From 52b8b55c2d0a631d091eee4d4c1fc6e867e766df Mon Sep 17 00:00:00 2001
From: Lynn <62256001+lynn-lumen@users.noreply.github.com>
Date: Sun, 3 Nov 2024 17:12:31 +0100
Subject: [PATCH] Implement `Measured2d` for `Arc2d`-based primitives. (#16213)

# Objective

- `CircularSegment` and `CircularSector` are well defined 2D shapes with
both an area and a perimeter.

# Solution

- This PR implements `perimeter` for both and moves the existsing `area`
functions into the `Measured2d` implementations.

## Testing

- The `arc_tests` have been extended to also check for perimeters.
---
 crates/bevy_math/src/primitives/dim2.rs | 54 +++++++++++++++++++------
 1 file changed, 42 insertions(+), 12 deletions(-)

diff --git a/crates/bevy_math/src/primitives/dim2.rs b/crates/bevy_math/src/primitives/dim2.rs
index d734a1879d..62d1633622 100644
--- a/crates/bevy_math/src/primitives/dim2.rs
+++ b/crates/bevy_math/src/primitives/dim2.rs
@@ -292,6 +292,22 @@ impl Default for CircularSector {
     }
 }
 
+impl Measured2d for CircularSector {
+    #[inline(always)]
+    fn area(&self) -> f32 {
+        self.arc.radius.squared() * self.arc.half_angle
+    }
+
+    #[inline(always)]
+    fn perimeter(&self) -> f32 {
+        if self.half_angle() >= PI {
+            self.arc.radius * 2.0 * PI
+        } else {
+            2.0 * self.radius() + self.arc_length()
+        }
+    }
+}
+
 impl CircularSector {
     /// Create a new [`CircularSector`] from a `radius` and an `angle`
     #[inline(always)]
@@ -382,12 +398,6 @@ impl CircularSector {
     pub fn sagitta(&self) -> f32 {
         self.arc.sagitta()
     }
-
-    /// Returns the area of this sector
-    #[inline(always)]
-    pub fn area(&self) -> f32 {
-        self.arc.radius.squared() * self.arc.half_angle
-    }
 }
 
 /// A primitive representing a circular segment:
@@ -425,6 +435,17 @@ impl Default for CircularSegment {
     }
 }
 
+impl Measured2d for CircularSegment {
+    #[inline(always)]
+    fn area(&self) -> f32 {
+        0.5 * self.arc.radius.squared() * (self.arc.angle() - ops::sin(self.arc.angle()))
+    }
+
+    #[inline(always)]
+    fn perimeter(&self) -> f32 {
+        self.chord_length() + self.arc_length()
+    }
+}
 impl CircularSegment {
     /// Create a new [`CircularSegment`] from a `radius`, and an `angle`
     #[inline(always)]
@@ -515,17 +536,12 @@ impl CircularSegment {
     pub fn sagitta(&self) -> f32 {
         self.arc.sagitta()
     }
-
-    /// Returns the area of this segment
-    #[inline(always)]
-    pub fn area(&self) -> f32 {
-        0.5 * self.arc.radius.squared() * (self.arc.angle() - ops::sin(self.arc.angle()))
-    }
 }
 
 #[cfg(test)]
 mod arc_tests {
     use core::f32::consts::FRAC_PI_4;
+    use core::f32::consts::SQRT_2;
 
     use approx::assert_abs_diff_eq;
 
@@ -548,7 +564,9 @@ mod arc_tests {
         is_minor: bool,
         is_major: bool,
         sector_area: f32,
+        sector_perimeter: f32,
         segment_area: f32,
+        segment_perimeter: f32,
     }
 
     impl ArcTestCase {
@@ -581,6 +599,7 @@ mod arc_tests {
             assert_abs_diff_eq!(self.apothem, sector.apothem());
             assert_abs_diff_eq!(self.sagitta, sector.sagitta());
             assert_abs_diff_eq!(self.sector_area, sector.area());
+            assert_abs_diff_eq!(self.sector_perimeter, sector.perimeter());
         }
 
         fn check_segment(&self, segment: CircularSegment) {
@@ -593,6 +612,7 @@ mod arc_tests {
             assert_abs_diff_eq!(self.apothem, segment.apothem());
             assert_abs_diff_eq!(self.sagitta, segment.sagitta());
             assert_abs_diff_eq!(self.segment_area, segment.area());
+            assert_abs_diff_eq!(self.segment_perimeter, segment.perimeter());
         }
     }
 
@@ -615,7 +635,9 @@ mod arc_tests {
             is_minor: true,
             is_major: false,
             sector_area: 0.0,
+            sector_perimeter: 2.0,
             segment_area: 0.0,
+            segment_perimeter: 0.0,
         };
 
         tests.check_arc(Arc2d::new(1.0, 0.0));
@@ -642,7 +664,9 @@ mod arc_tests {
             is_minor: true,
             is_major: false,
             sector_area: 0.0,
+            sector_perimeter: 0.0,
             segment_area: 0.0,
+            segment_perimeter: 0.0,
         };
 
         tests.check_arc(Arc2d::new(0.0, FRAC_PI_4));
@@ -670,7 +694,9 @@ mod arc_tests {
             is_minor: true,
             is_major: false,
             sector_area: FRAC_PI_4,
+            sector_perimeter: FRAC_PI_2 + 2.0,
             segment_area: FRAC_PI_4 - 0.5,
+            segment_perimeter: FRAC_PI_2 + SQRT_2,
         };
 
         tests.check_arc(Arc2d::from_turns(1.0, 0.25));
@@ -697,7 +723,9 @@ mod arc_tests {
             is_minor: true,
             is_major: true,
             sector_area: FRAC_PI_2,
+            sector_perimeter: PI + 2.0,
             segment_area: FRAC_PI_2,
+            segment_perimeter: PI + 2.0,
         };
 
         tests.check_arc(Arc2d::from_radians(1.0, PI));
@@ -724,7 +752,9 @@ mod arc_tests {
             is_minor: false,
             is_major: true,
             sector_area: PI,
+            sector_perimeter: 2.0 * PI,
             segment_area: PI,
+            segment_perimeter: 2.0 * PI,
         };
 
         tests.check_arc(Arc2d::from_degrees(1.0, 360.0));