The Tor Browser: comparison gfx/skia/trunk/src/pathops/SkReduceOrder.cpp

--1:000000000000
+:7ecfa4f315df
+/*
+* Copyright 2012 Google Inc.
+*
+* Use of this source code is governed by a BSD-style license that can be
+* found in the LICENSE file.
+*/
+#include "SkReduceOrder.h"
+int SkReduceOrder::reduce(const SkDLine& line) {
+fLine[0] = line[0];
+int different = line[0] != line[1];
+fLine[1] = line[different];
+return 1 + different;
+}
+static int coincident_line(const SkDQuad& quad, SkDQuad& reduction) {
+reduction[0] = reduction[1] = quad[0];
+return 1;
+}
+static int reductionLineCount(const SkDQuad& reduction) {
+return 1 + !reduction[0].approximatelyEqual(reduction[1]);
+}
+static int vertical_line(const SkDQuad& quad, SkDQuad& reduction) {
+reduction[0] = quad[0];
+reduction[1] = quad[2];
+return reductionLineCount(reduction);
+}
+static int horizontal_line(const SkDQuad& quad, SkDQuad& reduction) {
+reduction[0] = quad[0];
+reduction[1] = quad[2];
+return reductionLineCount(reduction);
+}
+static int check_linear(const SkDQuad& quad,
+int minX, int maxX, int minY, int maxY, SkDQuad& reduction) {
+int startIndex = 0;
+int endIndex = 2;
+while (quad[startIndex].approximatelyEqual(quad[endIndex])) {
+--endIndex;
+if (endIndex == 0) {
+SkDebugf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
+SkASSERT(0);
+}
+}
+if (!quad.isLinear(startIndex, endIndex)) {
+return 0;
+}
+// four are colinear: return line formed by outside
+reduction[0] = quad[0];
+reduction[1] = quad[2];
+return reductionLineCount(reduction);
+}
+// reduce to a quadratic or smaller
+// look for identical points
+// look for all four points in a line
+// note that three points in a line doesn't simplify a cubic
+// look for approximation with single quadratic
+// save approximation with multiple quadratics for later
+int SkReduceOrder::reduce(const SkDQuad& quad) {
+int index, minX, maxX, minY, maxY;
+int minXSet, minYSet;
+minX = maxX = minY = maxY = 0;
+minXSet = minYSet = 0;
+for (index = 1; index < 3; ++index) {
+if (quad[minX].fX > quad[index].fX) {
+minX = index;
+}
+if (quad[minY].fY > quad[index].fY) {
+minY = index;
+}
+if (quad[maxX].fX < quad[index].fX) {
+maxX = index;
+}
+if (quad[maxY].fY < quad[index].fY) {
+maxY = index;
+}
+}
+for (index = 0; index < 3; ++index) {
+if (AlmostEqualUlps(quad[index].fX, quad[minX].fX)) {
+minXSet |= 1 << index;
+}
+if (AlmostEqualUlps(quad[index].fY, quad[minY].fY)) {
+minYSet |= 1 << index;
+}
+}
+if (minXSet == 0x7) {  // test for vertical line
+if (minYSet == 0x7) {  // return 1 if all four are coincident
+return coincident_line(quad, fQuad);
+}
+return vertical_line(quad, fQuad);
+}
+if (minYSet == 0xF) {  // test for horizontal line
+return horizontal_line(quad, fQuad);
+}
+int result = check_linear(quad, minX, maxX, minY, maxY, fQuad);
+if (result) {
+return result;
+}
+fQuad = quad;
+return 3;
+}
+////////////////////////////////////////////////////////////////////////////////////
+static int coincident_line(const SkDCubic& cubic, SkDCubic& reduction) {
+reduction[0] = reduction[1] = cubic[0];
+return 1;
+}
+static int reductionLineCount(const SkDCubic& reduction) {
+return 1 + !reduction[0].approximatelyEqual(reduction[1]);
+}
+static int vertical_line(const SkDCubic& cubic, SkDCubic& reduction) {
+reduction[0] = cubic[0];
+reduction[1] = cubic[3];
+return reductionLineCount(reduction);
+}
+static int horizontal_line(const SkDCubic& cubic, SkDCubic& reduction) {
+reduction[0] = cubic[0];
+reduction[1] = cubic[3];
+return reductionLineCount(reduction);
+}
+// check to see if it is a quadratic or a line
+static int check_quadratic(const SkDCubic& cubic, SkDCubic& reduction) {
+double dx10 = cubic[1].fX - cubic[0].fX;
+double dx23 = cubic[2].fX - cubic[3].fX;
+double midX = cubic[0].fX + dx10 * 3 / 2;
+double sideAx = midX - cubic[3].fX;
+double sideBx = dx23 * 3 / 2;
+if (approximately_zero(sideAx) ? !approximately_equal(sideAx, sideBx)
+: !AlmostEqualUlps(sideAx, sideBx)) {
+return 0;
+}
+double dy10 = cubic[1].fY - cubic[0].fY;
+double dy23 = cubic[2].fY - cubic[3].fY;
+double midY = cubic[0].fY + dy10 * 3 / 2;
+double sideAy = midY - cubic[3].fY;
