diff -r 000000000000 -r 6474c204b198 gfx/skia/trunk/src/pathops/SkDLineIntersection.cpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/gfx/skia/trunk/src/pathops/SkDLineIntersection.cpp Wed Dec 31 06:09:35 2014 +0100 @@ -0,0 +1,354 @@ +/* + * 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 "SkIntersections.h" +#include "SkPathOpsLine.h" + +/* Determine the intersection point of two lines. This assumes the lines are not parallel, + and that that the lines are infinite. + From http://en.wikipedia.org/wiki/Line-line_intersection + */ +SkDPoint SkIntersections::Line(const SkDLine& a, const SkDLine& b) { + double axLen = a[1].fX - a[0].fX; + double ayLen = a[1].fY - a[0].fY; + double bxLen = b[1].fX - b[0].fX; + double byLen = b[1].fY - b[0].fY; + double denom = byLen * axLen - ayLen * bxLen; + SkASSERT(denom); + double term1 = a[1].fX * a[0].fY - a[1].fY * a[0].fX; + double term2 = b[1].fX * b[0].fY - b[1].fY * b[0].fX; + SkDPoint p; + p.fX = (term1 * bxLen - axLen * term2) / denom; + p.fY = (term1 * byLen - ayLen * term2) / denom; + return p; +} + +void SkIntersections::cleanUpCoincidence() { + SkASSERT(fUsed == 2); + // both t values are good + bool startMatch = fT[0][0] == 0 && (fT[1][0] == 0 || fT[1][0] == 1); + bool endMatch = fT[0][1] == 1 && (fT[1][1] == 0 || fT[1][1] == 1); + if (startMatch || endMatch) { + removeOne(startMatch); + return; + } + // either t value is good + bool pStartMatch = fT[0][0] == 0 || fT[1][0] == 0 || fT[1][0] == 1; + bool pEndMatch = fT[0][1] == 1 || fT[1][1] == 0 || fT[1][1] == 1; + removeOne(pStartMatch || !pEndMatch); +} + +void SkIntersections::cleanUpParallelLines(bool parallel) { + while (fUsed > 2) { + removeOne(1); + } + if (fUsed == 2 && !parallel) { + bool startMatch = fT[0][0] == 0 || fT[1][0] == 0 || fT[1][0] == 1; + bool endMatch = fT[0][1] == 1 || fT[1][1] == 0 || fT[1][1] == 1; + if ((!startMatch && !endMatch) || approximately_equal(fT[0][0], fT[0][1])) { + SkASSERT(startMatch || endMatch); + removeOne(endMatch); + } + } +} + +void SkIntersections::computePoints(const SkDLine& line, int used) { + fPt[0] = line.ptAtT(fT[0][0]); + if ((fUsed = used) == 2) { + fPt[1] = line.ptAtT(fT[0][1]); + } +} + +int SkIntersections::intersectRay(const SkDLine& a, const SkDLine& b) { + fMax = 2; + SkDVector aLen = a[1] - a[0]; + SkDVector bLen = b[1] - b[0]; + /* Slopes match when denom goes to zero: + axLen / ayLen == bxLen / byLen + (ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen + byLen * axLen == ayLen * bxLen + byLen * axLen - ayLen * bxLen == 0 ( == denom ) + */ + double denom = bLen.fY * aLen.fX - aLen.fY * bLen.fX; + SkDVector ab0 = a[0] - b[0]; + double numerA = ab0.fY * bLen.fX - bLen.fY * ab0.fX; + double numerB = ab0.fY * aLen.fX - aLen.fY * ab0.fX; + numerA /= denom; + numerB /= denom; + int used; + if (!approximately_zero(denom)) { + fT[0][0] = numerA; + fT[1][0] = numerB; + used = 1; + } else { + /* See if the axis intercepts match: + ay - ax * ayLen / axLen == by - bx * ayLen / axLen + axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen) + axLen * ay - ax * ayLen == axLen * by - bx * ayLen + */ + if (!AlmostEqualUlps(aLen.fX * a[0].fY - aLen.fY * a[0].fX, + aLen.fX * b[0].fY - aLen.fY * b[0].fX)) { + return fUsed = 0; + } + // there's no great answer for intersection points for coincident rays, but return something + fT[0][0] = fT[1][0] = 0; + fT[1][0] = fT[1][1] = 1; + used = 2; + } + computePoints(a, used); + return fUsed; +} + +// note that this only works if both lines are neither horizontal nor vertical +int SkIntersections::intersect(const SkDLine& a, const SkDLine& b) { + fMax = 