Precompute rounded vertices (#1547)

Co-authored-by: Daniel Buch Hansen <boogiewasthere@gmail.com>

epaint/CHANGELOG.md

@@ -21,6 +21,7 @@ All notable changes to the epaint crate will be documented in this file.
 * MSRV (Minimum Supported Rust Version) is now `1.60.0` ([#1467](https://github.com/emilk/egui/pull/1467)).
 * Renamed the feature `convert_bytemuck` to `bytemuck` ([#1467](https://github.com/emilk/egui/pull/1467)).
 * Renamed the feature `serialize` to `serde` ([#1467](https://github.com/emilk/egui/pull/1467)).
+* Optimize tessellation of circles and boxes with rounded corners ([#1547](https://github.com/emilk/egui/pull/1547)).
 
 
 ## 0.17.0 - 2022-02-22

epaint/src/tessellator.rs

@@ -7,7 +7,293 @@
 
 use crate::*;
 use emath::*;
-use std::f32::consts::TAU;
+
+// ----------------------------------------------------------------------------
+
+#[allow(clippy::approx_constant)]
+mod precomputed_vertices {
+    /*
+    fn main() {
+        let n = 64;
+        println!("pub const CIRCLE_{}: [Vec2; {}] = [", n, n+1);
+        for i in 0..=n {
+            let a = std::f64::consts::TAU * i as f64 / n as f64;
+            println!("    vec2({:.06}, {:.06}),", a.cos(), a.sin());
+        }
+        println!("];")
+    }
+    */
+
+    use emath::{vec2, Vec2};
+
+    pub const CIRCLE_8: [Vec2; 9] = [
+        vec2(1.000000, 0.000000),
+        vec2(0.707107, 0.707107),
+        vec2(0.000000, 1.000000),
+        vec2(-0.707107, 0.707107),
+        vec2(-1.000000, 0.000000),
+        vec2(-0.707107, -0.707107),
+        vec2(0.000000, -1.000000),
+        vec2(0.707107, -0.707107),
+        vec2(1.000000, 0.000000),
+    ];
+
+    pub const CIRCLE_16: [Vec2; 17] = [
+        vec2(1.000000, 0.000000),
+        vec2(0.923880, 0.382683),
+        vec2(0.707107, 0.707107),
+        vec2(0.382683, 0.923880),
+        vec2(0.000000, 1.000000),
+        vec2(-0.382684, 0.923880),
+        vec2(-0.707107, 0.707107),
+        vec2(-0.923880, 0.382683),
+        vec2(-1.000000, 0.000000),
+        vec2(-0.923880, -0.382683),
+        vec2(-0.707107, -0.707107),
+        vec2(-0.382684, -0.923880),
+        vec2(0.000000, -1.000000),
+        vec2(0.382684, -0.923879),
+        vec2(0.707107, -0.707107),
+        vec2(0.923880, -0.382683),
+        vec2(1.000000, 0.000000),
+    ];
+
+    pub const CIRCLE_32: [Vec2; 33] = [
+        vec2(1.000000, 0.000000),
+        vec2(0.980785, 0.195090),
+        vec2(0.923880, 0.382683),
+        vec2(0.831470, 0.555570),
+        vec2(0.707107, 0.707107),
+        vec2(0.555570, 0.831470),
+        vec2(0.382683, 0.923880),
+        vec2(0.195090, 0.980785),
+        vec2(0.000000, 1.000000),
+        vec2(-0.195090, 0.980785),
+        vec2(-0.382683, 0.923880),
+        vec2(-0.555570, 0.831470),
+        vec2(-0.707107, 0.707107),
+        vec2(-0.831470, 0.555570),
+        vec2(-0.923880, 0.382683),
+        vec2(-0.980785, 0.195090),
+        vec2(-1.000000, 0.000000),
+        vec2(-0.980785, -0.195090),
+        vec2(-0.923880, -0.382683),
+        vec2(-0.831470, -0.555570),
+        vec2(-0.707107, -0.707107),
+        vec2(-0.555570, -0.831470),
+        vec2(-0.382683, -0.923880),
+        vec2(-0.195090, -0.980785),
+        vec2(-0.000000, -1.000000),
+        vec2(0.195090, -0.980785),
+        vec2(0.382683, -0.923880),
+        vec2(0.555570, -0.831470),
+        vec2(0.707107, -0.707107),
+        vec2(0.831470, -0.555570),
+        vec2(0.923880, -0.382683),
+        vec2(0.980785, -0.195090),
+        vec2(1.000000, -0.000000),
