Support rotating Direction3d by Quat (bevyengine#11649)

# Objective

It's often necessary to rotate directions, but it currently has to be
done like this:

```rust
Direction3d::new_unchecked(quat * *direction)
```

It'd be nice if you could rotate `Direction3d` directly:

```rust
quat * direction
```

## Solution

Implement `Mul<Direction3d>` for `Quat` ~~and the other way around.~~
(Glam doesn't impl `Mul<Quat>` or `MulAssign<Quat>` for `Vec3`)

The quaternion must be a unit quaternion to keep the direction
normalized, so there is a `debug_assert!` to be sure. Almost all `Quat`
constructors produce unit quaternions, so there should only be issues if
doing something like `quat + quat` instead of `quat * quat`, using
`Quat::from_xyzw` directly, or when you have significant enough drift
caused by e.g. physics simulation that doesn't normalize rotation. In
general, these would probably cause unexpected results anyway.

I also moved tests around slightly to make `dim2` and `dim3` more
consistent (`dim3` had *two* separate `test` modules for some reason).

In the future, we'll probably want a `Rotation2d` type that would
support the same for `Direction2d`. I considered implementing
`Mul<Mat2>` for `Direction2d`, but that would probably be more
questionable since `Mat2` isn't as clearly associated with rotations as
`Quat` is.

crates/bevy_math/src/primitives/dim2.rs

@@ -785,31 +785,6 @@ mod tests {
     use super::*;
     use approx::assert_relative_eq;
 
-    #[test]
-    fn circle_math() {
-        let circle = Circle { radius: 3.0 };
-        assert_eq!(circle.diameter(), 6.0, "incorrect diameter");
-        assert_eq!(circle.area(), 28.274334, "incorrect area");
-        assert_eq!(circle.perimeter(), 18.849556, "incorrect perimeter");
-    }
-
-    #[test]
-    fn ellipse_math() {
-        let ellipse = Ellipse::new(3.0, 1.0);
-        assert_eq!(ellipse.area(), 9.424778, "incorrect area");
-    }
-
-    #[test]
-    fn triangle_math() {
-        let triangle = Triangle2d::new(
-            Vec2::new(-2.0, -1.0),
-            Vec2::new(1.0, 4.0),
-            Vec2::new(7.0, 0.0),
-        );
-        assert_eq!(triangle.area(), 21.0, "incorrect area");
-        assert_eq!(triangle.perimeter(), 22.097439, "incorrect perimeter");
-    }
-
     #[test]
     fn direction_creation() {
         assert_eq!(Direction2d::new(Vec2::X * 12.5), Ok(Direction2d::X));
@@ -835,6 +810,56 @@ mod tests {
         );
     }
 
