Add compass direction constants to Dir2 (#13636)

# Objective

When working on `leafwing-input-manager` and in my games, I've found
these compass directions to be both clear and useful when attempting to
describe angles in 2 dimensions.

This was directly used when mapping gamepad inputs into 4-way movement
as a virtual dpad, and I expect other uses are common in games.

## Solution

- Add constants corresponding to the 4 cardinal and 4 semi-cardinal
directions.

## Testing

- I've validated the quadrants of each of the directions through
self-review.

---------

Co-authored-by: Alice Cecile <alice.i.cecil@gmail.com>

crates/bevy_math/src/direction.rs

@@ -3,6 +3,8 @@ use crate::{
     Quat, Rotation2d, Vec2, Vec3, Vec3A,
 };
 
+use core::f32::consts::FRAC_1_SQRT_2;
+
 #[cfg(feature = "bevy_reflect")]
 use bevy_reflect::Reflect;
 #[cfg(all(feature = "serialize", feature = "bevy_reflect"))]
@@ -105,6 +107,23 @@ impl Dir2 {
     /// The directional axes.
     pub const AXES: [Self; 2] = [Self::X, Self::Y];
 
+    /// The "north" direction, equivalent to [`Dir2::Y`].
+    pub const NORTH: Self = Self(Vec2::Y);
+    /// The "south" direction, equivalent to [`Dir2::NEG_Y`].
+    pub const SOUTH: Self = Self(Vec2::NEG_Y);
+    /// The "east" direction, equivalent to [`Dir2::X`].
+    pub const EAST: Self = Self(Vec2::X);
+    /// The "west" direction, equivalent to [`Dir2::NEG_X`].
+    pub const WEST: Self = Self(Vec2::NEG_X);
+    /// The "north-east" direction, between [`Dir2::NORTH`] and [`Dir2::EAST`].
+    pub const NORTH_EAST: Self = Self(Vec2::new(FRAC_1_SQRT_2, FRAC_1_SQRT_2));
+    /// The "north-west" direction, between [`Dir2::NORTH`] and [`Dir2::WEST`].
+    pub const NORTH_WEST: Self = Self(Vec2::new(-FRAC_1_SQRT_2, FRAC_1_SQRT_2));
+    /// The "south-east" direction, between [`Dir2::SOUTH`] and [`Dir2::EAST`].
+    pub const SOUTH_EAST: Self = Self(Vec2::new(FRAC_1_SQRT_2, -FRAC_1_SQRT_2));
+    /// The "south-west" direction, between [`Dir2::SOUTH`] and [`Dir2::WEST`].
+    pub const SOUTH_WEST: Self = Self(Vec2::new(-FRAC_1_SQRT_2, -FRAC_1_SQRT_2));
+
     /// Create a direction from a finite, nonzero [`Vec2`], normalizing it.
     ///
     /// Returns [`Err(InvalidDirectionError)`](InvalidDirectionError) if the length

crates/bevy_math/src/rotation2d.rs

@@ -81,8 +81,8 @@ impl Rotation2d {
 
     /// A counterclockwise rotation of π/4 radians.
     pub const FRAC_PI_4: Self = Self {
-        cos: std::f32::consts::FRAC_1_SQRT_2,
-        sin: std::f32::consts::FRAC_1_SQRT_2,
+        cos: core::f32::consts::FRAC_1_SQRT_2,
+        sin: core::f32::consts::FRAC_1_SQRT_2,
     };
 
     /// A counterclockwise rotation of π/6 radians.