Add inscribe circle node

Author: 0HyperCube

node-graph/gcore/src/vector/algorithms/bezpath_algorithms.rs

@@ -674,3 +674,213 @@ mod tests {
 		assert!(bezpath_is_inside_bezpath(&line_inside, &boundary_polygon, None, None));
 	}
 }
+
+pub mod inscribe_circles_algorithms {
+	use core::ops::Range;
+	use kurbo::{ParamCurve, ParamCurveDeriv, ParamCurveExtrema};
+
+	const ROUND_ACCURACY: f64 = 1e-5;
+
+	#[derive(Clone, Copy, Debug, PartialEq)]
+	pub struct CircleInscription {
+		pub time_1: f64,
+		pub time_2: f64,
+		pub theta: f64,
+		pub circle_centre1: glam::DVec2,
+		pub circle_centre2: glam::DVec2,
+	}
+
+	/// Find the normalised tangent at a particular time. Avoid using for t=0 or t=1 due to errors.
+	fn tangent(segment: kurbo::PathSeg, t: f64) -> kurbo::Vec2 {
+		let tangent = match segment {
+			kurbo::PathSeg::Line(line) => line.deriv().eval(t),
+			kurbo::PathSeg::Quad(quad_bez) => quad_bez.deriv().eval(t),
+			kurbo::PathSeg::Cubic(cubic_bez) => cubic_bez.deriv().eval(t),
+		}
+		.to_vec2()
+		.normalize();
+		debug_assert!(tangent.is_finite(), "cannot round corner with NaN tangent");
+		tangent
+	}
+
+	/// Rotate 90 degrees in one direction
+	fn offset_1(value: kurbo::Vec2, radius: f64) -> kurbo::Vec2 {
+		kurbo::Vec2::new(-value.y, value.x) * radius
+	}
+
+	/// Rotate 90 degrees in one direction
+	fn offset_2(value: kurbo::Vec2, radius: f64) -> kurbo::Vec2 {
+		kurbo::Vec2::new(value.y, -value.x) * radius
+	}
+
+	/// Compute the tangent at t=0 for the path segment
+	pub fn tangent_at_start(segment: kurbo::PathSeg) -> kurbo::Vec2 {
+		let tangent = match segment {
+			kurbo::PathSeg::Line(line) => (line.p1 - line.p0).normalize(),
+			kurbo::PathSeg::Quad(quad_bez) => {
+				let first = (quad_bez.p1 - quad_bez.p0).normalize();
+				if first.is_finite() { first } else { (quad_bez.p2 - quad_bez.p0).normalize() }
+			}
+			kurbo::PathSeg::Cubic(cubic_bez) => {
+				let first = (cubic_bez.p1 - cubic_bez.p0).normalize();
+				if first.is_finite() {
+					first
+				} else {
+					let second = (cubic_bez.p2 - cubic_bez.p0).normalize();
+					if second.is_finite() { second } else { (cubic_bez.p3 - cubic_bez.p0).normalize() }
+				}
+			}
+		};
+		debug_assert!(tangent.is_finite(), "cannot round corner with NaN tangent {segment:?}");
+		tangent
+	}
+
+	/// Resolve the bounding boxes offset by radius in either direciton.
+	fn offset_bounding_boxes(segment: kurbo::PathSeg, radius: f64) -> [kurbo::Rect; 2] {
+		let [start_tangent, end_tangent] = [tangent_at_start(segment), -tangent_at_start(segment.reverse())];
+
+		let mut bbox1 = kurbo::Rect::from_points(segment.start() + offset_1(start_tangent, radius), segment.end() + offset_1(end_tangent, radius));
+		let mut bbox2 = kurbo::Rect::from_points(segment.start() + offset_2(start_tangent, radius), segment.end() + offset_2(end_tangent, radius));
+		// The extrema for the original curve should be the same as for the offset curve
+		for extremum in segment.extrema() {
+			let value = segment.eval(extremum);
+			let derivative = tangent(segment, extremum);
+			bbox1 = bbox1.union_pt(value + offset_1(derivative, radius));
+			bbox2 = bbox2.union_pt(value + offset_2(derivative, radius));