+    ];
+
+    pub const CIRCLE_64: [Vec2; 65] = [
+        vec2(1.000000, 0.000000),
+        vec2(0.995185, 0.098017),
+        vec2(0.980785, 0.195090),
+        vec2(0.956940, 0.290285),
+        vec2(0.923880, 0.382683),
+        vec2(0.881921, 0.471397),
+        vec2(0.831470, 0.555570),
+        vec2(0.773010, 0.634393),
+        vec2(0.707107, 0.707107),
+        vec2(0.634393, 0.773010),
+        vec2(0.555570, 0.831470),
+        vec2(0.471397, 0.881921),
+        vec2(0.382683, 0.923880),
+        vec2(0.290285, 0.956940),
+        vec2(0.195090, 0.980785),
+        vec2(0.098017, 0.995185),
+        vec2(0.000000, 1.000000),
+        vec2(-0.098017, 0.995185),
+        vec2(-0.195090, 0.980785),
+        vec2(-0.290285, 0.956940),
+        vec2(-0.382683, 0.923880),
+        vec2(-0.471397, 0.881921),
+        vec2(-0.555570, 0.831470),
+        vec2(-0.634393, 0.773010),
+        vec2(-0.707107, 0.707107),
+        vec2(-0.773010, 0.634393),
+        vec2(-0.831470, 0.555570),
+        vec2(-0.881921, 0.471397),
+        vec2(-0.923880, 0.382683),
+        vec2(-0.956940, 0.290285),
+        vec2(-0.980785, 0.195090),
+        vec2(-0.995185, 0.098017),
+        vec2(-1.000000, 0.000000),
+        vec2(-0.995185, -0.098017),
+        vec2(-0.980785, -0.195090),
+        vec2(-0.956940, -0.290285),
+        vec2(-0.923880, -0.382683),
+        vec2(-0.881921, -0.471397),
+        vec2(-0.831470, -0.555570),
+        vec2(-0.773010, -0.634393),
+        vec2(-0.707107, -0.707107),
+        vec2(-0.634393, -0.773010),
+        vec2(-0.555570, -0.831470),
+        vec2(-0.471397, -0.881921),
+        vec2(-0.382683, -0.923880),
+        vec2(-0.290285, -0.956940),
+        vec2(-0.195090, -0.980785),
+        vec2(-0.098017, -0.995185),
+        vec2(-0.000000, -1.000000),
+        vec2(0.098017, -0.995185),
+        vec2(0.195090, -0.980785),
+        vec2(0.290285, -0.956940),
+        vec2(0.382683, -0.923880),
+        vec2(0.471397, -0.881921),
+        vec2(0.555570, -0.831470),
+        vec2(0.634393, -0.773010),
+        vec2(0.707107, -0.707107),
+        vec2(0.773010, -0.634393),
+        vec2(0.831470, -0.555570),
+        vec2(0.881921, -0.471397),
+        vec2(0.923880, -0.382683),
+        vec2(0.956940, -0.290285),
+        vec2(0.980785, -0.195090),
+        vec2(0.995185, -0.098017),
+        vec2(1.000000, -0.000000),
+    ];
+
+    pub const CIRCLE_128: [Vec2; 129] = [
+        vec2(1.000000, 0.000000),
+        vec2(0.998795, 0.049068),
+        vec2(0.995185, 0.098017),
+        vec2(0.989177, 0.146730),
+        vec2(0.980785, 0.195090),
+        vec2(0.970031, 0.242980),
+        vec2(0.956940, 0.290285),
+        vec2(0.941544, 0.336890),
+        vec2(0.923880, 0.382683),
+        vec2(0.903989, 0.427555),
+        vec2(0.881921, 0.471397),
+        vec2(0.857729, 0.514103),
+        vec2(0.831470, 0.555570),
+        vec2(0.803208, 0.595699),
+        vec2(0.773010, 0.634393),
+        vec2(0.740951, 0.671559),
+        vec2(0.707107, 0.707107),
+        vec2(0.671559, 0.740951),
+        vec2(0.634393, 0.773010),
+        vec2(0.595699, 0.803208),
+        vec2(0.555570, 0.831470),
+        vec2(0.514103, 0.857729),
+        vec2(0.471397, 0.881921),
+        vec2(0.427555, 0.903989),
+        vec2(0.382683, 0.923880),
+        vec2(0.336890, 0.941544),
+        vec2(0.290285, 0.956940),
+        vec2(0.242980, 0.970031),
+        vec2(0.195090, 0.980785),
+        vec2(0.146730, 0.989177),
+        vec2(0.098017, 0.995185),
+        vec2(0.049068, 0.998795),
