Clean up GrPathUtils
Removes unused code, including utilities for dealing with KLM functionals for the implicit cubic function. The implicit has proven to not be a very good tool for rendering cubics. Change-Id: I577b50a9eb296c52dc0101a20394480a4a008654 Reviewed-on: https://skia-review.googlesource.com/c/skia/+/329440 Reviewed-by: Greg Daniel <egdaniel@google.com> Commit-Queue: Chris Dalton <csmartdalton@google.com>
This commit is contained in:
Chris Dalton
Skia Commit-Bot
parent
81b270a659
commit
0e13db707f
@ -1,63 +0,0 @@
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/*
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* Copyright 2017 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "bench/Benchmark.h"
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#include "src/core/SkGeometry.h"
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#include "src/gpu/geometry/GrPathUtils.h"
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class CubicKLMBench : public Benchmark {
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public:
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CubicKLMBench(SkScalar x0, SkScalar y0, SkScalar x1, SkScalar y1,
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SkScalar x2, SkScalar y2, SkScalar x3, SkScalar y3) {
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fPoints[0].set(x0, y0);
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fPoints[1].set(x1, y1);
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fPoints[2].set(x2, y2);
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fPoints[3].set(x3, y3);
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fName = "cubic_klm_";
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switch (SkClassifyCubic(fPoints)) {
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case SkCubicType::kSerpentine:
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fName.append("serp");
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break;
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case SkCubicType::kLoop:
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fName.append("loop");
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break;
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default:
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SK_ABORT("Unexpected cubic type");
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break;
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}
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}
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bool isSuitableFor(Backend backend) override {
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return backend == kNonRendering_Backend;
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}
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const char* onGetName() override {
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return fName.c_str();
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}
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void onDraw(int loops, SkCanvas*) override {
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SkPoint dst[10];
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SkMatrix klm;
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int loopIdx;
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for (int i = 0; i < loops * 50000; ++i) {
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GrPathUtils::chopCubicAtLoopIntersection(fPoints, dst, &klm, &loopIdx);
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}
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}
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private:
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SkPoint fPoints[4];
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SkString fName;
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using INHERITED = Benchmark;
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};
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DEF_BENCH( return new CubicKLMBench(285.625f, 499.687f, 411.625f, 808.188f,
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1064.62f, 135.688f, 1042.63f, 585.187f); )
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DEF_BENCH( return new CubicKLMBench(635.625f, 614.687f, 171.625f, 236.188f,
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1064.62f, 135.688f, 516.625f, 570.187f); )
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@ -38,7 +38,6 @@ bench_sources = [
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"$_bench/ControlBench.cpp",
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"$_bench/CoverageBench.cpp",
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"$_bench/CreateBackendTextureBench.cpp",
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"$_bench/CubicKLMBench.cpp",
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"$_bench/CubicMapBench.cpp",
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"$_bench/DDLRecorderBench.cpp",
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"$_bench/DashBench.cpp",
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@ -67,7 +67,6 @@ class CCPRGeometryView : public Sample {
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PrimitiveType fPrimitiveType = PrimitiveType::kCubics;
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SkCubicType fCubicType;
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SkMatrix fCubicKLM;
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SkPoint fPoints[4] = {
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{100.05f, 100.05f}, {400.75f, 100.05f}, {400.75f, 300.95f}, {100.05f, 300.95f}};
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@ -154,27 +153,6 @@ private:
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GrGLSLFragmentProcessor* onCreateGLSLInstance() const override { return new Impl; }
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};
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static void draw_klm_line(int w, int h, SkCanvas* canvas, const SkScalar line[3], SkColor color) {
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SkPoint p1, p2;
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if (SkScalarAbs(line[1]) > SkScalarAbs(line[0])) {
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// Draw from vertical edge to vertical edge.
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p1 = {0, -line[2] / line[1]};
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p2 = {(SkScalar)w, (-line[2] - w * line[0]) / line[1]};
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} else {
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// Draw from horizontal edge to horizontal edge.
