Implement approx traits for direction types (#11650)

# Objective

`approx` has traits like
[`AbsDiffEq`](https://docs.rs/approx/latest/approx/trait.AbsDiffEq.html),
[`RelativeEq`](https://docs.rs/approx/latest/approx/trait.RelativeEq.html),
and [`UlpsEq`](https://docs.rs/approx/latest/approx/trait.UlpsEq.html).
Glam implements them for its math types when the `approx` feature is
enabled. Bevy's `Direction2d` and `Direction3d` should implement these
too.

## Solution

Implement the traits. See [how Glam implements them for its own math
types](https://github.com/bitshifter/glam-rs/blob/main/src/features/impl_approx.rs).
For the epsilon values, I use the same as `Vec2`/`Vec3` (just
`f32::EPSILON`).

crates/bevy_math/Cargo.toml

@@ -11,6 +11,7 @@ keywords = ["bevy"]
 [dependencies]
 glam = { version = "0.25", features = ["bytemuck"] }
 serde = { version = "1", features = ["derive"], optional = true }
+approx = { version = "0.5", optional = true }
 
 [dev-dependencies]
 approx = "0.5"
@@ -18,7 +19,7 @@ approx = "0.5"
 [features]
 serialize = ["dep:serde", "glam/serde"]
 # Enable approx for glam types to approximate floating point equality comparisons and assertions
-approx = ["glam/approx"]
+approx = ["dep:approx", "glam/approx"]
 # Enable interoperation of glam types with mint-compatible libraries
 mint = ["glam/mint"]
 # Enable libm mathematical functions for glam types to ensure consistent outputs

crates/bevy_math/src/primitives/dim2.rs

@@ -81,6 +81,38 @@ impl std::ops::Neg for Direction2d {
     }
 }
 
+#[cfg(feature = "approx")]
+impl approx::AbsDiffEq for Direction2d {
+    type Epsilon = f32;
+    fn default_epsilon() -> f32 {
+        f32::EPSILON
+    }
+    fn abs_diff_eq(&self, other: &Self, epsilon: f32) -> bool {
+        self.as_ref().abs_diff_eq(other.as_ref(), epsilon)
+    }
+}
+
+#[cfg(feature = "approx")]
+impl approx::RelativeEq for Direction2d {
+    fn default_max_relative() -> f32 {
+        f32::EPSILON
+    }
+    fn relative_eq(&self, other: &Self, epsilon: f32, max_relative: f32) -> bool {
+        self.as_ref()
+            .relative_eq(other.as_ref(), epsilon, max_relative)
+    }
+}
+
+#[cfg(feature = "approx")]
+impl approx::UlpsEq for Direction2d {
+    fn default_max_ulps() -> u32 {
+        4
+    }
+    fn ulps_eq(&self, other: &Self, epsilon: f32, max_ulps: u32) -> bool {
+        self.as_ref().ulps_eq(other.as_ref(), epsilon, max_ulps)
+    }
+}
+
 /// A circle primitive
 #[derive(Clone, Copy, Debug, PartialEq)]
 #[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]

crates/bevy_math/src/primitives/dim3.rs

@@ -85,6 +85,38 @@ impl std::ops::Neg for Direction3d {
     }
 }
 
+#[cfg(feature = "approx")]
+impl approx::AbsDiffEq for Direction3d {
+    type Epsilon = f32;
+    fn default_epsilon() -> f32 {
+        f32::EPSILON
+    }
+    fn abs_diff_eq(&self, other: &Self, epsilon: f32) -> bool {
+        self.as_ref().abs_diff_eq(other.as_ref(), epsilon)
+    }
+}
+
+#[cfg(feature = "approx")]
+impl approx::RelativeEq for Direction3d {
+    fn default_max_relative() -> f32 {
+        f32::EPSILON
+    }
+    fn relative_eq(&self, other: &Self, epsilon: f32, max_relative: f32) -> bool {
+        self.as_ref()
+            .relative_eq(other.as_ref(), epsilon, max_relative)
+    }
+}
+
+#[cfg(feature = "approx")]
+impl approx::UlpsEq for Direction3d {
+    fn default_max_ulps() -> u32 {
+        4
+    }
+    fn ulps_eq(&self, other: &Self, epsilon: f32, max_ulps: u32) -> bool {
+        self.as_ref().ulps_eq(other.as_ref(), epsilon, max_ulps)
+    }
+}
+
 /// A sphere primitive
 #[derive(Clone, Copy, Debug, PartialEq)]
 #[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]