+    #[test]
+    fn rectangle_closest_point() {
+        let rectangle = Rectangle::new(2.0, 2.0);
+        assert_eq!(rectangle.closest_point(Vec2::X * 10.0), Vec2::X);
+        assert_eq!(rectangle.closest_point(Vec2::NEG_ONE * 10.0), Vec2::NEG_ONE);
+        assert_eq!(
+            rectangle.closest_point(Vec2::new(0.25, 0.1)),
+            Vec2::new(0.25, 0.1)
+        );
+    }
+
+    #[test]
+    fn circle_closest_point() {
+        let circle = Circle { radius: 1.0 };
+        assert_eq!(circle.closest_point(Vec2::X * 10.0), Vec2::X);
+        assert_eq!(
+            circle.closest_point(Vec2::NEG_ONE * 10.0),
+            Vec2::NEG_ONE.normalize()
+        );
+        assert_eq!(
+            circle.closest_point(Vec2::new(0.25, 0.1)),
+            Vec2::new(0.25, 0.1)
+        );
+    }
+
+    #[test]
+    fn circle_math() {
+        let circle = Circle { radius: 3.0 };
+        assert_eq!(circle.diameter(), 6.0, "incorrect diameter");
+        assert_eq!(circle.area(), 28.274334, "incorrect area");
+        assert_eq!(circle.perimeter(), 18.849556, "incorrect perimeter");
+    }
+
+    #[test]
+    fn ellipse_math() {
+        let ellipse = Ellipse::new(3.0, 1.0);
+        assert_eq!(ellipse.area(), 9.424778, "incorrect area");
+    }
+
+    #[test]
+    fn triangle_math() {
+        let triangle = Triangle2d::new(
+            Vec2::new(-2.0, -1.0),
+            Vec2::new(1.0, 4.0),
+            Vec2::new(7.0, 0.0),
+        );
+        assert_eq!(triangle.area(), 21.0, "incorrect area");
+        assert_eq!(triangle.perimeter(), 22.097439, "incorrect perimeter");
+    }
+
     #[test]
     fn triangle_winding_order() {
         let mut cw_triangle = Triangle2d::new(
@@ -936,29 +961,4 @@ mod tests {
                 < 1e-7,
         );
     }
-
-    #[test]
-    fn rectangle_closest_point() {
-        let rectangle = Rectangle::new(2.0, 2.0);
-        assert_eq!(rectangle.closest_point(Vec2::X * 10.0), Vec2::X);
-        assert_eq!(rectangle.closest_point(Vec2::NEG_ONE * 10.0), Vec2::NEG_ONE);
-        assert_eq!(
-            rectangle.closest_point(Vec2::new(0.25, 0.1)),
-            Vec2::new(0.25, 0.1)
-        );
-    }
-
-    #[test]
-    fn circle_closest_point() {
-        let circle = Circle { radius: 1.0 };
-        assert_eq!(circle.closest_point(Vec2::X * 10.0), Vec2::X);
-        assert_eq!(
-            circle.closest_point(Vec2::NEG_ONE * 10.0),
-            Vec2::NEG_ONE.normalize()
-        );
-        assert_eq!(
-            circle.closest_point(Vec2::new(0.25, 0.1)),
-            Vec2::new(0.25, 0.1)
-        );
-    }
 }

crates/bevy_math/src/primitives/dim3.rs

@@ -1,7 +1,7 @@
 use std::f32::consts::{FRAC_PI_3, PI};
 
 use super::{Circle, InvalidDirectionError, Primitive3d};
-use crate::Vec3;
+use crate::{Quat, Vec3};
 
 /// A normalized vector pointing in a direction in 3D space
 #[derive(Clone, Copy, Debug, PartialEq)]
@@ -85,6 +85,21 @@ impl std::ops::Neg for Direction3d {
     }
 }
 
+impl std::ops::Mul<Direction3d> for Quat {
+    type Output = Direction3d;
+
+    /// Rotates the [`Direction3d`] using a [`Quat`].
+    fn mul(self, direction: Direction3d) -> Self::Output {
+        let rotated = self * *direction;
+
+        // Make sure the result is normalized.
+        // This can fail for non-unit quaternions.
+        debug_assert!(rotated.is_normalized());
+
+        Direction3d::new_unchecked(rotated)
+    }
+}
+
 #[cfg(feature = "approx")]
 impl approx::AbsDiffEq for Direction3d {
     type Epsilon = f32;
@@ -687,6 +702,62 @@ mod tests {
     use super::*;
     use approx::assert_relative_eq;
 