+		}
+		debug_assert!(bbox1.is_finite() && bbox2.is_finite(), "a wild NaN appeared :(");
+		[bbox1, bbox2]
+	}
+
+	/// If the width and height both smaller than accuracy then we can end the recursion
+	fn rect_within_accuracy(rect: kurbo::Rect, accuracy: f64) -> bool {
+		rect.width().abs() < accuracy && rect.height().abs() < accuracy
+	}
+
+	/// Resursively find position to inscribe circles
+	fn inscribe_internal(segment1: kurbo::PathSeg, t1: Range<f64>, segment2: kurbo::PathSeg, t2: Range<f64>, radius: f64) -> Option<CircleInscription> {
+		let bbox1 = offset_bounding_boxes(segment1.subsegment(t1.clone()), radius);
+		let bbox2 = offset_bounding_boxes(segment2.subsegment(t2.clone()), radius);
+		let mid_t1 = (t1.start + t1.end) / 2.;
+		let mid_t2 = (t2.start + t2.end) / 2.;
+
+		// Check if the bounding boxes overlap
+		let mut any_overlap = false;
+		for i in 0..4usize {
+			let [index_1, index_2] = [i >> 1, i & 1];
+			let [first, second] = [bbox1[index_1], bbox2[index_2]];
+
+			// Ignore non overlapping
+			if !first.overlaps(second) {
+				continue;
+			}
+			// If the rects are small enough then complete the recursion
+			if rect_within_accuracy(first, ROUND_ACCURACY) && rect_within_accuracy(second, ROUND_ACCURACY) {
+				let tangents = [(segment1, mid_t1), (segment2, mid_t2)].map(|(segment, t)| tangent(segment, t));
+				let normal_1 = [offset_1, offset_2][index_1](tangents[0], 1.);
+				let normal_2 = [offset_1, offset_2][index_2](tangents[1], 1.);
+				let circle_centre_1 = segment1.eval(mid_t1) + normal_1 * radius;
+				let circle_centre_2 = segment2.eval(mid_t2) + normal_2 * radius;
+				return Some(CircleInscription {
+					time_1: mid_t1,
+					time_2: mid_t2,
+					theta: normal_1.dot(normal_2).clamp(-1., 1.).acos(),
+					circle_centre1: glam::DVec2::new(circle_centre_1.x, circle_centre_1.y),
+					circle_centre2: glam::DVec2::new(circle_centre_2.x, circle_centre_2.y),
+				});
+			}
+			any_overlap = true;
+		}
+		if !any_overlap {
+			return None;
+		}
+
+		let [start_t1, end_t1] = [t1.start, t1.end];
+		let [start_t2, end_t2] = [t2.start, t2.end];
+
+		// Repeat checking the intersection with the combinations of the two halves of each curve
+		if let Some(result) = None
+			.or_else(|| inscribe_internal(segment1, start_t1..mid_t1, segment2, start_t2..mid_t2, radius))
+			.or_else(|| inscribe_internal(segment1, start_t1..mid_t1, segment2, mid_t2..end_t2, radius))
+			.or_else(|| inscribe_internal(segment1, mid_t1..end_t1, segment2, start_t2..mid_t2, radius))
+			.or_else(|| inscribe_internal(segment1, mid_t1..end_t1, segment2, mid_t2..end_t2, radius))
+		{
+			return Some(result);
+		}
+		None
+	}
+
+	/// Convert [`crate::subpath::Bezier`] to [`kurbo::PathSeg`]
+	pub fn bezier_to_path_seg(bezier: crate::subpath::Bezier) -> kurbo::PathSeg {
+		let [start, end] = [(bezier.start().x, bezier.start().y), (bezier.end().x, bezier.end().y)];
+		match bezier.handles {
+			crate::subpath::BezierHandles::Linear => kurbo::Line::new(start, end).into(),
+			crate::subpath::BezierHandles::Quadratic { handle } => kurbo::QuadBez::new(start, (handle.x, handle.y), end).into(),