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p1 = {-line[2] / line[0], 0};
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p2 = {(-line[2] - h * line[1]) / line[0], (SkScalar)h};
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}
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SkPaint linePaint;
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linePaint.setColor(color);
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linePaint.setAlpha(128);
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linePaint.setStyle(SkPaint::kStroke_Style);
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linePaint.setStrokeWidth(0);
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linePaint.setAntiAlias(true);
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canvas->drawLine(p1, p2, linePaint);
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}
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void CCPRGeometryView::onDrawContent(SkCanvas* canvas) {
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canvas->clear(SK_ColorBLACK);
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@ -248,12 +226,6 @@ void CCPRGeometryView::onDrawContent(SkCanvas* canvas) {
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if (PrimitiveType::kCubics == fPrimitiveType) {
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canvas->drawPoints(SkCanvas::kPoints_PointMode, 4, fPoints, pointsPaint);
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if (!fDoStroke) {
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int w = this->width(), h = this->height();
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draw_klm_line(w, h, canvas, &fCubicKLM[0], SK_ColorYELLOW);
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draw_klm_line(w, h, canvas, &fCubicKLM[3], SK_ColorBLUE);
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draw_klm_line(w, h, canvas, &fCubicKLM[6], SK_ColorRED);
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}
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} else {
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canvas->drawPoints(SkCanvas::kPoints_PointMode, 2, fPoints, pointsPaint);
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canvas->drawPoints(SkCanvas::kPoints_PointMode, 1, fPoints + 3, pointsPaint);
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@ -274,8 +246,6 @@ void CCPRGeometryView::updateGpuData() {
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fPath.moveTo(fPoints[0]);
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if (PrimitiveType::kCubics == fPrimitiveType) {
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double t[2], s[2];
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fCubicType = GrPathUtils::getCubicKLM(fPoints, &fCubicKLM, t, s);
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GrCCFillGeometry geometry;
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geometry.beginContour(fPoints[0]);
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geometry.cubicTo(fPoints, kDebugBloat / 2, kDebugBloat / 2);
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@ -162,54 +162,6 @@ uint32_t GrPathUtils::generateCubicPoints(const SkPoint& p0,
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return a + b;
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}
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int GrPathUtils::worstCasePointCount(const SkPath& path, int* subpaths, SkScalar tol) {
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// You should have called scaleToleranceToSrc, which guarantees this
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SkASSERT(tol >= gMinCurveTol);
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int pointCount = 0;
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*subpaths = 1;
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bool first = true;
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SkPath::Iter iter(path, false);
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SkPath::Verb verb;
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SkPoint pts[4];
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while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
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switch (verb) {
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case SkPath::kLine_Verb:
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pointCount += 1;
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break;
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case SkPath::kConic_Verb: {
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SkScalar weight = iter.conicWeight();
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SkAutoConicToQuads converter;
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const SkPoint* quadPts = converter.computeQuads(pts, weight, tol);
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for (int i = 0; i < converter.countQuads(); ++i) {
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pointCount += quadraticPointCount(quadPts + 2*i, tol);
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}
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[[fallthrough]];
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}
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case SkPath::kQuad_Verb:
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pointCount += quadraticPointCount(pts, tol);
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break;
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case SkPath::kCubic_Verb:
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pointCount += cubicPointCount(pts, tol);
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break;
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case SkPath::kMove_Verb:
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pointCount += 1;
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if (!first) {
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++(*subpaths);
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}
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break;
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default:
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break;
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}
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first = false;
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}
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return pointCount;
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}
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void GrPathUtils::QuadUVMatrix::set(const SkPoint qPts[3]) {
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SkMatrix m;
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// We want M such that M * xy_pt = uv_pt
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@ -631,230 +583,3 @@ void GrPathUtils::convertCubicToQuadsConstrainToTangents(const SkPoint p[4],
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convert_noninflect_cubic_to_quads_with_constraint(cubic, tolSqd, dir, quads);
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}
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}
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////////////////////////////////////////////////////////////////////////////////
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using ExcludedTerm = GrPathUtils::ExcludedTerm;
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ExcludedTerm GrPathUtils::calcCubicInverseTransposePowerBasisMatrix(const SkPoint p[4],
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SkMatrix* out) {
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static_assert(SK_SCALAR_IS_FLOAT);
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// First convert the bezier coordinates p[0..3] to power basis coefficients X,Y(,W=[0 0 0 1]).