+    #[test]
+    fn direction_creation() {
+        assert_eq!(Direction3d::new(Vec3::X * 12.5), Ok(Direction3d::X));
+        assert_eq!(
+            Direction3d::new(Vec3::new(0.0, 0.0, 0.0)),
+            Err(InvalidDirectionError::Zero)
+        );
+        assert_eq!(
+            Direction3d::new(Vec3::new(f32::INFINITY, 0.0, 0.0)),
+            Err(InvalidDirectionError::Infinite)
+        );
+        assert_eq!(
+            Direction3d::new(Vec3::new(f32::NEG_INFINITY, 0.0, 0.0)),
+            Err(InvalidDirectionError::Infinite)
+        );
+        assert_eq!(
+            Direction3d::new(Vec3::new(f32::NAN, 0.0, 0.0)),
+            Err(InvalidDirectionError::NaN)
+        );
+        assert_eq!(
+            Direction3d::new_and_length(Vec3::X * 6.5),
+            Ok((Direction3d::X, 6.5))
+        );
+
+        // Test rotation
+        assert!(
+            (Quat::from_rotation_z(std::f32::consts::FRAC_PI_2) * Direction3d::X)
+                .abs_diff_eq(Vec3::Y, 10e-6)
+        );
+    }
+
+    #[test]
+    fn cuboid_closest_point() {
+        let cuboid = Cuboid::new(2.0, 2.0, 2.0);
+        assert_eq!(cuboid.closest_point(Vec3::X * 10.0), Vec3::X);
+        assert_eq!(cuboid.closest_point(Vec3::NEG_ONE * 10.0), Vec3::NEG_ONE);
+        assert_eq!(
+            cuboid.closest_point(Vec3::new(0.25, 0.1, 0.3)),
+            Vec3::new(0.25, 0.1, 0.3)
+        );
+    }
+
+    #[test]
+    fn sphere_closest_point() {
+        let sphere = Sphere { radius: 1.0 };
+        assert_eq!(sphere.closest_point(Vec3::X * 10.0), Vec3::X);
+        assert_eq!(
+            sphere.closest_point(Vec3::NEG_ONE * 10.0),
+            Vec3::NEG_ONE.normalize()
+        );
+        assert_eq!(
+            sphere.closest_point(Vec3::new(0.25, 0.1, 0.3)),
+            Vec3::new(0.25, 0.1, 0.3)
+        );
+    }
+
     #[test]
     fn sphere_math() {
         let sphere = Sphere { radius: 4.0 };
@@ -790,58 +861,3 @@ mod tests {
         assert_relative_eq!(torus.volume(), 4.97428, epsilon = 0.00001);
     }
 }
-
-#[cfg(test)]
-mod test {
-    use super::*;
-
-    #[test]
-    fn direction_creation() {
-        assert_eq!(Direction3d::new(Vec3::X * 12.5), Ok(Direction3d::X));
-        assert_eq!(
-            Direction3d::new(Vec3::new(0.0, 0.0, 0.0)),
-            Err(InvalidDirectionError::Zero)
-        );
-        assert_eq!(
-            Direction3d::new(Vec3::new(f32::INFINITY, 0.0, 0.0)),
-            Err(InvalidDirectionError::Infinite)
-        );
-        assert_eq!(
-            Direction3d::new(Vec3::new(f32::NEG_INFINITY, 0.0, 0.0)),
-            Err(InvalidDirectionError::Infinite)
-        );
-        assert_eq!(
-            Direction3d::new(Vec3::new(f32::NAN, 0.0, 0.0)),
-            Err(InvalidDirectionError::NaN)
-        );
-        assert_eq!(
-            Direction3d::new_and_length(Vec3::X * 6.5),
-            Ok((Direction3d::X, 6.5))
-        );
-    }
-
-    #[test]
-    fn cuboid_closest_point() {
-        let cuboid = Cuboid::new(2.0, 2.0, 2.0);
-        assert_eq!(cuboid.closest_point(Vec3::X * 10.0), Vec3::X);
-        assert_eq!(cuboid.closest_point(Vec3::NEG_ONE * 10.0), Vec3::NEG_ONE);
-        assert_eq!(
-            cuboid.closest_point(Vec3::new(0.25, 0.1, 0.3)),
-            Vec3::new(0.25, 0.1, 0.3)
-        );
-    }
-
-    #[test]
-    fn sphere_closest_point() {
-        let sphere = Sphere { radius: 1.0 };
-        assert_eq!(sphere.closest_point(Vec3::X * 10.0), Vec3::X);
-        assert_eq!(
-            sphere.closest_point(Vec3::NEG_ONE * 10.0),
-            Vec3::NEG_ONE.normalize()
-        );
-        assert_eq!(
-            sphere.closest_point(Vec3::new(0.25, 0.1, 0.3)),
-            Vec3::new(0.25, 0.1, 0.3)
-        );
-    }
-}