+			crate::subpath::BezierHandles::Cubic { handle_start, handle_end } => kurbo::CubicBez::new(start, (handle_start.x, handle_start.y), (handle_end.x, handle_end.y), end).into(),
+		}
+	}
+
+	/// Convert [`kurbo::PathSeg`] to [`crate::subpath::BezierHandles`]
+	pub fn path_seg_to_handles(segment: kurbo::PathSeg) -> crate::subpath::BezierHandles {
+		match segment {
+			kurbo::PathSeg::Line(_line) => crate::subpath::BezierHandles::Linear,
+			kurbo::PathSeg::Quad(quad_bez) => crate::subpath::BezierHandles::Quadratic {
+				handle: glam::DVec2::new(quad_bez.p1.x, quad_bez.p1.y),
+			},
+			kurbo::PathSeg::Cubic(cubic_bez) => crate::subpath::BezierHandles::Cubic {
+				handle_start: glam::DVec2::new(cubic_bez.p1.x, cubic_bez.p1.y),
+				handle_end: glam::DVec2::new(cubic_bez.p2.x, cubic_bez.p2.y),
+			},
+		}
+	}
+
+	/// Attemt to inscribe circle into the start of the [`kurbo::PathSeg`]s
+	pub fn inscribe(first: kurbo::PathSeg, second: kurbo::PathSeg, radius: f64) -> Option<CircleInscription> {
+		inscribe_internal(first, 0.0..1., second, 0.0..1., radius)
+	}
+
+	#[cfg(test)]
+	mod inscribe_tests {
+		#[test]
+		fn test_perpendicular_lines() {
+			let l1 = kurbo::PathSeg::Line(kurbo::Line::new((0., 0.), (100., 0.)));
+			let l2 = kurbo::PathSeg::Line(kurbo::Line::new((0., 0.), (0., 100.)));
+
+			let result = super::inscribe(l1, l2, 5.);
+			assert!(result.unwrap().circle_centre1.abs_diff_eq(glam::DVec2::new(5., 5.), super::ROUND_ACCURACY * 10.), "{result:?}");
+			assert_eq!(result.unwrap().theta, std::f64::consts::FRAC_PI_2, "unexpected {result:?}");
+		}
+
+		#[test]
+		fn test_skew_lines() {
+			let l1 = kurbo::PathSeg::Line(kurbo::Line::new((0., 0.), (100., 100.)));
+			let l2 = kurbo::PathSeg::Line(kurbo::Line::new((0., 0.), (0., 100.)));
+
+			let result = super::inscribe(l1, l2, 5.);
+			let expected_centre = glam::DVec2::new(5., 5. + 5. * std::f64::consts::SQRT_2);
+			assert!(result.unwrap().circle_centre1.abs_diff_eq(expected_centre, super::ROUND_ACCURACY * 10.), "unexpected {result:?}");
+			assert_eq!(result.unwrap().theta, std::f64::consts::FRAC_PI_4 * 3., "unexpected {result:?}");
+		}
+
+		#[test]
+		fn test_skew_lines2() {
+			let l1 = kurbo::PathSeg::Line(kurbo::Line::new((0., 0.), (30., 40.)));
+			let l2 = kurbo::PathSeg::Line(kurbo::Line::new((0., 0.), (40., 30.)));
+
+			let result = super::inscribe(l1, l2, 5.);
+			let expected_centre = glam::DVec2::new(25., 25.);
+			assert!(result.unwrap().circle_centre1.abs_diff_eq(expected_centre, super::ROUND_ACCURACY * 10.), "{result:?}");
+			assert_eq!(result.unwrap().theta, (-24f64 / 25.).acos(), "{result:?}");
+		}
+
+		#[test]
+		fn test_perpendicular_cubic() {
+			let l1 = kurbo::PathSeg::Cubic(kurbo::CubicBez::new((0., 0.), (0., 0.), (100., 0.), (100., 0.)));
+			let l2 = kurbo::PathSeg::Cubic(kurbo::CubicBez::new((0., 0.), (0., 33.), (0., 67.), (0., 100.)));
+
+			let result = super::inscribe(l1, l2, 5.);
+			assert!(result.unwrap().circle_centre1.abs_diff_eq(glam::DVec2::new(5., 5.), super::ROUND_ACCURACY * 10.), "{result:?}");
+			assert_eq!(result.unwrap().theta, std::f64::consts::FRAC_PI_2, "unexpected {result:?}");
+		}
+	}
+}