3; // note that we clean up so that there is no more than two in the end + // see if end points intersect the opposite line + double t; + for (int iA = 0; iA < 2; ++iA) { + if ((t = b.exactPoint(a[iA])) >= 0) { + insert(iA, t, a[iA]); + } + } + for (int iB = 0; iB < 2; ++iB) { + if ((t = a.exactPoint(b[iB])) >= 0) { + insert(t, iB, b[iB]); + } + } + /* Determine the intersection point of two line segments + Return FALSE if the lines don't intersect + from: http://paulbourke.net/geometry/lineline2d/ */ + double axLen = a[1].fX - a[0].fX; + double ayLen = a[1].fY - a[0].fY; + double bxLen = b[1].fX - b[0].fX; + double byLen = b[1].fY - b[0].fY; + /* Slopes match when denom goes to zero: + axLen / ayLen == bxLen / byLen + (ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen + byLen * axLen == ayLen * bxLen + byLen * axLen - ayLen * bxLen == 0 ( == denom ) + */ + double axByLen = axLen * byLen; + double ayBxLen = ayLen * bxLen; + // detect parallel lines the same way here and in SkOpAngle operator < + // so that non-parallel means they are also sortable + bool unparallel = fAllowNear ? NotAlmostEqualUlps(axByLen, ayBxLen) + : NotAlmostDequalUlps(axByLen, ayBxLen); + if (unparallel && fUsed == 0) { + double ab0y = a[0].fY - b[0].fY; + double ab0x = a[0].fX - b[0].fX; + double numerA = ab0y * bxLen - byLen * ab0x; + double numerB = ab0y * axLen - ayLen * ab0x; + double denom = axByLen - ayBxLen; + if (between(0, numerA, denom) && between(0, numerB, denom)) { + fT[0][0] = numerA / denom; + fT[1][0] = numerB / denom; + computePoints(a, 1); + } + } + if (fAllowNear || !unparallel) { + for (int iA = 0; iA < 2; ++iA) { + if ((t = b.nearPoint(a[iA])) >= 0) { + insert(iA, t, a[iA]); + } + } + for (int iB = 0; iB < 2; ++iB) { + if ((t = a.nearPoint(b[iB])) >= 0) { + insert(t, iB, b[iB]); + } + } + } + cleanUpParallelLines(!unparallel); + SkASSERT(fUsed <= 2); + return fUsed; +} + +static int horizontal_coincident(const SkDLine& line, double y) { + double min = line[0].fY; + double max = line[1].fY; + if (min > max) { + SkTSwap(min, max); + } + if (min > y || max < y) { + return 0; + } + if (AlmostEqualUlps(min, max) && max - min < fabs(line[0].fX - line[1].fX)) { + return 2; + } + return 1; +} + +static double horizontal_intercept(const SkDLine& line, double y) { + return SkPinT((y - line[0].fY) / (line[1].fY - line[0].fY)); +} + +int SkIntersections::horizontal(const SkDLine& line, double y) { + fMax = 2; + int horizontalType = horizontal_coincident(line, y); + if (horizontalType == 1) { + fT[0][0] = horizontal_intercept(line, y); + } else if (horizontalType == 2) { + fT[0][0] = 0; + fT[0][1] = 1; + } + return fUsed = horizontalType; +} + +int SkIntersections::horizontal(const SkDLine& line, double left, double right, + double y, bool flipped) { + fMax = 2; + // see if end points intersect the opposite line + double t; + const SkDPoint leftPt = { left, y }; + if ((t = line.exactPoint(leftPt)) >= 0) { + insert(t, (double) flipped, leftPt); + } + if (left != right) { + const SkDPoint rightPt = { right, y }; + if ((t = line.exactPoint(rightPt)) >= 0) { + insert(t, (double) !flipped, rightPt); + } + for (int index = 0; index < 2; ++index) { + if ((t = SkDLine::ExactPointH(line[index], left, right, y)) >= 0) { + insert((double) index, flipped ? 