Bezier-rs: Add joins and caps to offsets and outlines (#1083)

* Intial work

* Improve miter and add round join

* Get arcs to go opposite direction

* Add cap and other refactors

* Rename joint to join, fix some bugs

* Fix single point issue

* Clean up

* Fix iframe sizes and update UI

* Address comments and handle single point outline

* Rename variables, fix branches in outline

* Address comments

libraries/bezier-rs/src/utils.rs

@@ -1,4 +1,5 @@
 use crate::consts::{MAX_ABSOLUTE_DIFFERENCE, MIN_SEPARATION_VALUE, STRICT_MAX_ABSOLUTE_DIFFERENCE};
+use crate::ManipulatorGroup;
 
 use glam::{BVec2, DMat2, DVec2};
 use std::f64::consts::PI;
@@ -29,12 +30,23 @@ pub enum SubpathTValue {
 }
 
 #[derive(Copy, Clone)]
-pub enum Joint {
-	Miter,
+/// Enum to represent the join type between subpaths.
+/// As defined in SVG: https://www.w3.org/TR/SVG2/painting.html#LineJoin.
+pub enum Join {
 	Bevel,
+	Miter,
 	Round,
 }
 
+#[derive(Copy, Clone)]
+/// Enum to represent the cap type at the ends of an outline
+/// As defined in SVG: https://www.w3.org/TR/SVG2/painting.html#LineCaps.
+pub enum Cap {
+	Butt,
+	Round,
+	Square,
+}
+
 /// Helper to perform the computation of a and c, where b is the provided point on the curve.
 /// Given the correct power of `t` and `(1-t)`, the computation is the same for quadratic and cubic cases.
 /// Relevant derivation and the definitions of a, b, and c can be found in [the projection identity section](https://pomax.github.io/bezierinfo/#abc) of Pomax's bezier curve primer.
@@ -266,6 +278,31 @@ pub fn scale_point_from_origin(point: DVec2, origin: DVec2, should_flip_directio
 	scale_point_from_direction_vector(point, (origin - point).normalize(), should_flip_direction, distance)
 }
 
+/// Computes the necessary details to form a circular join from `left` to `right`, along a circle around `center`.
+/// By default, the angle is assumed to be 180 degrees.
+pub fn compute_circular_subpath_details<ManipulatorGroupId: crate::Identifier>(
+	left: DVec2,
+	arc_point: DVec2,
+	right: DVec2,
+	center: DVec2,
+	angle: Option<f64>,
+) -> (DVec2, ManipulatorGroup<ManipulatorGroupId>, DVec2) {
+	let center_to_arc_point = arc_point - center;
+
+	// Based on https://pomax.github.io/bezierinfo/#circles_cubic
+	let handle_offset_factor = if let Some(angle) = angle { 4. / 3. * (angle / 4.).tan() } else { 0.551784777779014 };
+
+	(
+		left - (left - center).perp() * handle_offset_factor,
+		ManipulatorGroup::new(
+			arc_point,
+			Some(arc_point + center_to_arc_point.perp() * handle_offset_factor),
+			Some(arc_point - center_to_arc_point.perp() * handle_offset_factor),
+		),
+		right + (right - center).perp() * handle_offset_factor,
+	)
+}
+
 #[cfg(test)]
 mod tests {
 	use super::*;