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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 "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 (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]; } } computePoints(line, result); } } 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 (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]; } } computePoints(line, result); } } 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]); }