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diff --git a/gfx/skia/skia/src/pathops/SkReduceOrder.cpp b/gfx/skia/skia/src/pathops/SkReduceOrder.cpp
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+/*
+ * 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 "src/pathops/SkReduceOrder.h"
+
+#include "include/core/SkPoint.h"
+#include "src/core/SkGeometry.h"
+#include "src/pathops/SkPathOpsPoint.h"
+#include "src/pathops/SkPathOpsTypes.h"
+
+#include <algorithm>
+#include <cmath>
+
+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) {
+ if (!quad.isLinear(0, 2)) {
+ 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 & 0x05) == 0x5 && (minYSet & 0x05) == 0x5) { // test for degenerate
+ // this quad starts and ends at the same place, so never contributes
+ // to the fill
+ return coincident_line(quad, fQuad);
+ }
+ if (minXSet == 0x7) { // test for vertical line
+ return vertical_line(quad, fQuad);
+ }
+ if (minYSet == 0x7) { // 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_Pin(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_Pin(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) {
+ if (!cubic.isLinear(0, 3)) {
+ 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 = std::max(fabs(cx), std::max(fabs(cy),
+ std::max(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::Conic(const SkConic& c, SkPoint* reducePts) {
+ SkPath::Verb verb = SkReduceOrder::Quad(c.fPts, reducePts);
+ if (verb > SkPath::kLine_Verb && c.fW == 1) {
+ return SkPath::kQuad_Verb;
+ }
+ return verb == SkPath::kQuad_Verb ? SkPath::kConic_Verb : verb;
+}
+
+SkPath::Verb SkReduceOrder::Cubic(const SkPoint a[4], SkPoint* reducePts) {
+ if (SkDPoint::ApproximatelyEqual(a[0], a[1]) && SkDPoint::ApproximatelyEqual(a[0], a[2])
+ && SkDPoint::ApproximatelyEqual(a[0], a[3])) {
+ reducePts[0] = a[0];
+ return SkPath::kMove_Verb;
+ }
+ 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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