Sameer Puri
4 years ago
committed by
GitHub
commit
97b76ca0d0
@ -0,0 +1,428 @@
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use euclid::Angle;
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use lyon_geom::{
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Arc, ArcFlags, CubicBezierSegment, Line, LineSegment, Point, Scalar, SvgArc, Transform, Vector,
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};
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pub enum ArcOrLineSegment<S> {
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Arc(SvgArc<S>),
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Line(LineSegment<S>),
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}
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fn arc_from_endpoints_and_tangents<S: Scalar>(
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from: Point<S>,
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from_tangent: Vector<S>,
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to: Point<S>,
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to_tangent: Vector<S>,
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) -> Option<SvgArc<S>> {
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let from_to = (from - to).length();
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let incenter = {
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let from_tangent = Line {
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point: from,
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vector: from_tangent,
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};
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let to_tangent = Line {
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point: to,
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vector: to_tangent,
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};
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let intersection = from_tangent.intersection(&to_tangent)?;
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let from_intersection = (from - intersection).length();
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let to_intersection = (to - intersection).length();
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(((from * to_intersection).to_vector()
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+ (to * from_intersection).to_vector()
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+ (intersection * from_to).to_vector())
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/ (from_intersection + to_intersection + from_to))
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.to_point()
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};
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let get_perpendicular_bisector = |a, b| {
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let vector: Vector<S> = a - b;
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let perpendicular_vector = Vector::from([-vector.y, vector.x]).normalize();
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Line {
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point: LineSegment { from: a, to: b }.sample(S::HALF),
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vector: perpendicular_vector,
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}
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};
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let from_incenter_bisector = get_perpendicular_bisector(from, incenter);
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let to_incenter_bisector = get_perpendicular_bisector(to, incenter);
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let center = from_incenter_bisector.intersection(&to_incenter_bisector)?;
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let radius = (from - center).length();
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// Use the 2D determinant + dot product to identify winding direction
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// See https://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands for
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// a nice visual explanation of large arc and sweep
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let flags = {
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let from_center = (from - center).normalize();
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let to_center = (to - center).normalize();
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let det = from_center.x * to_center.y - from_center.y * to_center.x;
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let dot = from_center.dot(to_center);
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let atan2 = det.atan2(dot);
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ArcFlags {
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large_arc: atan2.abs() >= S::PI(),
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sweep: atan2.is_sign_positive(),
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}
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};
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Some(SvgArc {
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from,
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to,
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radii: Vector::splat(radius),
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// This is a circular arc
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x_rotation: Angle::zero(),
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flags,
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})
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}
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pub trait FlattenWithArcs<S> {
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fn flattened(&self, tolerance: S) -> Vec<ArcOrLineSegment<S>>;
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}
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impl<S> FlattenWithArcs<S> for CubicBezierSegment<S>
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where
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S: Scalar + Copy,
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{
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/// Implementation of [Modeling of Bézier Curves Using a Combination of Linear and Circular Arc Approximations](https://sci-hub.st/https://doi.org/10.1109/CGIV.2012.20)
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///
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/// There are some slight deviations like using monotonic ranges instead of bounding by inflection points.
