From 2c82d7fe81167a676a068d71aca53a4d695202bf Mon Sep 17 00:00:00 2001
From: Bruce Mitchener <bruce.mitchener@gmail.com>
Date: Sat, 14 Sep 2024 23:43:34 +0700
Subject: [PATCH 1/2] Impl `ParamCurve`, `ParamCurveArclen` for `Arc`

This uses an approximation of the arc length using beziers as the
analytic solution is quite involved.
---
 CHANGELOG.md |  3 +++
 src/arc.rs   | 40 ++++++++++++++++++++++++++++++++++++++--
 2 files changed, 41 insertions(+), 2 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7810278f..33cdb28b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -15,6 +15,8 @@ You can find its changes [documented below](#0111-2024-09-12).
 
 This release has an [MSRV][] of 1.65.
 
+### `Arc` now implements `ParamCurve` and `ParamCurveArclen`. ([#378] by [@waywardmonkeys])
+
 ## [0.11.1][] (2024-09-12)
 
 This release has an [MSRV][] of 1.65.
@@ -75,6 +77,7 @@ Note: A changelog was not kept for or before this release
 [#370]: https://github.com/linebender/kurbo/pull/370
 [#375]: https://github.com/linebender/kurbo/pull/375
 [#376]: https://github.com/linebender/kurbo/pull/376
+[#378]: https://github.com/linebender/kurbo/pull/378
 
 [Unreleased]: https://github.com/linebender/kurbo/compare/v0.11.1...HEAD
 [0.11.0]: https://github.com/linebender/kurbo/releases/tag/v0.11.0
diff --git a/src/arc.rs b/src/arc.rs
index 9ac642be..ac18e874 100644
--- a/src/arc.rs
+++ b/src/arc.rs
@@ -3,11 +3,11 @@
 
 //! An ellipse arc.
 
-use crate::{Affine, Ellipse, PathEl, Point, Rect, Shape, Vec2};
+use crate::{Affine, Ellipse, ParamCurve, ParamCurveArclen, PathEl, Point, Rect, Shape, Vec2};
 use core::{
     f64::consts::{FRAC_PI_2, PI},
     iter,
-    ops::Mul,
+    ops::{Mul, Range},
 };
 
 #[cfg(not(feature = "std"))]
@@ -171,6 +171,42 @@ fn rotate_pt(pt: Vec2, angle: f64) -> Vec2 {
     )
 }
 
+impl ParamCurve for Arc {
+    fn eval(&self, t: f64) -> Point {
+        let angle = self.start_angle + (self.sweep_angle * t);
+        sample_ellipse(self.radii, self.x_rotation, angle).to_point()
+    }
+
+    fn subsegment(&self, range: Range<f64>) -> Self {
+        Self {
+            center: self.center,
+            radii: self.radii,
+            start_angle: self.start_angle + (self.sweep_angle * range.start),
+            sweep_angle: self.sweep_angle - (self.sweep_angle * (1.0 - range.end)),
+            x_rotation: self.x_rotation,
+        }
+    }
+
+    fn start(&self) -> Point {
+        sample_ellipse(self.radii, self.x_rotation, self.start_angle).to_point()
+    }
+
+    fn end(&self) -> Point {
+        sample_ellipse(
+            self.radii,
+            self.x_rotation,
+            self.start_angle + self.sweep_angle,
+        )
+        .to_point()
+    }
+}
+
+impl ParamCurveArclen for Arc {
+    fn arclen(&self, accuracy: f64) -> f64 {
+        self.path_segments(0.1).perimeter(accuracy)
+    }
+}
+
 impl Shape for Arc {
     type PathElementsIter<'iter> = iter::Chain<iter::Once<PathEl>, ArcAppendIter>;
 

From 060d6319b5b395454a000c3fdf25bf3cf71d5ed4 Mon Sep 17 00:00:00 2001
From: Bruce Mitchener <bruce.mitchener@gmail.com>
Date: Fri, 20 Sep 2024 23:25:43 +0700
Subject: [PATCH 2/2] Update CHANGELOG.md

Co-authored-by: Daniel McNab <36049421+DJMcNab@users.noreply.github.com>
---
 CHANGELOG.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 33cdb28b..be5b580c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -15,7 +15,9 @@ You can find its changes [documented below](#0111-2024-09-12).
 
 This release has an [MSRV][] of 1.65.
 
-### `Arc` now implements `ParamCurve` and `ParamCurveArclen`. ([#378] by [@waywardmonkeys])
+### Changes
+
+- `Arc` now implements `ParamCurve` and `ParamCurveArclen`. ([#378] by [@waywardmonkeys])
 
 ## [0.11.1][] (2024-09-12)