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// M3 is the matrix that does this conversion. The homogeneous equation for the cubic becomes:
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//
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// | X Y 0 |
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// C(t,s) = [t^3 t^2*s t*s^2 s^3] * | . . 0 |
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// | . . 0 |
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// | . . 1 |
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//
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const Sk4f M3[3] = {Sk4f(-1, 3, -3, 1),
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Sk4f(3, -6, 3, 0),
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Sk4f(-3, 3, 0, 0)};
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// 4th col of M3 = Sk4f(1, 0, 0, 0)};
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Sk4f X(p[3].x(), 0, 0, 0);
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Sk4f Y(p[3].y(), 0, 0, 0);
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for (int i = 2; i >= 0; --i) {
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X += M3[i] * p[i].x();
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Y += M3[i] * p[i].y();
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}
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// The matrix is 3x4. In order to invert it, we first need to make it square by throwing out one
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// of the middle two rows. We toss the row that leaves us with the largest absolute determinant.
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// Since the right column will be [0 0 1], the respective determinants reduce to x0*y2 - y0*x2
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// and x0*y1 - y0*x1.
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SkScalar dets[4];
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Sk4f D = SkNx_shuffle<0,0,2,1>(X) * SkNx_shuffle<2,1,0,0>(Y);
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D -= SkNx_shuffle<2,3,0,1>(D);
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D.store(dets);
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ExcludedTerm skipTerm = SkScalarAbs(dets[0]) > SkScalarAbs(dets[1]) ?
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ExcludedTerm::kQuadraticTerm : ExcludedTerm::kLinearTerm;
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SkScalar det = dets[ExcludedTerm::kQuadraticTerm == skipTerm ? 0 : 1];
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if (0 == det) {
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return ExcludedTerm::kNonInvertible;
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}
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SkScalar rdet = 1 / det;
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// Compute the inverse-transpose of the power basis matrix with the 'skipRow'th row removed.
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// Since W=[0 0 0 1], it follows that our corresponding solution will be equal to:
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//
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// | y1 -x1 x1*y2 - y1*x2 |
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// 1/det * | -y0 x0 -x0*y2 + y0*x2 |
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// | 0 0 det |
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//
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SkScalar x[4], y[4], z[4];
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X.store(x);
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Y.store(y);
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(X * SkNx_shuffle<3,3,3,3>(Y) - Y * SkNx_shuffle<3,3,3,3>(X)).store(z);
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int middleRow = ExcludedTerm::kQuadraticTerm == skipTerm ? 2 : 1;
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out->setAll( y[middleRow] * rdet, -x[middleRow] * rdet, z[middleRow] * rdet,
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-y[0] * rdet, x[0] * rdet, -z[0] * rdet,
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0, 0, 1);
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return skipTerm;
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}
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inline static void calc_serp_kcoeffs(SkScalar tl, SkScalar sl, SkScalar tm, SkScalar sm,
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ExcludedTerm skipTerm, SkScalar outCoeffs[3]) {
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SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
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outCoeffs[0] = 0;
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outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? sl*sm : -tl*sm - tm*sl;
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outCoeffs[2] = tl*tm;
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}
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inline static void calc_serp_lmcoeffs(SkScalar t, SkScalar s, ExcludedTerm skipTerm,
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SkScalar outCoeffs[3]) {
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SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
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outCoeffs[0] = -s*s*s;
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outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? 3*s*s*t : -3*s*t*t;
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outCoeffs[2] = t*t*t;
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}
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inline static void calc_loop_kcoeffs(SkScalar td, SkScalar sd, SkScalar te, SkScalar se,
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SkScalar tdse, SkScalar tesd, ExcludedTerm skipTerm,
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SkScalar outCoeffs[3]) {
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SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
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outCoeffs[0] = 0;
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outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? sd*se : -tdse - tesd;
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outCoeffs[2] = td*te;
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}
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inline static void calc_loop_lmcoeffs(SkScalar t2, SkScalar s2, SkScalar t1, SkScalar s1,
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SkScalar t2s1, SkScalar t1s2, ExcludedTerm skipTerm,
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SkScalar outCoeffs[3]) {
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SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
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outCoeffs[0] = -s2*s2*s1;
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outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? s2 * (2*t2s1 + t1s2)
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: -t2 * (t2s1 + 2*t1s2);
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outCoeffs[2] = t2*t2*t1;
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}
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// For the case when a cubic bezier is actually a quadratic. We duplicate k in l so that the
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// implicit becomes:
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//
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// k^3 - l*m == k^3 - l*k == k * (k^2 - l)
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//
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// In the quadratic case we can simply assign fixed values at each control point:
