| /* |
| * 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; |
| #if 0 |
| if (!between(0, numerA, denom) || !between(0, numerB, denom)) { |
| fUsed = 0; |
| return 0; |
| } |
| #endif |
| 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); |
| } |
| } |
| /* Allow tracking that both sets of end points are near each other -- the lines are entirely |
| coincident -- even when the end points are not exactly the same. |
| Mark this as a 'wild card' for the end points, so that either point is considered totally |
| coincident. Then, avoid folding the lines over each other, but allow either end to mate |
| to the next set of lines. |
| */ |
| if (fAllowNear || !unparallel) { |
| double aNearB[2]; |
| double bNearA[2]; |
| bool aNotB[2] = {false, false}; |
| bool bNotA[2] = {false, false}; |
| int nearCount = 0; |
| for (int index = 0; index < 2; ++index) { |
| aNearB[index] = t = b.nearPoint(a[index], &aNotB[index]); |
| nearCount += t >= 0; |
| bNearA[index] = t = a.nearPoint(b[index], &bNotA[index]); |
| nearCount += t >= 0; |
| } |
| if (nearCount > 0) { |
| // Skip if each segment contributes to one end point. |
| if (nearCount != 2 || aNotB[0] == aNotB[1]) { |
| for (int iA = 0; iA < 2; ++iA) { |
| if (!aNotB[iA]) { |
| continue; |
| } |
| int nearer = aNearB[iA] > 0.5; |
| if (!bNotA[nearer]) { |
| continue; |
| } |
| SkASSERT(a[iA] != b[nearer]); |
| SkASSERT(iA == (bNearA[nearer] > 0.5)); |
| fNearlySame[iA] = true; |
| insertNear(iA, nearer, a[iA], b[nearer]); |
| aNearB[iA] = -1; |
| bNearA[nearer] = -1; |
| nearCount -= 2; |
| } |
| } |
| if (nearCount > 0) { |
| for (int iA = 0; iA < 2; ++iA) { |
| if (aNearB[iA] >= 0) { |
| insert(iA, aNearB[iA], a[iA]); |
| } |
| } |
| for (int iB = 0; iB < 2; ++iB) { |
| if (bNearA[iB] >= 0) { |
| insert(bNearA[iB], 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 = 3; // clean up parallel at the end will limit the result to 2 at the most |
| // 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, NULL)) >= 0) { |
| insert(t, (double) flipped, leftPt); |
| } |
| if (left != right) { |
| const SkDPoint rightPt = { right, y }; |
| if ((t = line.nearPoint(rightPt, NULL)) >= 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 = 3; // cleanup parallel lines will bring this back line |
| // 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, NULL)) >= 0) { |
| insert(t, (double) flipped, topPt); |
| } |
| if (top != bottom) { |
| SkDPoint bottomPt = { x, bottom }; |
| if ((t = line.nearPoint(bottomPt, NULL)) >= 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); |
| SkASSERT(fUsed <= 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]); |
| } |