node-graph/gcore/src/vector/vector_attributes.rs

@@ -300,6 +300,10 @@ impl SegmentDomain {
 		self.end_point[segment_index] = new;
 	}
 
+	pub fn set_handles(&mut self, segment_index: usize, new: BezierHandles) {
+		self.handles[segment_index] = new;
+	}
+
 	pub fn handles(&self) -> &[BezierHandles] {
 		&self.handles
 	}

node-graph/gcore/src/vector/vector_nodes.rs

@@ -530,6 +530,73 @@ async fn round_corners(
 		.collect()
 }
 
+/// Attempt to inscribe circles at the anchors (that have exactly two segments connected).
+#[node_macro::node(category("Vector: Modifier"), path(graphene_core::vector))]
+async fn inscribe_circles(
+	_: impl Ctx,
+	mut source: Table<Vector>,
+	#[hard_min(0.)]
+	#[default(10.)]
+	radius: PixelLength,
+) -> Table<Vector> {
+	for TableRowMut { transform, element: vector, .. } in source.iter_mut() {
+		let mut new_point_id = vector.point_domain.next_id();
+		let mut new_segment_id = vector.segment_domain.next_id();
+		let point_ids_count = vector.point_domain.ids().len();
+		for point_index in 0..point_ids_count {
+			let point_id = vector.point_domain.ids()[point_index];
+			let [Some((first_index, first)), Some((second_index, second)), None] = ({
+				let mut connected_segments = vector.segment_bezier_iter().enumerate().filter(|&(_, (_, _, start, end))| (start == point_id) != (end == point_id));
+				[connected_segments.next(), connected_segments.next(), connected_segments.next()]
+			}) else {
+				continue;
+			};
+			let flipped = [first.3, second.3].map(|end| end == point_id);
+			let [first, second] = [first.1, second.1]
+				.map(|t| t.apply_transformation(|x| transform.transform_point2(x)))
+				.map(bezpath_algorithms::inscribe_circles_algorithms::bezier_to_path_seg);
+			let first = if flipped[0] { first.reverse() } else { first };
+			let second = if flipped[1] { second.reverse() } else { second };
+
+			let Some(pos) = bezpath_algorithms::inscribe_circles_algorithms::inscribe(first, second, radius) else {
+				continue;
+			};
+			let [first, second] = [first.subsegment(pos.time_1..1.0), second.subsegment(pos.time_2..1.0)];
+			let start_positions = [first, second].map(|segment| DVec2::new(segment.start().x, segment.start().y));
+			let start_tangents = [first, second].map(bezpath_algorithms::inscribe_circles_algorithms::tangent_at_start).map(|v| DVec2::new(v.x, v.y));
+			let k = (4. / 3.) * (pos.theta / 4.).tan();
+			if !k.is_finite() {
+				warn!("k is not finite corner {pos:?}, skipping");
+				continue;
+			}
+			let handle_positions = [start_positions[0] - start_tangents[0] * k * radius, start_positions[1] - start_tangents[1] * k * radius];
+			let rounded_handles = BezierHandles::Cubic {
+				handle_start: handle_positions[0],
+				handle_end: handle_positions[1],
+			};
+			let first = if flipped[0] { first.reverse() } else { first };
+			let second = if flipped[1] { second.reverse() } else { second };
+			let handles = [first, second].map(bezpath_algorithms::inscribe_circles_algorithms::path_seg_to_handles);
+			vector.segment_domain.set_handles(first_index, handles[0]);
+			vector.segment_domain.set_handles(second_index, handles[1]);
+			let end_point_index = vector.point_domain.len();
+			if flipped[1] {
+				vector.segment_domain.set_end_point(second_index, end_point_index);
+			} else {
+				vector.segment_domain.set_start_point(second_index, end_point_index);
+			}
+
+			vector.point_domain.set_position(point_index, start_positions[0]);
+			vector.point_domain.push(new_point_id.next_id(), start_positions[1]);
+			vector
+				.segment_domain
+				.push(new_segment_id.next_id(), point_index, end_point_index, rounded_handles, StrokeId::generate());
+		}
+	}
+
+	source
+}
+
 #[node_macro::node(name("Merge by Distance"), category("Vector: Modifier"), path(graphene_core::vector))]
 pub fn merge_by_distance(
 	_: impl Ctx,