| /* |
| * 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 "SkGeometry.h" |
| #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) { |
| 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 = 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::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); |
| } |