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///
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/// Kaewsaiha, P., & Dejdumrong, N. (2012). Modeling of Bézier Curves Using a Combination of Linear and Circular Arc Approximations. 2012 Ninth International Conference on Computer Graphics, Imaging and Visualization. doi:10.1109/cgiv.2012.20
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///
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fn flattened(&self, tolerance: S) -> Vec<ArcOrLineSegment<S>> {
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if (self.to - self.from).square_length() < S::EPSILON {
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return vec![];
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} else if self.is_linear(tolerance) {
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return vec![ArcOrLineSegment::Line(self.baseline())];
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}
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let mut acc = vec![];
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self.for_each_monotonic_range(|range| {
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let inner_bezier = self.split_range(range);
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if (inner_bezier.to - inner_bezier.from).square_length() < S::EPSILON {
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return;
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} else if inner_bezier.is_linear(tolerance) {
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acc.push(ArcOrLineSegment::Line(inner_bezier.baseline()));
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return;
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}
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if let Some(svg_arc) = arc_from_endpoints_and_tangents(
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inner_bezier.from,
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inner_bezier.derivative(S::ZERO),
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inner_bezier.to,
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inner_bezier.derivative(S::ONE),
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)
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.filter(|svg_arc| {
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let arc = svg_arc.to_arc();
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let mut max_deviation = S::ZERO;
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// TODO: find a better way to check tolerance
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// Ideally: derivative of |f(x) - g(x)| and look at 0 crossings
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for i in 1..20 {
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let t = S::from(i).unwrap() / S::from(20).unwrap();
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max_deviation =
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max_deviation.max((arc.sample(t) - inner_bezier.sample(t)).length());
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}
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max_deviation < tolerance
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}) {
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acc.push(ArcOrLineSegment::Arc(svg_arc));
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} else {
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let (left, right) = inner_bezier.split(S::HALF);
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acc.append(&mut FlattenWithArcs::flattened(&left, tolerance));
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acc.append(&mut FlattenWithArcs::flattened(&right, tolerance));
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}
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});
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acc
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}
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}
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impl<S> FlattenWithArcs<S> for SvgArc<S>
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where
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S: Scalar,
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{
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fn flattened(&self, tolerance: S) -> Vec<ArcOrLineSegment<S>> {
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if (self.to - self.from).square_length() < S::EPSILON {
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return vec![];
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} else if self.is_straight_line() {
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return vec![ArcOrLineSegment::Line(LineSegment {
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from: self.from,
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to: self.to,
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})];
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} else if (self.radii.x.abs() - self.radii.y.abs()).abs() < S::EPSILON {
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return vec![ArcOrLineSegment::Arc(*self)];
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}
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let self_arc = self.to_arc();
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if let Some(svg_arc) = arc_from_endpoints_and_tangents(
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self.from,
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self_arc.sample_tangent(S::ZERO),
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self.to,
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self_arc.sample_tangent(S::ONE),
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)
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.filter(|approx_svg_arc| {
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let approx_arc = approx_svg_arc.to_arc();
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let mut max_deviation = S::ZERO;
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// TODO: find a better way to check tolerance
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// Ideally: derivative of |f(x) - g(x)| and look at 0 crossings
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for i in 1..20 {
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let t = S::from(i).unwrap() / S::from(20).unwrap();
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max_deviation =
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max_deviation.max((approx_arc.sample(t) - self_arc.sample(t)).length());
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}
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max_deviation < tolerance
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}) {
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vec![ArcOrLineSegment::Arc(svg_arc)]
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} else {
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let (left, right) = self_arc.split(S::HALF);
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let mut acc = FlattenWithArcs::flattened(&to_svg_arc(left), tolerance);
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acc.append(&mut FlattenWithArcs::flattened(
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&to_svg_arc(right),
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tolerance,
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));
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acc
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}
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}
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}
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/// Sanity holdover until https://github.com/nical/lyon/pull/693 is merged
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pub fn to_svg_arc<S: Scalar>(arc: Arc<S>) -> SvgArc<S> {
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let from = arc.sample(S::ZERO);
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let to = arc.sample(S::ONE);
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let flags = ArcFlags {
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sweep: arc.sweep_angle.get() >= S::ZERO,
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large_arc: S::abs(arc.sweep_angle.get()) >= S::PI(),
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};
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SvgArc {
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from,
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to,
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radii: arc.radii,
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x_rotation: arc.x_rotation,
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flags,
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}
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}
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pub trait Transformed<S> {
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fn transformed(&self, transform: &Transform<S>) -> Self;
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}
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impl<S: Scalar> Transformed<S> for SvgArc<S> {
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/// A lot of the math here is heavily borrowed from [Vitaly Putzin's svgpath](https://github.com/fontello/svgpath).
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///
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/// The code is Rust-ified with only one or two changes, but I plan to understand the math here and
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/// merge changes upstream to lyon-geom.