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//
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// | ..K.. | | pts[0] pts[1] pts[2] pts[3] | | 0 1/3 2/3 1 |
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// | ..L.. | * | . . . . | == | 0 0 1/3 1 |
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// | ..K.. | | 1 1 1 1 | | 0 1/3 2/3 1 |
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//
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static void calc_quadratic_klm(const SkPoint pts[4], double d3, SkMatrix* klm) {
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SkMatrix klmAtPts;
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klmAtPts.setAll(0, 1.f/3, 1,
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0, 0, 1,
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0, 1.f/3, 1);
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SkMatrix inversePts;
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inversePts.setAll(pts[0].x(), pts[1].x(), pts[3].x(),
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pts[0].y(), pts[1].y(), pts[3].y(),
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1, 1, 1);
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SkAssertResult(inversePts.invert(&inversePts));
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klm->setConcat(klmAtPts, inversePts);
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// If d3 > 0 we need to flip the orientation of our curve
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// This is done by negating the k and l values
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if (d3 > 0) {
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klm->postScale(-1, -1);
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}
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}
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// For the case when a cubic bezier is actually a line. We set K=0, L=1, M=-line, which results in
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// the following implicit:
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//
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// k^3 - l*m == 0^3 - 1*(-line) == -(-line) == line
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//
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static void calc_line_klm(const SkPoint pts[4], SkMatrix* klm) {
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SkScalar ny = pts[0].x() - pts[3].x();
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SkScalar nx = pts[3].y() - pts[0].y();
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SkScalar k = nx * pts[0].x() + ny * pts[0].y();
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klm->setAll( 0, 0, 0,
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0, 0, 1,
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-nx, -ny, k);
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}
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SkCubicType GrPathUtils::getCubicKLM(const SkPoint src[4], SkMatrix* klm, double tt[2],
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double ss[2]) {
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double d[4];
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SkCubicType type = SkClassifyCubic(src, tt, ss, d);
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if (SkCubicType::kLineOrPoint == type) {
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calc_line_klm(src, klm);
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return SkCubicType::kLineOrPoint;
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}
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if (SkCubicType::kQuadratic == type) {
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calc_quadratic_klm(src, d[3], klm);
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return SkCubicType::kQuadratic;
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}
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SkMatrix CIT;
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ExcludedTerm skipTerm = calcCubicInverseTransposePowerBasisMatrix(src, &CIT);
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if (ExcludedTerm::kNonInvertible == skipTerm) {
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// This could technically also happen if the curve were quadratic, but SkClassifyCubic
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// should have detected that case already with tolerance.
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calc_line_klm(src, klm);
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return SkCubicType::kLineOrPoint;
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}
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const SkScalar t0 = static_cast<SkScalar>(tt[0]), t1 = static_cast<SkScalar>(tt[1]),
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s0 = static_cast<SkScalar>(ss[0]), s1 = static_cast<SkScalar>(ss[1]);
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SkMatrix klmCoeffs;
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switch (type) {
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case SkCubicType::kCuspAtInfinity:
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SkASSERT(1 == t1 && 0 == s1); // Infinity.
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[[fallthrough]];
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case SkCubicType::kLocalCusp:
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case SkCubicType::kSerpentine:
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calc_serp_kcoeffs(t0, s0, t1, s1, skipTerm, &klmCoeffs[0]);
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calc_serp_lmcoeffs(t0, s0, skipTerm, &klmCoeffs[3]);
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calc_serp_lmcoeffs(t1, s1, skipTerm, &klmCoeffs[6]);
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break;
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case SkCubicType::kLoop: {
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const SkScalar tdse = t0 * s1;
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const SkScalar tesd = t1 * s0;
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calc_loop_kcoeffs(t0, s0, t1, s1, tdse, tesd, skipTerm, &klmCoeffs[0]);
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calc_loop_lmcoeffs(t0, s0, t1, s1, tdse, tesd, skipTerm, &klmCoeffs[3]);
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calc_loop_lmcoeffs(t1, s1, t0, s0, tesd, tdse, skipTerm, &klmCoeffs[6]);
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break;
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}
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default:
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SK_ABORT("Unexpected cubic type.");
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break;
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}
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klm->setConcat(klmCoeffs, CIT);
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return type;
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}
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int GrPathUtils::chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10], SkMatrix* klm,
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int* loopIndex) {
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SkSTArray<2, SkScalar> chops;
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*loopIndex = -1;
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||||
|
||||
double t[2], s[2];
|
||||
if (SkCubicType::kLoop == GrPathUtils::getCubicKLM(src, klm, t, s)) {
|
||||
SkScalar t0 = static_cast<SkScalar>(t[0] / s[0]);
|
||||
SkScalar t1 = static_cast<SkScalar>(t[1] / s[1]);
|
||||
SkASSERT(t0 <= t1); // Technically t0 != t1 in a loop, but there may be FP error.