1 - t : t, line[index]); + } + } + } + int result = horizontal_coincident(line, y); + if (result == 1 && fUsed == 0) { + fT[0][0] = horizontal_intercept(line, y); + double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX); + if (between(left, xIntercept, right)) { + fT[1][0] = (xIntercept - left) / (right - left); + if (flipped) { + // OPTIMIZATION: ? instead of swapping, pass original line, use [1].fX - [0].fX + for (int index = 0; index < result; ++index) { + fT[1][index] = 1 - fT[1][index]; + } + } + fPt[0].fX = xIntercept; + fPt[0].fY = y; + fUsed = 1; + } + } + if (fAllowNear || result == 2) { + if ((t = line.nearPoint(leftPt)) >= 0) { + insert(t, (double) flipped, leftPt); + } + if (left != right) { + const SkDPoint rightPt = { right, y }; + if ((t = line.nearPoint(rightPt)) >= 0) { + insert(t, (double) !flipped, rightPt); + } + for (int index = 0; index < 2; ++index) { + if ((t = SkDLine::NearPointH(line[index], left, right, y)) >= 0) { + insert((double) index, flipped ? 1 - t : t, line[index]); + } + } + } + } + cleanUpParallelLines(result == 2); + return fUsed; +} + +static int vertical_coincident(const SkDLine& line, double x) { + double min = line[0].fX; + double max = line[1].fX; + if (min > max) { + SkTSwap(min, max); + } + if (!precisely_between(min, x, max)) { + return 0; + } + if (AlmostEqualUlps(min, max)) { + return 2; + } + return 1; +} + +static double vertical_intercept(const SkDLine& line, double x) { + return SkPinT((x - line[0].fX) / (line[1].fX - line[0].fX)); +} + +int SkIntersections::vertical(const SkDLine& line, double x) { + fMax = 2; + int verticalType = vertical_coincident(line, x); + if (verticalType == 1) { + fT[0][0] = vertical_intercept(line, x); + } else if (verticalType == 2) { + fT[0][0] = 0; + fT[0][1] = 1; + } + return fUsed = verticalType; +} + +int SkIntersections::vertical(const SkDLine& line, double top, double bottom, + double x, bool flipped) { + fMax = 2; + // see if end points intersect the opposite line + double t; + SkDPoint topPt = { x, top }; + if ((t = line.exactPoint(topPt)) >= 0) { + insert(t, (double) flipped, topPt); + } + if (top != bottom) { + SkDPoint bottomPt = { x, bottom }; + if ((t = line.exactPoint(bottomPt)) >= 0) { + insert(t, (double) !flipped, bottomPt); + } + for (int index = 0; index < 2; ++index) { + if ((t = SkDLine::ExactPointV(line[index], top, bottom, x)) >= 0) { + insert((double) index, flipped ? 1 - t : t, line[index]); + } + } + } + int result = vertical_coincident(line, x); + if (result == 1 && fUsed == 0) { + fT[0][0] = vertical_intercept(line, x); + double yIntercept = line[0].fY + fT[0][0] * (line[1].fY - line[0].fY); + if (between(top, yIntercept, bottom)) { + fT[1][0] = (yIntercept - top) / (bottom - top); + if (flipped) { + // OPTIMIZATION: instead of swapping, pass original line, use [1].fY - [0].fY + for (int index = 0; index < result; ++index) { + fT[1][index] = 1 - fT[1][index]; + } + } + fPt[0].fX = x; + fPt[0].fY = yIntercept; + fUsed = 1; + } + } + if (fAllowNear || result == 2) { + if ((t = line.nearPoint(topPt)) >= 0) { + insert(t, (double) flipped, topPt); + } + if (top != bottom) { + SkDPoint bottomPt = { x, bottom }; + if ((t = line.nearPoint(bottomPt)) >= 0) { + insert(t, (double) !flipped, bottomPt); + } + for (int index = 0; index < 2; ++index) { + if ((t = SkDLine::NearPointV(line[index], top, bottom, x)) >= 0) { + insert((double) index, flipped ? 1 - t : t, line[index]); + } + } + } + } + cleanUpParallelLines(result == 2); + return fUsed; +} + +// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py +// 4 subs, 2 muls, 1 cmp +static bool ccw(const SkDPoint& A, const SkDPoint& B, const SkDPoint& C) { + return (C.fY - A.fY) * (B.fX - A.fX) > (B.fY - A.fY) * (C.fX - A.fX); +} + +// 16 subs, 8 muls, 6 cmps +bool SkIntersections::Test(const SkDLine& a, const SkDLine& b) { + return ccw(a[0], b[0], b[1]) != ccw(a[1], b[0], b[1]) + && ccw(a[0], a[1], b[0]) != ccw(a[0], a[1], b[1]); +}