate_triangle.bounding_sphere(Vec3::ZERO, Quat::IDENTITY);
+        assert_eq!(
+            bs.center,
+            Vec3::new(0.5, 0.0, 0.0).into(),
+            "incorrect bounding sphere center"
+        );
+        assert_eq!(bs.sphere.radius, 0.5, "incorrect bounding sphere radius");
+        let br = dup_degenerate_triangle.aabb_3d(Vec3::ZERO, Quat::IDENTITY);
+        assert_eq!(
+            br.center(),
+            Vec3::new(0.5, 0.0, 0.0).into(),
+            "incorrect bounding box center"
+        );
+        assert_eq!(
+            br.half_size(),
+            Vec3::new(0.5, 0.0, 0.0).into(),
+            "incorrect bounding box half extents"
+        );
+
+        let collinear_degenerate_triangle = Triangle3d::new(Vec3::NEG_X, Vec3::ZERO, Vec3::X);
+        let bs = collinear_degenerate_triangle.bounding_sphere(Vec3::ZERO, Quat::IDENTITY);
+        assert_eq!(
+            bs.center,
+            Vec3::ZERO.into(),
+            "incorrect bounding sphere center"
+        );
+        assert_eq!(bs.sphere.radius, 1.0, "incorrect bounding sphere radius");
+        let br = collinear_degenerate_triangle.aabb_3d(Vec3::ZERO, Quat::IDENTITY);
+        assert_eq!(
+            br.center(),
+            Vec3::ZERO.into(),
+            "incorrect bounding box center"
+        );
+        assert_eq!(
+            br.half_size(),
+            Vec3::new(1.0, 0.0, 0.0).into(),
+            "incorrect bounding box half extents"
+        );
+    }
 }

crates/bevy_math/src/primitives/dim2.rs

@@ -527,6 +527,54 @@ impl Triangle2d {
         (Circle { radius }, center)
     }
 
+    /// Checks if the triangle is degenerate, meaning it has zero area.
+    ///
+    /// A triangle is degenerate if the cross product of the vectors `ab` and `ac` has a length less than `10e-7`.
+    /// This indicates that the three vertices are collinear or nearly collinear.
+    #[inline(always)]
+    pub fn is_degenerate(&self) -> bool {
+        let [a, b, c] = self.vertices;
+        let ab = (b - a).extend(0.);
+        let ac = (c - a).extend(0.);
+        ab.cross(ac).length() < 10e-7
+    }
+
+    /// Checks if the triangle is acute, meaning all angles are less than 90 degrees
+    #[inline(always)]
+    pub fn is_acute(&self) -> bool {
+        let [a, b, c] = self.vertices;
+        let ab = b - a;
+        let bc = c - b;
+        let ca = a - c;
+
+        // a^2 + b^2 < c^2 for an acute triangle
+        let mut side_lengths = [
+            ab.length_squared(),
+            bc.length_squared(),
+            ca.length_squared(),
+        ];
+        side_lengths.sort_by(|a, b| a.partial_cmp(b).unwrap());
+        side_lengths[0] + side_lengths[1] > side_lengths[2]
+    }
+
+    /// Checks if the triangle is obtuse, meaning one angle is greater than 90 degrees
+    #[inline(always)]
+    pub fn is_obtuse(&self) -> bool {
+        let [a, b, c] = self.vertices;
+        let ab = b - a;
+        let bc = c - b;
+        let ca = a - c;
+
+        // a^2 + b^2 > c^2 for an obtuse triangle
+        let mut side_lengths = [
+            ab.length_squared(),
+            bc.length_squared(),
+            ca.length_squared(),
+        ];
+        side_lengths.sort_by(|a, b| a.partial_cmp(b).unwrap());
+        side_lengths[0] + side_lengths[1] < side_lengths[2]
+    }
+
     /// Reverse the [`WindingOrder`] of the triangle
     /// by swapping the first and last vertices.
     #[inline(always)]
@@ -975,6 +1023,20 @@ mod tests {
         );
         assert_eq!(triangle.area(), 21.0, "incorrect area");
         assert_eq!(triangle.perimeter(), 22.097439, "incorrect perimeter");
+
+        let degenerate_triangle =
+            Triangle2d::new(Vec2::new(-1., 0.), Vec2::new(0., 0.), Vec2::new(1., 0.));
+        assert!(degenerate_triangle.is_degenerate());
+
+        let acute_triangle =
+            Triangle2d::new(Vec2::new(-1., 0.), Vec2::new(1., 0.), Vec2::new(0., 5.));
+        let obtuse_triangle =
+            Triangle2d::new(Vec2::new(-1., 0.), Vec2::new(1., 0.), Vec2::new(0., 0.5));
+
+        assert!(acute_triangle.is_acute());
+        assert!(!acute_triangle.is_obtuse());
+        assert!(!obtuse_triangle.is_acute());
+        assert!(obtuse_triangle.is_obtuse());
     }
 