|
||||
|
||||
if (t0 < 1 && t1 > 0) {
|
||||
*loopIndex = 0;
|
||||
if (t0 > 0) {
|
||||
chops.push_back(t0);
|
||||
*loopIndex = 1;
|
||||
}
|
||||
if (t1 < 1) {
|
||||
chops.push_back(t1);
|
||||
*loopIndex = chops.count() - 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
SkChopCubicAt(src, dst, chops.begin(), chops.count());
|
||||
return chops.count() + 1;
|
||||
}
|
||||
|
||||
@ -19,199 +19,110 @@ class SkMatrix;
|
||||
* Utilities for evaluating paths.
|
||||
*/
|
||||
namespace GrPathUtils {
|
||||
// Very small tolerances will be increased to a minimum threshold value, to avoid division
|
||||
// problems in subsequent math.
|
||||
SkScalar scaleToleranceToSrc(SkScalar devTol,
|
||||
const SkMatrix& viewM,
|
||||
const SkRect& pathBounds);
|
||||
|
||||
int worstCasePointCount(const SkPath&,
|
||||
int* subpaths,
|
||||
SkScalar tol);
|
||||
// Very small tolerances will be increased to a minimum threshold value, to avoid division problems
|
||||
// in subsequent math.
|
||||
SkScalar scaleToleranceToSrc(SkScalar devTol,
|
||||
const SkMatrix& viewM,
|
||||
const SkRect& pathBounds);
|
||||
|
||||
uint32_t quadraticPointCount(const SkPoint points[], SkScalar tol);
|
||||
uint32_t quadraticPointCount(const SkPoint points[], SkScalar tol);
|
||||
|
||||
uint32_t generateQuadraticPoints(const SkPoint& p0,
|
||||
const SkPoint& p1,
|
||||
const SkPoint& p2,
|
||||
SkScalar tolSqd,
|
||||
SkPoint** points,
|
||||
uint32_t pointsLeft);
|
||||
|
||||
uint32_t cubicPointCount(const SkPoint points[], SkScalar tol);
|
||||
|
||||
uint32_t generateCubicPoints(const SkPoint& p0,
|
||||
uint32_t generateQuadraticPoints(const SkPoint& p0,
|
||||
const SkPoint& p1,
|
||||
const SkPoint& p2,
|
||||
const SkPoint& p3,
|
||||
SkScalar tolSqd,
|
||||
SkPoint** points,
|
||||
uint32_t pointsLeft);
|
||||
|
||||
// A 2x3 matrix that goes from the 2d space coordinates to UV space where
|
||||
// u^2-v = 0 specifies the quad. The matrix is determined by the control
|
||||
// points of the quadratic.
|
||||
class QuadUVMatrix {
|
||||
public:
|
||||
QuadUVMatrix() {}
|
||||
// Initialize the matrix from the control pts
|
||||
QuadUVMatrix(const SkPoint controlPts[3]) { this->set(controlPts); }
|
||||
void set(const SkPoint controlPts[3]);
|
||||
uint32_t cubicPointCount(const SkPoint points[], SkScalar tol);
|
||||
|
||||
/**
|
||||
* Applies the matrix to vertex positions to compute UV coords.
|
||||
*
|
||||
* vertices is a pointer to the first vertex.
|
||||
* vertexCount is the number of vertices.
|
||||
* stride is the size of each vertex.
|
||||
* uvOffset is the offset of the UV values within each vertex.
