Add to_inner_rectangle, area and perimeter methods to Capsule2d (#15388)

# Objective

Unlike `Capsule3d` which has the `.to_cylinder` method, `Capsule2d`
doesn't have an equivalent `.to_inner_rectangle` method and as shown by
#15191 this is surprisingly easy to get wrong

## Solution

Implemented a `Capsule2d::to_inner_rectangle` method as it is
implemented in the fixed `Capsule2d` shape sampling, and as I was adding
tests I noticed `Capsule2d` didn't implement `Measure2d` so I did this
as well.

## Changelog
### Added
- `Capsule2d::to_inner_rectangle`, `Capsule2d::area` and
`Capsule2d::perimeter`

---------

Co-authored-by: Joona Aalto <[email protected]>
Co-authored-by: James Liu <[email protected]>
Co-authored-by: Alice Cecile <[email protected]>

Author: 4 people

crates/bevy_math/src/primitives/dim2.rs

@@ -1817,6 +1817,28 @@ impl Capsule2d {
             half_length: length / 2.0,
         }
     }
+
+    /// Get the part connecting the semicircular ends of the capsule as a [`Rectangle`]
+    #[inline]
+    pub fn to_inner_rectangle(&self) -> Rectangle {
+        Rectangle::new(self.radius * 2.0, self.half_length * 2.0)
+    }
+}
+
+impl Measured2d for Capsule2d {
+    /// Get the area of the capsule
+    #[inline]
+    fn area(&self) -> f32 {
+        // pi*r^2 + (2r)*l
+        PI * self.radius.squared() + self.to_inner_rectangle().area()
+    }
+
+    /// Get the perimeter of the capsule
+    #[inline]
+    fn perimeter(&self) -> f32 {
+        // 2pi*r + 2l
+        2.0 * PI * self.radius + 4.0 * self.half_length
+    }
 }
 
 #[cfg(test)]
@@ -1892,6 +1914,18 @@ mod tests {
         assert_eq!(circle.perimeter(), 18.849556, "incorrect perimeter");
     }
 
+    #[test]
+    fn capsule_math() {
+        let capsule = Capsule2d::new(2.0, 9.0);
+        assert_eq!(
+            capsule.to_inner_rectangle(),
+            Rectangle::new(4.0, 9.0),
+            "rectangle wasn't created correctly from a capsule"
+        );
+        assert_eq!(capsule.area(), 48.566371, "incorrect area");
+        assert_eq!(capsule.perimeter(), 30.566371, "incorrect perimeter");
+    }
+
     #[test]
     fn annulus_math() {
         let annulus = Annulus::new(2.5, 3.5);

crates/bevy_math/src/sampling/shape_sampling.rs

@@ -450,8 +450,7 @@ impl ShapeSample for Capsule2d {
         if capsule_area > 0.0 {
             // Check if the random point should be inside the rectangle
             if rng.gen_bool((rectangle_area / capsule_area) as f64) {
-                let rectangle = Rectangle::new(self.radius * 2.0, self.half_length * 2.0);
-                rectangle.sample_interior(rng)
+                self.to_inner_rectangle().sample_interior(rng)
             } else {
                 let circle = Circle::new(self.radius);
                 let point = circle.sample_interior(rng);