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fn transformed(&self, transform: &Transform<S>) -> Self {
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let from = transform.transform_point(self.from);
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let to = transform.transform_point(self.to);
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// Translation does not affect rotation, radii, or flags
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let [a, b, c, d, _tx, _ty] = transform.to_array();
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let (x_rotation, radii) = {
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let (sin, cos) = self.x_rotation.sin_cos();
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// Radii are axis-aligned -- rotate & transform
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let ma = [
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self.radii.x * (a * cos + c * sin),
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self.radii.x * (b * cos + d * sin),
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self.radii.y * (-a * sin + c * cos),
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self.radii.y * (-b * sin + d * cos),
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];
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// ma * transpose(ma) = [ J L ]
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// [ L K ]
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// L is calculated later (if the image is not a circle)
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let J = ma[0].powi(2) + ma[2].powi(2);
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let K = ma[1].powi(2) + ma[3].powi(2);
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// the discriminant of the characteristic polynomial of ma * transpose(ma)
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let D = ((ma[0] - ma[3]).powi(2) + (ma[2] + ma[1]).powi(2))
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* ((ma[0] + ma[3]).powi(2) + (ma[2] - ma[1]).powi(2));
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// the "mean eigenvalue"
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let JK = (J + K) / S::TWO;
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// check if the image is (almost) a circle
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if D < S::EPSILON * JK {
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// if it is
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(Angle::zero(), Vector::splat(JK.sqrt()))
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} else {
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// if it is not a circle
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let L = ma[0] * ma[1] + ma[2] * ma[3];
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let D = D.sqrt();
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// {l1,l2} = the two eigen values of ma * transpose(ma)
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let l1 = JK + D / S::TWO;
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let l2 = JK - D / S::TWO;
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// the x - axis - rotation angle is the argument of the l1 - eigenvector
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let ax = if L.abs() < S::EPSILON && (l1 - K).abs() < S::EPSILON {
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Angle::frac_pi_2()
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} else {
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Angle::radians(
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(if L.abs() > (l1 - K).abs() {
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(l1 - J) / L
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} else {
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L / (l1 - K)
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})
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.atan(),
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)
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};
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(ax, Vector::from([l1.sqrt(), l2.sqrt()]))
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}
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};
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// A mirror transform causes this flag to be flipped
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let invert_sweep = { (a * d) - (b * c) < S::ZERO };
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let flags = ArcFlags {
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sweep: if invert_sweep {
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!self.flags.sweep
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} else {
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self.flags.sweep
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},
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large_arc: self.flags.large_arc,
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};
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Self {
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from,
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to,
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radii,
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x_rotation,
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flags,
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}
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}
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}
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#[cfg(test)]
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mod tests {
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use cairo::{Context, SvgSurface};
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use lyon_geom::{point, vector, CubicBezierSegment, Point, Vector};
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use std::path::PathBuf;
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use svgtypes::PathParser;
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use crate::arc::{ArcOrLineSegment, FlattenWithArcs};
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#[test]
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fn flatten_returns_expected_arcs() {
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const PATH: &'static str = "M 8.0549,11.9023
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c
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0.13447,1.69916 8.85753,-5.917903 7.35159,-6.170957
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z";
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let mut surf =
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SvgSurface::new(128., 128., Some(PathBuf::from("approx_circle.svg"))).unwrap();
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surf.set_document_unit(cairo::SvgUnit::Mm);
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let ctx = Context::new(&surf).unwrap();
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ctx.set_line_width(0.2);
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let mut current_position = Point::zero();
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let mut acc = 0;
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for path in PathParser::from(PATH) {
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use svgtypes::PathSegment::*;
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match path.unwrap() {
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MoveTo { x, y, abs } => {
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if abs {
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ctx.move_to(x, y);
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current_position = point(x, y);
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} else {
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ctx.rel_move_to(x, y);
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current_position += vector(x, y);
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}
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}
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LineTo { x, y, abs } => {
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if abs {
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ctx.line_to(x, y);
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current_position = point(x, y);