     #[test]

crates/bevy_math/src/primitives/dim3.rs

@@ -780,6 +780,42 @@ impl Triangle3d {
         ab.cross(ac).length() < 10e-7
     }
 
+    /// Checks if the triangle is acute, meaning all angles are less than 90 degrees
+    #[inline(always)]
+    pub fn is_acute(&self) -> bool {
+        let [a, b, c] = self.vertices;
+        let ab = b - a;
+        let bc = c - b;
+        let ca = a - c;
+
+        // a^2 + b^2 < c^2 for an acute triangle
+        let mut side_lengths = [
+            ab.length_squared(),
+            bc.length_squared(),
+            ca.length_squared(),
+        ];
+        side_lengths.sort_by(|a, b| a.partial_cmp(b).unwrap());
+        side_lengths[0] + side_lengths[1] > side_lengths[2]
+    }
+
+    /// Checks if the triangle is obtuse, meaning one angle is greater than 90 degrees
+    #[inline(always)]
+    pub fn is_obtuse(&self) -> bool {
+        let [a, b, c] = self.vertices;
+        let ab = b - a;
+        let bc = c - b;
+        let ca = a - c;
+
+        // a^2 + b^2 > c^2 for an obtuse triangle
+        let mut side_lengths = [
+            ab.length_squared(),
+            bc.length_squared(),
+            ca.length_squared(),
+        ];
+        side_lengths.sort_by(|a, b| a.partial_cmp(b).unwrap());
+        side_lengths[0] + side_lengths[1] < side_lengths[2]
+    }
+
     /// Reverse the triangle by swapping the first and last vertices.
     #[inline(always)]
     pub fn reverse(&mut self) {
@@ -1010,7 +1046,7 @@ mod tests {
     // Reference values were computed by hand and/or with external tools
 
     use super::*;
-    use crate::Quat;
+    use crate::{InvalidDirectionError, Quat};
     use approx::assert_relative_eq;
 
     #[test]
@@ -1210,8 +1246,91 @@ mod tests {
         assert_relative_eq!(Tetrahedron::default().centroid(), Vec3::ZERO);
     }
 
+    #[test]
+    fn extrusion_math() {
+        let circle = Circle::new(0.75);
+        let cylinder = Extrusion::new(circle, 2.5);
+        assert_eq!(cylinder.area(), 15.315264, "incorrect surface area");
+        assert_eq!(cylinder.volume(), 4.417865, "incorrect volume");
+
+        let annulus = crate::primitives::Annulus::new(0.25, 1.375);
+        let tube = Extrusion::new(annulus, 0.333);
+        assert_eq!(tube.area(), 14.886437, "incorrect surface area");
+        assert_eq!(tube.volume(), 1.9124937, "incorrect volume");
+
+        let polygon = crate::primitives::RegularPolygon::new(3.8, 7);
+        let regular_prism = Extrusion::new(polygon, 1.25);
+        assert_eq!(regular_prism.area(), 107.8808, "incorrect surface area");
+        assert_eq!(regular_prism.volume(), 49.392204, "incorrect volume");
+    }
+
     #[test]
     fn triangle_math() {
+        // Default triangle tests
+        let mut default_triangle = Triangle3d::default();
+        let reverse_default_triangle = Triangle3d::new(
+            Vec3::new(0.5, -0.5, 0.0),
+            Vec3::new(-0.5, -0.5, 0.0),
+            Vec3::new(0.0, 0.5, 0.0),
+        );
+        assert_eq!(default_triangle.area(), 0.5, "incorrect area");
+        assert_relative_eq!(
+            default_triangle.perimeter(),
+            1.0 + 2.0 * 1.25_f32.sqrt(),
+            epsilon = 10e-9
+        );
+        assert_eq!(default_triangle.normal(), Ok(Dir3::Z), "incorrect normal");
+        assert!(
+            !default_triangle.is_degenerate(),
+            "incorrect degenerate check"
+        );
+        assert_eq!(
+            default_triangle.centroid(),
+            Vec3::new(0.0, -0.16666667, 0.0),
+            "incorrect centroid"
+        );
+        assert_eq!(
+            default_triangle.largest_side(),
+            (Vec3::new(0.0, 0.5, 0.0), Vec3::new(-0.5, -0.5, 0.0))
+        );
+        default_triangle.reverse();
+        assert_eq!(
+            default_triangle, reverse_default_triangle,
+            "incorrect reverse"
+        );
+        assert_eq!(
+            default_triangle.circumcenter(),
+            Vec3::new(0.0, -0.125, 0.0),
+            "incorrect circumcenter"
+        );
+
+        // Custom triangle tests
+        let right_triangle = Triangle3d::new(Vec3::ZERO, Vec3::X, Vec3::Y);
+        let obtuse_triangle = Triangle3d::new(Vec3::NEG_X, Vec3::X, Vec3::new(0.0, 0.1, 0.0));
+        let acute_triangle = Triangle3d::new(Vec3::ZERO, Vec3::X, Vec3::new(0.5, 5.0, 0.0));
+
+        assert_eq!(
+            right_triangle.circumcenter(),
+            Vec3::new(0.5, 0.5, 0.0),
+            "incorrect circumcenter"
+        );
+        assert_eq!(
+            obtuse_triangle.circumcenter(),
+            Vec3::new(0.0, -4.95, 0.0),
+            "incorrect circumcenter"
+        );
+        assert_eq!(
+            acute_triangle.circumcenter(),
+            Vec3::new(0.5, 2.475, 0.0),
+            "incorrect circumcenter"
+        );
+
+        assert!(acute_triangle.is_acute());
+        assert!(!acute_triangle.is_obtuse());
+        assert!(!obtuse_triangle.is_acute());
+        assert!(obtuse_triangle.is_obtuse());
+
+        // Arbitrary triangle tests
         let [a, b, c] = [Vec3::ZERO, Vec3::new(1., 1., 0.5), Vec3::new(-3., 2.5, 1.)];
         let triangle = Triangle3d::new(a, b, c);
 