|
||||
*/
|
||||
void apply(void* vertices, int vertexCount, size_t stride, size_t uvOffset) const {
|
||||
intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices);
|
||||
intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + uvOffset;
|
||||
float sx = fM[0];
|
||||
float kx = fM[1];
|
||||
float tx = fM[2];
|
||||
float ky = fM[3];
|
||||
float sy = fM[4];
|
||||
float ty = fM[5];
|
||||
for (int i = 0; i < vertexCount; ++i) {
|
||||
const SkPoint* xy = reinterpret_cast<const SkPoint*>(xyPtr);
|
||||
SkPoint* uv = reinterpret_cast<SkPoint*>(uvPtr);
|
||||
uv->fX = sx * xy->fX + kx * xy->fY + tx;
|
||||
uv->fY = ky * xy->fX + sy * xy->fY + ty;
|
||||
xyPtr += stride;
|
||||
uvPtr += stride;
|
||||
}
|
||||
uint32_t generateCubicPoints(const SkPoint& p0,
|
||||
const SkPoint& p1,
|
||||
const SkPoint& p2,
|
||||
const SkPoint& p3,
|
||||
SkScalar tolSqd,
|
||||
SkPoint** points,
|
||||
uint32_t pointsLeft);
|
||||
|
||||
// A 2x3 matrix that goes from the 2d space coordinates to UV space where u^2-v = 0 specifies the
|
||||
// quad. The matrix is determined by the control points of the quadratic.
|
||||
class QuadUVMatrix {
|
||||
public:
|
||||
QuadUVMatrix() {}
|
||||
// Initialize the matrix from the control pts
|
||||
QuadUVMatrix(const SkPoint controlPts[3]) { this->set(controlPts); }
|
||||
void set(const SkPoint controlPts[3]);
|
||||
|
||||
/**
|
||||
* Applies the matrix to vertex positions to compute UV coords.
|
||||
*
|
||||
* vertices is a pointer to the first vertex.
|
||||
* vertexCount is the number of vertices.
|
||||
* stride is the size of each vertex.
|
||||
* uvOffset is the offset of the UV values within each vertex.
|
||||
*/
|
||||
void apply(void* vertices, int vertexCount, size_t stride, size_t uvOffset) const {
|
||||
intptr_t xyPtr = reinterpret_cast<intptr_t>(vertices);
|
||||
intptr_t uvPtr = reinterpret_cast<intptr_t>(vertices) + uvOffset;
|
||||
float sx = fM[0];
|
||||
float kx = fM[1];
|
||||
float tx = fM[2];
|
||||
float ky = fM[3];
|
||||
float sy = fM[4];
|
||||
float ty = fM[5];
|
||||
for (int i = 0; i < vertexCount; ++i) {
|
||||
const SkPoint* xy = reinterpret_cast<const SkPoint*>(xyPtr);
|
||||
SkPoint* uv = reinterpret_cast<SkPoint*>(uvPtr);
|
||||
uv->fX = sx * xy->fX + kx * xy->fY + tx;
|
||||
uv->fY = ky * xy->fX + sy * xy->fY + ty;
|
||||
xyPtr += stride;
|
||||
uvPtr += stride;
|
||||
}
|
||||
private:
|
||||
float fM[6];
|
||||
};
|
||||
}
|
||||
private:
|
||||
float fM[6];
|
||||
};
|
||||
|
||||
// Input is 3 control points and a weight for a bezier conic. Calculates the
|
||||
// three linear functionals (K,L,M) that represent the implicit equation of the
|
||||
// conic, k^2 - lm.
|
||||
//
|
||||
// Output: klm holds the linear functionals K,L,M as row vectors:
|
||||
//
|
||||
// | ..K.. | | x | | k |
|
||||
// | ..L.. | * | y | == | l |
|
||||
// | ..M.. | | 1 | | m |
|
||||
//
|
||||
void getConicKLM(const SkPoint p[3], const SkScalar weight, SkMatrix* klm);
|
||||
// Input is 3 control points and a weight for a bezier conic. Calculates the three linear
|
||||
// functionals (K,L,M) that represent the implicit equation of the conic, k^2 - lm.
