2019-01-11 18:50:09 -05:00
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// pathfinder/geometry/src/segment.rs
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//
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// Copyright © 2019 The Pathfinder Project Developers.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Line or curve segments, optimized with SIMD.
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use crate::line_segment::LineSegmentF32;
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use crate::point::Point2DF32;
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use crate::simd::F32x4;
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2019-01-11 18:50:09 -05:00
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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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pub ctrl: LineSegmentF32,
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pub kind: SegmentKind,
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pub flags: SegmentFlags,
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}
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impl Segment {
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#[inline]
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pub fn none() -> Segment {
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Segment {
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baseline: LineSegmentF32::default(),
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ctrl: LineSegmentF32::default(),
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kind: SegmentKind::None,
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flags: SegmentFlags::empty(),
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}
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}
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#[inline]
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pub fn line(line: &LineSegmentF32) -> Segment {
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Segment {
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baseline: *line,
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ctrl: LineSegmentF32::default(),
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kind: SegmentKind::Line,
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flags: SegmentFlags::empty(),
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}
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}
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#[inline]
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pub fn quadratic(baseline: &LineSegmentF32, ctrl: &Point2DF32) -> Segment {
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Segment {
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baseline: *baseline,
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ctrl: LineSegmentF32::new(ctrl, &Point2DF32::default()),
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kind: SegmentKind::Cubic,
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flags: SegmentFlags::empty(),
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}
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}
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#[inline]
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pub fn cubic(baseline: &LineSegmentF32, ctrl: &LineSegmentF32) -> Segment {
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Segment {
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baseline: *baseline,
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ctrl: *ctrl,
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kind: SegmentKind::Cubic,
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flags: SegmentFlags::empty(),
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}
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}
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#[inline]
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pub fn as_line_segment(&self) -> LineSegmentF32 {
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debug_assert!(self.is_line());
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self.baseline
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}
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#[inline]
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pub fn is_none(&self) -> bool {
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self.kind == SegmentKind::None
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}
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#[inline]
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pub fn is_line(&self) -> bool {
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self.kind == SegmentKind::Line
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}
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#[inline]
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pub fn is_quadratic(&self) -> bool {
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self.kind == SegmentKind::Quadratic
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}
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#[inline]
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pub fn is_cubic(&self) -> bool {
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self.kind == SegmentKind::Cubic
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}
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#[inline]
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pub fn as_cubic_segment(&self) -> CubicSegment {
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debug_assert!(self.is_cubic());
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CubicSegment(self)
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}
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// FIXME(pcwalton): We should basically never use this function.
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// FIXME(pcwalton): Handle lines!
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#[inline]
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pub fn to_cubic(&self) -> Segment {
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if self.is_cubic() {
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return *self;
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}
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let mut new_segment = *self;
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let p1_2 = self.ctrl.from() + self.ctrl.from();
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new_segment.ctrl =
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LineSegmentF32::new(&(self.baseline.from() + p1_2), &(p1_2 + self.baseline.to()))
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.scale(1.0 / 3.0);
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new_segment
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}
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#[inline]
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pub fn reversed(&self) -> Segment {
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Segment {
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baseline: self.baseline.reversed(),
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ctrl: if self.is_quadratic() {
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self.ctrl
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} else {
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self.ctrl.reversed()
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},
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kind: self.kind,
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flags: self.flags,
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}
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}
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// Reverses if necessary so that the from point is above the to point. Calling this method
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// again will undo the transformation.