+        vec2(0.000000, 1.000000),
+        vec2(-0.049068, 0.998795),
+        vec2(-0.098017, 0.995185),
+        vec2(-0.146730, 0.989177),
+        vec2(-0.195090, 0.980785),
+        vec2(-0.242980, 0.970031),
+        vec2(-0.290285, 0.956940),
+        vec2(-0.336890, 0.941544),
+        vec2(-0.382683, 0.923880),
+        vec2(-0.427555, 0.903989),
+        vec2(-0.471397, 0.881921),
+        vec2(-0.514103, 0.857729),
+        vec2(-0.555570, 0.831470),
+        vec2(-0.595699, 0.803208),
+        vec2(-0.634393, 0.773010),
+        vec2(-0.671559, 0.740951),
+        vec2(-0.707107, 0.707107),
+        vec2(-0.740951, 0.671559),
+        vec2(-0.773010, 0.634393),
+        vec2(-0.803208, 0.595699),
+        vec2(-0.831470, 0.555570),
+        vec2(-0.857729, 0.514103),
+        vec2(-0.881921, 0.471397),
+        vec2(-0.903989, 0.427555),
+        vec2(-0.923880, 0.382683),
+        vec2(-0.941544, 0.336890),
+        vec2(-0.956940, 0.290285),
+        vec2(-0.970031, 0.242980),
+        vec2(-0.980785, 0.195090),
+        vec2(-0.989177, 0.146730),
+        vec2(-0.995185, 0.098017),
+        vec2(-0.998795, 0.049068),
+        vec2(-1.000000, 0.000000),
+        vec2(-0.998795, -0.049068),
+        vec2(-0.995185, -0.098017),
+        vec2(-0.989177, -0.146730),
+        vec2(-0.980785, -0.195090),
+        vec2(-0.970031, -0.242980),
+        vec2(-0.956940, -0.290285),
+        vec2(-0.941544, -0.336890),
+        vec2(-0.923880, -0.382683),
+        vec2(-0.903989, -0.427555),
+        vec2(-0.881921, -0.471397),
+        vec2(-0.857729, -0.514103),
+        vec2(-0.831470, -0.555570),
+        vec2(-0.803208, -0.595699),
+        vec2(-0.773010, -0.634393),
+        vec2(-0.740951, -0.671559),
+        vec2(-0.707107, -0.707107),
+        vec2(-0.671559, -0.740951),
+        vec2(-0.634393, -0.773010),
+        vec2(-0.595699, -0.803208),
+        vec2(-0.555570, -0.831470),
+        vec2(-0.514103, -0.857729),
+        vec2(-0.471397, -0.881921),
+        vec2(-0.427555, -0.903989),
+        vec2(-0.382683, -0.923880),
+        vec2(-0.336890, -0.941544),
+        vec2(-0.290285, -0.956940),
+        vec2(-0.242980, -0.970031),
+        vec2(-0.195090, -0.980785),
+        vec2(-0.146730, -0.989177),
+        vec2(-0.098017, -0.995185),
+        vec2(-0.049068, -0.998795),
+        vec2(-0.000000, -1.000000),
+        vec2(0.049068, -0.998795),
+        vec2(0.098017, -0.995185),
+        vec2(0.146730, -0.989177),
+        vec2(0.195090, -0.980785),
+        vec2(0.242980, -0.970031),
+        vec2(0.290285, -0.956940),
+        vec2(0.336890, -0.941544),
+        vec2(0.382683, -0.923880),
+        vec2(0.427555, -0.903989),
+        vec2(0.471397, -0.881921),
+        vec2(0.514103, -0.857729),
+        vec2(0.555570, -0.831470),
+        vec2(0.595699, -0.803208),
+        vec2(0.634393, -0.773010),
+        vec2(0.671559, -0.740951),
+        vec2(0.707107, -0.707107),
+        vec2(0.740951, -0.671559),
+        vec2(0.773010, -0.634393),
+        vec2(0.803208, -0.595699),
+        vec2(0.831470, -0.555570),
+        vec2(0.857729, -0.514103),
+        vec2(0.881921, -0.471397),
+        vec2(0.903989, -0.427555),
+        vec2(0.923880, -0.382683),
+        vec2(0.941544, -0.336890),
+        vec2(0.956940, -0.290285),
+        vec2(0.970031, -0.242980),
+        vec2(0.980785, -0.195090),
+        vec2(0.989177, -0.146730),
+        vec2(0.995185, -0.098017),
+        vec2(0.998795, -0.049068),
+        vec2(1.000000, -0.000000),
+    ];
+}
 
