Add egui::math::Rot2 rotation helper

CHANGELOG.md

@@ -18,6 +18,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 * Mouse-over explanation to duplicate ID warning.
 * You can now easily constrain Egui to a portion of the screen using `RawInput::screen_rect`.
 * You can now control the minimum and maixumum number of decimals to show in a `Slider` or `DragValue`.
+* Add `egui::math::Rot2`: rotation helper.
 
 ### Changed 🔧
 

egui/src/containers/collapsing_header.rs

@@ -109,11 +109,9 @@ pub fn paint_icon(ui: &mut Ui, openness: f32, response: &Response) {
     // Draw a pointy triangle arrow:
     let rect = Rect::from_center_size(rect.center(), vec2(rect.width(), rect.height()) * 0.75);
     let mut points = vec![rect.left_top(), rect.right_top(), rect.center_bottom()];
-    let rotation = Vec2::angled(remap(openness, 0.0..=1.0, -TAU / 4.0..=0.0));
+    let rotation = Rot2::from_angle(remap(openness, 0.0..=1.0, -TAU / 4.0..=0.0));
     for p in &mut points {
-        let v = *p - rect.center();
+        *p = rect.center() + rotation * (*p - rect.center());
-        let v = rotation.rotate_other(v);
-        *p = rect.center() + v;
     }
 
     ui.painter().add(PaintCmd::closed_line(points, stroke));

egui/src/demos/fractal_clock.rs

@@ -141,8 +141,8 @@ impl FractalClock {
         ];
 
         let hand_rotors = [
-            hands[0].length * Vec2::angled(hand_rotations[0]),
+            hands[0].length * Rot2::from_angle(hand_rotations[0]),
-            hands[1].length * Vec2::angled(hand_rotations[1]),
+            hands[1].length * Rot2::from_angle(hand_rotations[1]),
         ];
 
         #[derive(Clone, Copy)]
@@ -179,9 +179,9 @@ impl FractalClock {
 
             let luminance_u8 = (255.0 * luminance).round() as u8;
 
-            for rotor in &hand_rotors {
+            for &rotor in &hand_rotors {
                 for a in &nodes {
-                    let new_dir = rotor.rotate_other(a.dir);
+                    let new_dir = rotor * a.dir;
                     let b = Node {
                         pos: a.pos + new_dir,
                         dir: new_dir,

egui/src/math/mod.rs

@@ -6,10 +6,11 @@ use std::ops::{Add, Div, Mul, RangeInclusive, Sub};
 
 mod pos2;
 mod rect;
+mod rot2;
 pub mod smart_aim;
 mod vec2;
 
-pub use {pos2::*, rect::*, vec2::*};
+pub use {pos2::*, rect::*, rot2::*, vec2::*};
 
