Add new Rect::intersects_ray_from_center method (#5415)

<!--
Please read the "Making a PR" section of
[`CONTRIBUTING.md`](https://github.com/emilk/egui/blob/master/CONTRIBUTING.md)
before opening a Pull Request!

* Keep your PR:s small and focused.
* The PR title is what ends up in the changelog, so make it descriptive!
* If applicable, add a screenshot or gif.
* If it is a non-trivial addition, consider adding a demo for it to
`egui_demo_lib`, or a new example.
* Do NOT open PR:s from your `master` branch, as that makes it hard for
maintainers to test and add commits to your PR.
* Remember to run `cargo fmt` and `cargo clippy`.
* Open the PR as a draft until you have self-reviewed it and run
`./scripts/check.sh`.
* When you have addressed a PR comment, mark it as resolved.

Please be patient! I will review your PR, but my time is limited!
-->
Title.

* [x] I have followed the instructions in the PR template

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"
+        );
+    }
 }