 // ----------------------------------------------------------------------------
 
@@ -50,13 +336,36 @@ impl Path {
     }
 
     pub fn add_circle(&mut self, center: Pos2, radius: f32) {
-        let n = (radius * 4.0).round() as i32; // TODO: tweak a bit more
+        use precomputed_vertices::*;
-        let n = n.clamp(4, 64);
+
-        self.reserve(n as usize);
+        // These cutoffs are based on a high-dpi display. TODO: use pixels_per_point here?
-        for i in 0..n {
+        // same cutoffs as in add_circle_quadrant
-            let angle = remap(i as f32, 0.0..=n as f32, 0.0..=TAU);
+
-            let normal = vec2(angle.cos(), angle.sin());
+        if radius <= 2.0 {
-            self.add_point(center + radius * normal, normal);
+            self.0.extend(CIRCLE_8.iter().map(|&n| PathPoint {
+                pos: center + radius * n,
+                normal: n,
+            }));
+        } else if radius <= 5.0 {
+            self.0.extend(CIRCLE_16.iter().map(|&n| PathPoint {
+                pos: center + radius * n,
+                normal: n,
+            }));
+        } else if radius < 18.0 {
+            self.0.extend(CIRCLE_32.iter().map(|&n| PathPoint {
+                pos: center + radius * n,
+                normal: n,
+            }));
+        } else if radius < 50.0 {
+            self.0.extend(CIRCLE_64.iter().map(|&n| PathPoint {
+                pos: center + radius * n,
+                normal: n,
+            }));
+        } else {
+            self.0.extend(CIRCLE_128.iter().map(|&n| PathPoint {
+                pos: center + radius * n,
+                normal: n,
+            }));
         }
     }
 
@@ -189,8 +498,7 @@ impl Path {
 pub mod path {
     //! Helpers for constructing paths
     use crate::shape::Rounding;
-
+    use emath::*;
-    use super::*;
 
     /// overwrites existing points
     pub fn rounded_rectangle(path: &mut Vec<Pos2>, rect: Rect, rounding: Rounding) {
@@ -236,19 +544,33 @@ pub mod path {
     //   - quadrant 3: right top
     // * angle 4 * TAU / 4 = right
     pub fn add_circle_quadrant(path: &mut Vec<Pos2>, center: Pos2, radius: f32, quadrant: f32) {
-        // TODO: optimize with precalculated vertices for some radii ranges
+        use super::precomputed_vertices::*;
 
-        let n = (radius * 0.75).round() as i32; // TODO: tweak a bit more
+        // These cutoffs are based on a high-dpi display. TODO: use pixels_per_point here?
-        let n = n.clamp(2, 32);
+        // same cutoffs as in add_circle
-        const RIGHT_ANGLE: f32 = TAU / 4.0;
+
-        path.reserve(n as usize + 1);
+        if radius <= 0.0 {
-        for i in 0..=n {
+            path.push(center);
-            let angle = remap(
+        } else if radius <= 2.0 {
-                i as f32,
+            let offset = quadrant as usize * 2;
-                0.0..=n as f32,
+            let quadrant_vertices = &CIRCLE_8[offset..=offset + 2];
-                quadrant * RIGHT_ANGLE..=(quadrant + 1.0) * RIGHT_ANGLE,
+            path.extend(quadrant_vertices.iter().map(|&n| center + radius * n));
-            );
+        } else if radius <= 5.0 {
-            path.push(center + radius * Vec2::angled(angle));
+            let offset = quadrant as usize * 4;
+            let quadrant_vertices = &CIRCLE_16[offset..=offset + 4];
+            path.extend(quadrant_vertices.iter().map(|&n| center + radius * n));
+        } else if radius < 18.0 {
+            let offset = quadrant as usize * 8;
+            let quadrant_vertices = &CIRCLE_32[offset..=offset + 8];
+            path.extend(quadrant_vertices.iter().map(|&n| center + radius * n));
+        } else if radius < 50.0 {
+            let offset = quadrant as usize * 16;
+            let quadrant_vertices = &CIRCLE_64[offset..=offset + 16];
+            path.extend(quadrant_vertices.iter().map(|&n| center + radius * n));
+        } else {
+            let offset = quadrant as usize * 32;
+            let quadrant_vertices = &CIRCLE_128[offset..=offset + 32];
+            path.extend(quadrant_vertices.iter().map(|&n| center + radius * n));
         }
     }