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#[inline]
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pub fn orient(&self, y_winding: i32) -> Segment {
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if y_winding >= 0 {
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*self
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} else {
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self.reversed()
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}
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}
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}
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[repr(u8)]
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pub enum SegmentKind {
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None,
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Line,
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Quadratic,
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Cubic,
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}
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bitflags! {
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pub struct SegmentFlags: u8 {
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const FIRST_IN_SUBPATH = 0x01;
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const CLOSES_SUBPATH = 0x02;
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}
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}
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#[derive(Clone, Copy, Debug)]
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pub struct CubicSegment<'s>(&'s Segment);
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impl<'s> CubicSegment<'s> {
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#[inline]
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pub fn flatten_once(self, tolerance: f32) -> Option<Segment> {
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let (baseline, ctrl) = (self.0.baseline.0, self.0.ctrl.0);
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let from_from = baseline.splat_low_half();
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let v0102 = ctrl - from_from;
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// v01.x v01.y v02.x v02.y
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// * v01.x v01.y v01.y v01.x
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// -------------------------
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// v01.x^2 v01.y^2 ad bc
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// | | | |
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// +-------+ +-----+
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// + -
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// v01 len^2 determinant
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let products = v0102 * F32x4::new(v0102[0], v0102[1], v0102[1], v0102[0]);
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let det = products[2] - products[3];
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if det == 0.0 {
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return None;
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}
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let s2inv = (products[0] + products[1]).sqrt() / det;
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2019-01-11 18:50:09 -05:00
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let t = 2.0 * ((tolerance / 3.0) * s2inv.abs()).sqrt();
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if t >= 1.0 - EPSILON || t == 0.0 {
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return None;
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}
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return Some(self.split_after(t));
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const EPSILON: f32 = 0.005;
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}
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#[inline]
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pub fn split(self, t: f32) -> (Segment, Segment) {
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let tttt = F32x4::splat(t);
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let p0p3 = self.0.baseline.0;
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let p1p2 = self.0.ctrl.0;
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let p0p1 = F32x4::new(p0p3[0], p0p3[1], p1p2[0], p1p2[1]);
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// p01 = lerp(p0, p1, t), p12 = lerp(p1, p2, t), p23 = lerp(p2, p3, t)
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let p01p12 = p0p1 + tttt * (p1p2 - p0p1);
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let pxxp23 = p1p2 + tttt * (p0p3 - p1p2);
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let p12p23 = F32x4::new(p01p12[2], p01p12[3], pxxp23[2], pxxp23[3]);
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// p012 = lerp(p01, p12, t), p123 = lerp(p12, p23, t)
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let p012p123 = p01p12 + tttt * (p12p23 - p01p12);
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let p123 = p012p123.splat_high_half();
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// p0123 = lerp(p012, p123, t)
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let p0123 = p012p123 + tttt * (p123 - p012p123);
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let baseline0 = F32x4::new(p0p3[0], p0p3[1], p0123[0], p0123[1]);
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let ctrl0 = F32x4::new(p01p12[0], p01p12[1], p012p123[0], p012p123[1]);
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let baseline1 = F32x4::new(p0123[0], p0123[1], p0p3[2], p0p3[3]);
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let ctrl1 = F32x4::new(p012p123[2], p012p123[3], p12p23[2], p12p23[3]);
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(Segment {
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baseline: LineSegmentF32(baseline0),
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ctrl: LineSegmentF32(ctrl0),
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kind: SegmentKind::Cubic,
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flags: self.0.flags & SegmentFlags::FIRST_IN_SUBPATH,
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}, Segment {
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baseline: LineSegmentF32(baseline1),
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ctrl: LineSegmentF32(ctrl1),
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kind: SegmentKind::Cubic,
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flags: self.0.flags & SegmentFlags::CLOSES_SUBPATH,
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})
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}
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#[inline]
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pub fn split_after(self, t: f32) -> Segment {
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self.split(t).1
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}
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#[inline]
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pub fn y_extrema(self) -> (Option<f32>, Option<f32>) {
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let (t0, t1);
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let p0p1p2p3 = F32x4::new(self.0.baseline.from_y(),
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self.0.ctrl.from_y(),
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self.0.ctrl.to_y(),
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self.0.baseline.to_y());
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let pxp0p1p2 = F32x4::new(self.0.baseline.from_y(),
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self.0.baseline.from_y(),
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self.0.ctrl.from_y(),
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self.0.ctrl.to_y());
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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 (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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t0 = (v0_to_v1 + discrim) * denom;
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t1 = (v0_to_v1 - discrim) * denom;
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return match (
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t0 > EPSILON && t0 < 1.0 - EPSILON,
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t1 > EPSILON && t1 < 1.0 - EPSILON,
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) {
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(false, false) => (None, None),
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(true, false) => (Some(t0), None),
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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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}
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