 // ----------------------------------------------------------------------------
 

egui/src/math/rot2.rs

@@ -0,0 +1,183 @@
+use super::Vec2;
+
+// {s,c} represents the rotation matrix:
+//
+// | c -s |
+// | s  c |
+//
+// `vec2(c,s)` represents where the X axis will end up after rotation.
+//
+/// Represents a rotation in the 2D plane.
+/// A rotation of 90° rotates the X axis to the Y axis.
+/// Normally a `Rot2` is normalized (unit-length).
+/// If not, it will also scale vectors.
+#[derive(Clone, Copy, PartialEq)]
+pub struct Rot2 {
+    /// angle.sin()
+    s: f32,
+    /// angle.cos()
+    c: f32,
+}
+
+/// Identity rotation
+impl Default for Rot2 {
+    /// Identity rotation
+    fn default() -> Self {
+        Self { s: 0.0, c: 1.0 }
+    }
+}
+
+impl Rot2 {
+    pub fn identity() -> Self {
+        Self { s: 0.0, c: 1.0 }
+    }
+
+    /// A `TAU / 4.0` rotation means rotating the X axis to the Y axis.
+    pub fn from_angle(angle: f32) -> Self {
+        let (s, c) = angle.sin_cos();
+        Self { s, c }
+    }
+
+    pub fn angle(self) -> f32 {
+        self.s.atan2(self.c)
+    }
+
+    /// The factor by which vectors will be scaled.
+    pub fn length(self) -> f32 {
+        self.c.hypot(self.s)
+    }
+
+    pub fn length_squared(self) -> f32 {
+        self.c.powi(2) + self.s.powi(2)
+    }
+
+    pub fn is_finite(self) -> bool {
+        self.c.is_finite() && self.s.is_finite()
+    }
+
+    #[must_use]
+    pub fn inverse(self) -> Rot2 {
+        Self {
+            s: -self.s,
+            c: self.c,
+        } / self.length_squared()
+    }
+
+    #[must_use]
+    pub fn normalized(self) -> Self {
+        let l = self.length();
+        let ret = Self {
+            c: self.c / l,
+            s: self.s / l,
+        };
+        debug_assert!(ret.is_finite());
+        ret
+    }
+}
+
+impl std::fmt::Debug for Rot2 {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(
+            f,
+            "Rot2 {{ angle: {:.1}°, length: {} }}",
+            self.angle().to_degrees(),
+            self.length()
+        )
+    }
+}
+
+impl std::ops::Mul<Rot2> for Rot2 {
+    type Output = Rot2;
+    fn mul(self, r: Rot2) -> Rot2 {
+        /*
+        |lc -ls| * |rc -rs|
+        |ls  lc|   |rs  rc|
+        */
+        Rot2 {
+            c: self.c * r.c - self.s * r.s,
+            s: self.s * r.c + self.c * r.s,
+        }
+    }
+}
+
+impl std::ops::Mul<Vec2> for Rot2 {
+    type Output = Vec2;
+    fn mul(self, v: Vec2) -> Vec2 {
+        Vec2 {
+            x: self.c * v.x - self.s * v.y,
+            y: self.s * v.x + self.c * v.y,
+        }
+    }
+}
+
+impl std::ops::Mul<Rot2> for f32 {
+    type Output = Rot2;
+    fn mul(self, r: Rot2) -> Rot2 {
+        Rot2 {
+            c: self * r.c,
+            s: self * r.s,
+        }
+    }
+}
+
+impl std::ops::Mul<f32> for Rot2 {
+    type Output = Rot2;
+    fn mul(self, r: f32) -> Rot2 {
+        Rot2 {
+            c: self.c * r,
+            s: self.s * r,
+        }
+    }
+}
+
+impl std::ops::Div<f32> for Rot2 {
+    type Output = Rot2;
+    fn div(self, r: f32) -> Rot2 {
+        Rot2 {
+            c: self.c / r,
+            s: self.s / r,
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::Rot2;
+    use crate::vec2;
+
+    #[test]
+    fn test_rotation2() {
+        {
+            let angle = std::f32::consts::TAU / 6.0;
+            let rot = Rot2::from_angle(angle);
+            assert!((rot.angle() - angle).abs() < 1e-5);
+            assert!((rot * rot.inverse()).angle().abs() < 1e-5);
+            assert!((rot.inverse() * rot).angle().abs() < 1e-5);
+        }
+
+        {
+            let angle = std::f32::consts::TAU / 4.0;
+            let rot = Rot2::from_angle(angle);
+            assert!(((rot * vec2(1.0, 0.0)) - vec2(0.0, 1.0)).length() < 1e-5);
+        }
+
+        {
+            // Test rotation and scaling
+            let angle = std::f32::consts::TAU / 4.0;
+            let rot = 3.0 * Rot2::from_angle(angle);
+            let rotated = rot * vec2(1.0, 0.0);
+            let expected = vec2(0.0, 3.0);
+            assert!(
+                (rotated - expected).length() < 1e-5,
+                "Expected {:?} to equal {:?}. rot: {:?}",
+                rotated,
+                expected,
+                rot,
+            );
+
+            let undone = rot.inverse() * rot;
+            assert!(undone.angle().abs() < 1e-5);
+            assert!((undone.length() - 1.0).abs() < 1e-5,);
+        }
+    }
+}

egui/src/math/vec2.rs

@@ -60,6 +60,8 @@ impl Vec2 {
         }
     }
 
+    /// Rotates the vector by 90°, i.e positive X to positive Y
+    /// (clockwise in Egui coordinates).
     #[inline(always)]
     pub fn rot90(self) -> Self {
         vec2(self.y, -self.x)
@@ -85,16 +87,6 @@ impl Vec2 {
         vec2(angle.cos(), angle.sin())
     }
 
-    /// Use this vector as a rotor, rotating something else.
-    /// Example: `Vec2::angled(angle).rotate_other(some_vec)`
-    #[must_use]
-    pub fn rotate_other(self, v: Vec2) -> Self {
-        Self {
-            x: v.x * self.x + v.y * -self.y,
-            y: v.x * self.y + v.y * self.x,
-        }
-    }
-
     #[must_use]
     pub fn floor(self) -> Self {
         vec2(self.x.floor(), self.y.floor())

egui/src/painter.rs

@@ -159,22 +159,10 @@ impl Painter {
         let tip_length = full_length / 3.0;
         let dir = dir.normalized();
         let tip = origin + dir * full_length;
-        let angle = TAU / 10.0;
+        let rot = Rot2::from_angle(TAU / 10.0);
         self.line_segment([origin, tip], stroke);
-        self.line_segment(
+        self.line_segment([tip, tip - tip_length * (rot * dir)], stroke);
-            [
+        self.line_segment([tip, tip - tip_length * (rot.inverse() * dir)], stroke);
-                tip,
-                tip - tip_length * Vec2::angled(angle).rotate_other(dir),
-            ],
-            stroke,
-        );
-        self.line_segment(
-            [
-                tip,
-                tip - tip_length * Vec2::angled(-angle).rotate_other(dir),
-            ],
-            stroke,
-        );
     }
 }