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} else {
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ctx.rel_line_to(x, y);
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current_position += vector(x, y);
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}
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}
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ClosePath { .. } => ctx.close_path(),
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CurveTo {
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x1,
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y1,
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x2,
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y2,
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x,
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y,
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abs,
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} => {
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ctx.set_dash(&[], 0.);
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match acc {
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0 => ctx.set_source_rgb(1., 0., 0.),
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1 => ctx.set_source_rgb(0., 1., 0.),
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2 => ctx.set_source_rgb(0., 0., 1.),
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3 => ctx.set_source_rgb(0., 0., 0.),
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_ => unreachable!(),
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}
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let curve = CubicBezierSegment {
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from: current_position,
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ctrl1: (vector(x1, y1)
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+ if !abs {
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current_position.to_vector()
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} else {
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Vector::zero()
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})
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.to_point(),
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ctrl2: (vector(x2, y2)
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+ if !abs {
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current_position.to_vector()
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} else {
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Vector::zero()
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})
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.to_point(),
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to: (vector(x, y)
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+ if !abs {
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current_position.to_vector()
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} else {
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Vector::zero()
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})
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.to_point(),
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};
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for segment in FlattenWithArcs::flattened(&curve, 0.02) {
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match segment {
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ArcOrLineSegment::Arc(svg_arc) => {
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let arc = svg_arc.to_arc();
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if svg_arc.flags.sweep {
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ctx.arc(
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arc.center.x,
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arc.center.y,
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arc.radii.x,
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arc.start_angle.radians,
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(arc.start_angle + arc.sweep_angle).radians,
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)
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} else {
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ctx.arc_negative(
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arc.center.x,
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arc.center.y,
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arc.radii.x,
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arc.start_angle.radians,
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(arc.start_angle + arc.sweep_angle).radians,
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)
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}
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}
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ArcOrLineSegment::Line(line) => ctx.line_to(line.to.x, line.to.y),
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}
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}
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ctx.stroke().unwrap();
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current_position = curve.to;
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ctx.set_dash(&[0.1], 0.);
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ctx.move_to(curve.from.x, curve.from.y);
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ctx.curve_to(
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curve.ctrl1.x,
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curve.ctrl1.y,
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curve.ctrl2.x,
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curve.ctrl2.y,
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curve.to.x,
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curve.to.y,
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);
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ctx.stroke().unwrap();
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acc += 1;
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}
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other => unimplemented!("{:?}", other),
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}
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}
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}
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}
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@ -0,0 +1,145 @@
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G21
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G90;svg#svg8 > g#layer1 > path
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G0 X1 Y9
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G1 X1.108112220817491 Y8.887981529182511 F300
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G1 X1.2153787137015988 Y8.768996286298401 F300
|
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G2 X1.4239916039361313 Y8.51350839606387 R5.11981430218831 F300
|
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G2 X1.7938566201357353 Y7.956143379864265 R4.835393156461376 F300
|
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G2 X1.9415770991666748 Y7.6677979008333255 R3.8134637231185913 F300
|
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G1 X2.0031742836480873 Y7.524169466351913 F300
|
||||
G1 X2.0554684608622846 Y7.382031539137715 F300
|
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G1 X2.0976139028758833 Y7.242229847124117 F300
|
||||
G1 X2.128764881755499 Y7.105610118244501 F300
|
||||
G1 X2.148075669567749 Y6.973018080432251 F300
|
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G2 X2.1547005383792515 Y6.8452994616207485 R1.2759926937417487 F300
|
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G2 X2.1397549853513067 Y6.668858900493001 R1.0008154063555685 F300
|
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G2 X2.0931488160479113 Y6.50733213111376 R0.7841189700439164 F300
|
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G2 X2.0122277651397247 Y6.363373418812364 R0.6809578083609312 F300
|
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G2 X1.8943375672974065 Y6.239637028918155 R0.6907022975872513 F300
|
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G1 X1.8206995803605288 Y6.186181662789164 F300
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Reference in new issue