+double sideBy = dy23 * 3 / 2;
+if (approximately_zero(sideAy) ? !approximately_equal(sideAy, sideBy)
+: !AlmostEqualUlps(sideAy, sideBy)) {
+return 0;
+}
+reduction[0] = cubic[0];
+reduction[1].fX = midX;
+reduction[1].fY = midY;
+reduction[2] = cubic[3];
+return 3;
+}
+static int check_linear(const SkDCubic& cubic,
+int minX, int maxX, int minY, int maxY, SkDCubic& reduction) {
+int startIndex = 0;
+int endIndex = 3;
+while (cubic[startIndex].approximatelyEqual(cubic[endIndex])) {
+--endIndex;
+if (endIndex == 0) {
+SkDebugf("%s shouldn't get here if all four points are about equal\n", __FUNCTION__);
+SkASSERT(0);
+}
+}
+if (!cubic.isLinear(startIndex, endIndex)) {
+return 0;
+}
+// four are colinear: return line formed by outside
+reduction[0] = cubic[0];
+reduction[1] = cubic[3];
+return reductionLineCount(reduction);
+}
+/* food for thought:
+http://objectmix.com/graphics/132906-fast-precision-driven-cubic-quadratic-piecewise-degree-reduction-algos-2-a.html
+Given points c1, c2, c3 and c4 of a cubic Bezier, the points of the
+corresponding quadratic Bezier are (given in convex combinations of
+points):
+q1 = (11/13)c1 + (3/13)c2 -(3/13)c3 + (2/13)c4
+q2 = -c1 + (3/2)c2 + (3/2)c3 - c4
+q3 = (2/13)c1 - (3/13)c2 + (3/13)c3 + (11/13)c4
+Of course, this curve does not interpolate the end-points, but it would
+be interesting to see the behaviour of such a curve in an applet.
+--
+Kalle Rutanen
+http://kaba.hilvi.org
+*/
+// reduce to a quadratic or smaller
+// look for identical points
+// look for all four points in a line
+// note that three points in a line doesn't simplify a cubic
+// look for approximation with single quadratic
+// save approximation with multiple quadratics for later
+int SkReduceOrder::reduce(const SkDCubic& cubic, Quadratics allowQuadratics) {
+int index, minX, maxX, minY, maxY;
+int minXSet, minYSet;
+minX = maxX = minY = maxY = 0;
+minXSet = minYSet = 0;
+for (index = 1; index < 4; ++index) {
+if (cubic[minX].fX > cubic[index].fX) {
+minX = index;
+}
+if (cubic[minY].fY > cubic[index].fY) {
+minY = index;
+}
+if (cubic[maxX].fX < cubic[index].fX) {
+maxX = index;
+}
+if (cubic[maxY].fY < cubic[index].fY) {
+maxY = index;
+}
+}
+for (index = 0; index < 4; ++index) {
+double cx = cubic[index].fX;
+double cy = cubic[index].fY;
+double denom = SkTMax(fabs(cx), SkTMax(fabs(cy),
+SkTMax(fabs(cubic[minX].fX), fabs(cubic[minY].fY))));
+if (denom == 0) {
+minXSet |= 1 << index;
+minYSet |= 1 << index;
+continue;
+}
+double inv = 1 / denom;
+if (approximately_equal_half(cx * inv, cubic[minX].fX * inv)) {
+minXSet |= 1 << index;
+}
+if (approximately_equal_half(cy * inv, cubic[minY].fY * inv)) {
+minYSet |= 1 << index;
+}
+}
+if (minXSet == 0xF) {  // test for vertical line
+if (minYSet == 0xF) {  // return 1 if all four are coincident
+return coincident_line(cubic, fCubic);
+}
+return vertical_line(cubic, fCubic);
+}
+if (minYSet == 0xF) {  // test for horizontal line
+return horizontal_line(cubic, fCubic);
+}
+int result = check_linear(cubic, minX, maxX, minY, maxY, fCubic);
+if (result) {
+return result;
+}
+if (allowQuadratics == SkReduceOrder::kAllow_Quadratics
+&& (result = check_quadratic(cubic, fCubic))) {
+return result;
+}
+fCubic = cubic;
+return 4;
+}
+SkPath::Verb SkReduceOrder::Quad(const SkPoint a[3], SkPoint* reducePts) {
+SkDQuad quad;
+quad.set(a);
+SkReduceOrder reducer;
+int order = reducer.reduce(quad);
+if (order == 2) {  // quad became line
+for (int index = 0; index < order; ++index) {
+*reducePts++ = reducer.fLine[index].asSkPoint();
+}
+}
+return SkPathOpsPointsToVerb(order - 1);
+}
+SkPath::Verb SkReduceOrder::Cubic(const SkPoint a[4], SkPoint* reducePts) {
+SkDCubic cubic;
+cubic.set(a);
+SkReduceOrder reducer;
+int order = reducer.reduce(cubic, kAllow_Quadratics);
+if (order == 2 || order == 3) {  // cubic became line or quad
+for (int index = 0; index < order; ++index) {
+*reducePts++ = reducer.fQuad[index].asSkPoint();
+}
+}
+return SkPathOpsPointsToVerb(order - 1);
+}

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comparison: gfx/skia/trunk/src/pathops/SkReduceOrder.cpp

gfx/skia/trunk/src/pathops/SkReduceOrder.cpp