Fall back to Newton's method instead of dividing by zero when finding critical
points during curve monotonic conversion. Closes #146.
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@ -503,6 +503,8 @@ impl Contour {
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}
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fn make_monotonic(&mut self) {
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debug!("--- make_monotonic() ---");
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let contour = self.take();
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self.bounds = contour.bounds;
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@ -550,6 +552,8 @@ impl Contour {
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}
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fn handle_cubic(contour: &mut Contour, segment: Segment) {
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debug!("handle_cubic({:?})", segment);
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match segment.as_cubic_segment().y_extrema() {
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(Some(t0), Some(t1)) => {
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let (segments_01, segment_2) = segment.as_cubic_segment().split(t1);
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@ -12,8 +12,11 @@
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use crate::basic::line_segment::LineSegmentF32;
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use crate::basic::point::Point2DF32;
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use crate::util::{self, EPSILON};
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use pathfinder_simd::default::F32x4;
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const MAX_NEWTON_ITERATIONS: u32 = 32;
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#[derive(Clone, Copy, Debug, PartialEq)]
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pub struct Segment {
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pub baseline: LineSegmentF32,
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@ -302,12 +305,35 @@ impl<'s> CubicSegment<'s> {
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let pxv0v1v2 = p0p1p2p3 - pxp0p1p2;
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let (v0, v1, v2) = (pxv0v1v2[1], pxv0v1v2[2], pxv0v1v2[3]);
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let (t0, t1);
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let (v0_to_v1, v2_to_v1) = (v0 - v1, v2 - v1);
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let discrim = f32::sqrt(v1 * v1 - v0 * v2);
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let denom = 1.0 / (v0_to_v1 + v2_to_v1);
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let denom = v0_to_v1 + v2_to_v1;
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let t0 = (v0_to_v1 + discrim) * denom;
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let t1 = (v0_to_v1 - discrim) * denom;
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if util::approx_eq(denom, 0.0) {
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// Let's not divide by zero (issue #146). Fall back to Newton's method.
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// FIXME(pcwalton): Can we have two roots here?
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let mut t = 0.5;
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for _ in 0..MAX_NEWTON_ITERATIONS {
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let dydt = 3.0 * ((denom * t - v0_to_v1 - v0_to_v1) * t + v0);
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if f32::abs(dydt) <= EPSILON {
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break
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}
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let d2ydt2 = 6.0 * (denom * t - v0_to_v1);
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t -= dydt / d2ydt2;
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}
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t0 = t;
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t1 = 0.0;
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debug!("... t=(newton) {}", t);
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} else {
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// Algebraically compute the values for t.
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let discrim = f32::sqrt(v1 * v1 - v0 * v2);
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let denom_recip = 1.0 / denom;
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t0 = (v0_to_v1 + discrim) * denom_recip;
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t1 = (v0_to_v1 - discrim) * denom_recip;
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debug!("... t=({} +/- {})/{} t0={} t1={}", v0_to_v1, discrim, denom, t0, t1);
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}
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return match (
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t0 > EPSILON && t0 < 1.0 - EPSILON,
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@ -318,8 +344,6 @@ impl<'s> CubicSegment<'s> {
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(false, true) => (Some(t1), None),
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(true, true) => (Some(f32::min(t0, t1)), Some(f32::max(t0, t1))),
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};
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const EPSILON: f32 = 0.001;
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}
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#[inline]
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@ -12,6 +12,14 @@
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use std::f32;
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pub const EPSILON: f32 = 0.001;
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/// Approximate equality.
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#[inline]
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pub fn approx_eq(a: f32, b: f32) -> bool {
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f32::abs(a - b) <= EPSILON
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}
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/// Linear interpolation.
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#[inline]
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pub fn lerp(a: f32, b: f32, t: f32) -> f32 {
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