@@ -1233,25 +1352,53 @@ mod tests {
             "incorrect normal"
         );
 
-        let degenerate = Triangle3d::new(Vec3::NEG_ONE, Vec3::ZERO, Vec3::ONE);
-        assert!(degenerate.is_degenerate(), "did not find degenerate");
-    }
+        // Degenerate triangle tests
+        let zero_degenerate_triangle = Triangle3d::new(Vec3::ZERO, Vec3::ZERO, Vec3::ZERO);
+        assert!(
+            zero_degenerate_triangle.is_degenerate(),
+            "incorrect degenerate check"
+        );
+        assert_eq!(
+            zero_degenerate_triangle.normal(),
+            Err(InvalidDirectionError::Zero),
+            "incorrect normal"
+        );
+        assert_eq!(
+            zero_degenerate_triangle.largest_side(),
+            (Vec3::ZERO, Vec3::ZERO),
+            "incorrect largest side"
+        );
 
-    #[test]
-    fn extrusion_math() {
-        let circle = Circle::new(0.75);
-        let cylinder = Extrusion::new(circle, 2.5);
-        assert_eq!(cylinder.area(), 15.315264, "incorrect surface area");
-        assert_eq!(cylinder.volume(), 4.417865, "incorrect volume");
+        let dup_degenerate_triangle = Triangle3d::new(Vec3::ZERO, Vec3::X, Vec3::X);
+        assert!(
+            dup_degenerate_triangle.is_degenerate(),
+            "incorrect degenerate check"
+        );
+        assert_eq!(
+            dup_degenerate_triangle.normal(),
+            Err(InvalidDirectionError::Zero),
+            "incorrect normal"
+        );
+        assert_eq!(
+            dup_degenerate_triangle.largest_side(),
+            (Vec3::ZERO, Vec3::X),
+            "incorrect largest side"
+        );
 
-        let annulus = crate::primitives::Annulus::new(0.25, 1.375);
-        let tube = Extrusion::new(annulus, 0.333);
-        assert_eq!(tube.area(), 14.886437, "incorrect surface area");
-        assert_eq!(tube.volume(), 1.9124937, "incorrect volume");
-
-        let polygon = crate::primitives::RegularPolygon::new(3.8, 7);
-        let regular_prism = Extrusion::new(polygon, 1.25);
-        assert_eq!(regular_prism.area(), 107.8808, "incorrect surface area");
-        assert_eq!(regular_prism.volume(), 49.392204, "incorrect volume");
+        let collinear_degenerate_triangle = Triangle3d::new(Vec3::NEG_X, Vec3::ZERO, Vec3::X);
+        assert!(
+            collinear_degenerate_triangle.is_degenerate(),
+            "incorrect degenerate check"
+        );
+        assert_eq!(
+            collinear_degenerate_triangle.normal(),
+            Err(InvalidDirectionError::Zero),
+            "incorrect normal"
+        );
+        assert_eq!(
+            collinear_degenerate_triangle.largest_side(),
+            (Vec3::NEG_X, Vec3::X),
+            "incorrect largest side"
+        );
     }
 }