Add new `Rect::intersects_ray_from_center` method (#5415)

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crates/emath/src/rect.rs

@@ -649,6 +649,8 @@ impl Rect {
     ///
     /// A ray that starts inside the rect will return `true`.
     pub fn intersects_ray(&self, o: Pos2, d: Vec2) -> bool {
+        debug_assert!(d.is_normalized(), "expected normalized direction");
+
         let mut tmin = -f32::INFINITY;
         let mut tmax = f32::INFINITY;
 
@@ -670,6 +672,32 @@ impl Rect {
 
         0.0 <= tmax && tmin <= tmax
     }
+
+    /// Where does a ray from the center intersect the rectangle?
+    ///
+    /// `d` is the direction of the ray and assumed to be normalized.
+    pub fn intersects_ray_from_center(&self, d: Vec2) -> Pos2 {
+        debug_assert!(d.is_normalized(), "expected normalized direction");
+
+        let mut tmin = f32::NEG_INFINITY;
+        let mut tmax = f32::INFINITY;
+
+        for i in 0..2 {
+            let inv_d = 1.0 / -d[i];
+            let mut t0 = (self.min[i] - self.center()[i]) * inv_d;
+            let mut t1 = (self.max[i] - self.center()[i]) * inv_d;
+
+            if inv_d < 0.0 {
+                std::mem::swap(&mut t0, &mut t1);
+            }
+
+            tmin = tmin.max(t0);
+            tmax = tmax.min(t1);
+        }
+
+        let t = tmax.min(tmin);
+        self.center() + t * -d
+    }
 }
 
 impl fmt::Debug for Rect {
@@ -792,4 +820,57 @@ mod tests {
         println!("Leftward ray from right:");
         assert!(rect.intersects_ray(pos2(4.0, 2.0), Vec2::LEFT));
     }
+
+    #[test]
+    fn test_ray_from_center_intersection() {
+        let rect = Rect::from_min_max(pos2(1.0, 1.0), pos2(3.0, 3.0));
+
+        assert_eq!(
+            rect.intersects_ray_from_center(Vec2::RIGHT),
+            pos2(3.0, 2.0),
+            "rightward ray"
+        );
+
+        assert_eq!(
+            rect.intersects_ray_from_center(Vec2::UP),
+            pos2(2.0, 1.0),
+            "upward ray"
+        );
+
+        assert_eq!(
+            rect.intersects_ray_from_center(Vec2::LEFT),
+            pos2(1.0, 2.0),
+            "leftward ray"
+        );
+
+        assert_eq!(
+            rect.intersects_ray_from_center(Vec2::DOWN),
+            pos2(2.0, 3.0),
+            "downward ray"
+        );
+
+        assert_eq!(
+            rect.intersects_ray_from_center((Vec2::LEFT + Vec2::DOWN).normalized()),
+            pos2(1.0, 3.0),
+            "bottom-left corner ray"
+        );
+
+        assert_eq!(
+            rect.intersects_ray_from_center((Vec2::LEFT + Vec2::UP).normalized()),
+            pos2(1.0, 1.0),
+            "top-left corner ray"
+        );
+
+        assert_eq!(
+            rect.intersects_ray_from_center((Vec2::RIGHT + Vec2::DOWN).normalized()),
+            pos2(3.0, 3.0),
+            "bottom-right corner ray"
+        );
+
+        assert_eq!(
+            rect.intersects_ray_from_center((Vec2::RIGHT + Vec2::UP).normalized()),
+            pos2(3.0, 1.0),
+            "top-right corner ray"
+        );
+    }
 }

crates/emath/src/vec2.rs

@@ -176,6 +176,12 @@ impl Vec2 {
         }
     }
 
+    /// Checks if `self` has length `1.0` up to a precision of `1e-6`.
+    #[inline(always)]
+    pub fn is_normalized(self) -> bool {
+        (self.length_sq() - 1.0).abs() < 2e-6
+    }
+
     /// Rotates the vector by 90°, i.e positive X to positive Y
     /// (clockwise in egui coordinates).
     #[inline(always)]
@@ -497,8 +503,10 @@ impl fmt::Display for Vec2 {
     }
 }
 
-#[test]
+#[cfg(test)]
-fn test_vec2() {
+mod test {
+    use super::*;
+
     macro_rules! almost_eq {
         ($left: expr, $right: expr) => {
             let left = $left;
@@ -506,6 +514,9 @@ fn test_vec2() {
             assert!((left - right).abs() < 1e-6, "{} != {}", left, right);
         };
     }
+
+    #[test]
+    fn test_vec2() {
         use std::f32::consts::TAU;
 
         assert_eq!(Vec2::ZERO.angle(), 0.0);
@@ -534,4 +545,27 @@ fn test_vec2() {
         let mut assignment = vec2(2.0, 4.0);
         assignment /= 2.0;
         assert_eq!(assignment, vec2(1.0, 2.0));
+    }
+
+    #[test]
+    fn test_vec2_normalized() {
+        fn generate_spiral(n: usize, start: Vec2, end: Vec2) -> impl Iterator<Item = Vec2> {
+            let angle_step = 2.0 * std::f32::consts::PI / n as f32;
+            let radius_step = (end.length() - start.length()) / n as f32;
+
+            (0..n).map(move |i| {
+                let angle = i as f32 * angle_step;
+                let radius = start.length() + i as f32 * radius_step;
+                let x = radius * angle.cos();
+                let y = radius * angle.sin();
+                vec2(x, y)
+            })
+        }
+
+        for v in generate_spiral(40, Vec2::splat(0.1), Vec2::splat(2.0)) {
+            let vn = v.normalized();
+            almost_eq!(vn.length(), 1.0);
+            assert!(vn.is_normalized());
+        }
+    }
 }