|
||||
//
|
||||
// Output: klm holds the linear functionals K,L,M as row vectors:
|
||||
//
|
||||
// | ..K.. | | x | | k |
|
||||
// | ..L.. | * | y | == | l |
|
||||
// | ..M.. | | 1 | | m |
|
||||
//
|
||||
void getConicKLM(const SkPoint p[3], const SkScalar weight, SkMatrix* klm);
|
||||
|
||||
// Converts a cubic into a sequence of quads. If working in device space
|
||||
// use tolScale = 1, otherwise set based on stretchiness of the matrix. The
|
||||
// result is sets of 3 points in quads. This will preserve the starting and
|
||||
// ending tangent vectors (modulo FP precision).
|
||||
void convertCubicToQuads(const SkPoint p[4],
|
||||
SkScalar tolScale,
|
||||
SkTArray<SkPoint, true>* quads);
|
||||
// Converts a cubic into a sequence of quads. If working in device space use tolScale = 1, otherwise
|
||||
// set based on stretchiness of the matrix. The result is sets of 3 points in quads. This will
|
||||
// preserve the starting and ending tangent vectors (modulo FP precision).
|
||||
void convertCubicToQuads(const SkPoint p[4],
|
||||
SkScalar tolScale,
|
||||
SkTArray<SkPoint, true>* quads);
|
||||
|
||||
// When we approximate a cubic {a,b,c,d} with a quadratic we may have to
|
||||
// ensure that the new control point lies between the lines ab and cd. The
|
||||
// convex path renderer requires this. It starts with a path where all the
|
||||
// control points taken together form a convex polygon. It relies on this
|
||||
// property and the quadratic approximation of cubics step cannot alter it.
|
||||
// This variation enforces this constraint. The cubic must be simple and dir
|
||||
// must specify the orientation of the contour containing the cubic.
|
||||
void convertCubicToQuadsConstrainToTangents(const SkPoint p[4],
|
||||
SkScalar tolScale,
|
||||
SkPathFirstDirection dir,
|
||||
SkTArray<SkPoint, true>* quads);
|
||||
// When we approximate a cubic {a,b,c,d} with a quadratic we may have to ensure that the new control
|
||||
// point lies between the lines ab and cd. The convex path renderer requires this. It starts with a
|
||||
// path where all the control points taken together form a convex polygon. It relies on this
|
||||
// property and the quadratic approximation of cubics step cannot alter it. This variation enforces
|
||||
// this constraint. The cubic must be simple and dir must specify the orientation of the contour
|
||||
// containing the cubic.
|
||||
void convertCubicToQuadsConstrainToTangents(const SkPoint p[4],
|
||||
SkScalar tolScale,
|
||||
SkPathFirstDirection dir,
|
||||
SkTArray<SkPoint, true>* quads);
|
||||
|
||||
enum class ExcludedTerm {
|
||||
kNonInvertible,
|
||||
kQuadraticTerm,
|
||||
kLinearTerm
|
||||
};
|
||||
// When tessellating curved paths into linear segments, this defines the maximum distance in screen
|
||||
// space which a segment may deviate from the mathematically correct value. Above this value, the
|
||||
// segment will be subdivided.
|
||||
// This value was chosen to approximate the supersampling accuracy of the raster path (16 samples,
|
||||
// or one quarter pixel).
|
||||
static const SkScalar kDefaultTolerance = SkDoubleToScalar(0.25);
|
||||
|
||||
// Computes the inverse-transpose of the cubic's power basis matrix, after removing a specific
|
||||
// row of coefficients.
|
||||
//
|
||||
// E.g. if the cubic is defined in power basis form as follows:
|
||||
//
|
||||
// | x3 y3 0 |
|
||||
// C(t,s) = [t^3 t^2*s t*s^2 s^3] * | x2 y2 0 |
|
||||
// | x1 y1 0 |
|
||||
// | x0 y0 1 |
|
||||
//
|
||||
// And the excluded term is "kQuadraticTerm", then the resulting inverse-transpose will be:
|
||||
//
|
||||
// | x3 y3 0 | -1 T
|
||||
// | x1 y1 0 |
|
||||
// | x0 y0 1 |
|
||||
//
|
||||
// (The term to exclude is chosen based on maximizing the resulting matrix determinant.)
|
||||
//
|
||||
// This can be used to find the KLM linear functionals:
|
||||
//
|
||||
// | ..K.. | | ..kcoeffs.. |
|
||||
// | ..L.. | = | ..lcoeffs.. | * inverse_transpose_power_basis_matrix
|
||||
// | ..M.. | | ..mcoeffs.. |
|
||||
//
|
||||
// NOTE: the same term that was excluded here must also be removed from the corresponding column
|
||||
// of the klmcoeffs matrix.
|
||||
//
|
||||
// Returns which row of coefficients was removed, or kNonInvertible if the cubic was degenerate.
|
||||
ExcludedTerm calcCubicInverseTransposePowerBasisMatrix(const SkPoint p[4], SkMatrix* out);
|
||||
// We guarantee that no quad or cubic will ever produce more than this many points
|
||||
static const int kMaxPointsPerCurve = 1 << 10;
|
||||
|
||||
// Computes the KLM linear functionals for the cubic implicit form. The "right" side of the
|
||||
// curve (when facing in the direction of increasing parameter values) will be the area that
|
||||
// satisfies:
|
||||
//
|
||||
// k^3 < l*m
|
||||
//
|
||||
// Output:
|
||||
//
|
||||
// klm: Holds the linear functionals K,L,M as row vectors:
|
||||
//
|
||||
// | ..K.. | | x | | k |
|
||||
// | ..L.. | * | y | == | l |
|
||||
// | ..M.. | | 1 | | m |
|
||||
//
|
||||
// NOTE: the KLM lines are calculated in the same space as the input control points. If you
|
||||
// transform the points the lines will also need to be transformed. This can be done by mapping
|
||||
// the lines with the inverse-transpose of the matrix used to map the points.
|
||||
//
|
||||
// t[],s[]: These are set to the two homogeneous parameter values at which points the lines L&M
|
||||
// intersect with K (See SkClassifyCubic).
|
||||
//
|
||||
// Returns the cubic's classification.
|
||||
SkCubicType getCubicKLM(const SkPoint src[4], SkMatrix* klm, double t[2], double s[2]);
|
||||
|
||||
// Chops the cubic bezier passed in by src, at the double point (intersection point)
|
||||
// if the curve is a cubic loop. If it is a loop, there will be two parametric values for
|
||||
// the double point: t1 and t2. We chop the cubic at these values if they are between 0 and 1.
|
||||
// Return value:
|
||||
// Value of 3: t1 and t2 are both between (0,1), and dst will contain the three cubics,
|
||||
// dst[0..3], dst[3..6], and dst[6..9] if dst is not nullptr
|
||||
// Value of 2: Only one of t1 and t2 are between (0,1), and dst will contain the two cubics,
|
||||
// dst[0..3] and dst[3..6] if dst is not nullptr
|
||||
// Value of 1: Neither t1 nor t2 are between (0,1), and dst will contain the one original cubic,
|
||||
// src[0..3]
|
||||
//
|
||||
// Output:
|
||||
//
|
||||
// klm: Holds the linear functionals K,L,M as row vectors. (See getCubicKLM().)
|
||||
//
|
||||
// loopIndex: This value will tell the caller which of the chopped sections (if any) are the
|
||||
// actual loop. A value of -1 means there is no loop section. The caller can then use
|
||||
// this value to decide how/if they want to flip the orientation of this section.
|
||||
// The flip should be done by negating the k and l values as follows:
|
||||
//
|
||||
// KLM.postScale(-1, -1)
|
||||
int chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10], SkMatrix* klm,
|
||||
int* loopIndex);
|
||||
|
||||
// When tessellating curved paths into linear segments, this defines the maximum distance
|
||||
// in screen space which a segment may deviate from the mathmatically correct value.
|
||||
// Above this value, the segment will be subdivided.
|
||||
// This value was chosen to approximate the supersampling accuracy of the raster path (16
|
||||
// samples, or one quarter pixel).
|
||||
static const SkScalar kDefaultTolerance = SkDoubleToScalar(0.25);
|
||||
|
||||
// We guarantee that no quad or cubic will ever produce more than this many points
|
||||
static const int kMaxPointsPerCurve = 1 << 10;
|
||||
} // namespace GrPathUtils
|
||||
|
||||
#endif
|
||||
|
||||
Loading…
Reference in New Issue
Block a user