| /* |
| * 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; |
| } |
| |
| int SkIntersections::computePoints(const SkDLine& line, int used) { |
| fPt[0] = line.xyAtT(fT[0][0]); |
| if ((fUsed = used) == 2) { |
| fPt[1] = line.xyAtT(fT[0][1]); |
| } |
| return fUsed; |
| } |
| |
| /* |
| Determine the intersection point of two line segments |
| Return FALSE if the lines don't intersect |
| from: http://paulbourke.net/geometry/lineline2d/ |
| */ |
| |
| int SkIntersections::intersect(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; |
| /* 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 = byLen * axLen - ayLen * bxLen; |
| 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; |
| bool mayNotOverlap = (numerA < 0 && denom > numerA) || (numerA > 0 && denom < numerA) |
| || (numerB < 0 && denom > numerB) || (numerB > 0 && denom < numerB); |
| numerA /= denom; |
| numerB /= denom; |
| if ((!approximately_zero(denom) || (!approximately_zero_inverse(numerA) |
| && !approximately_zero_inverse(numerB))) && !sk_double_isnan(numerA) |
| && !sk_double_isnan(numerB)) { |
| if (mayNotOverlap) { |
| return fUsed = 0; |
| } |
| fT[0][0] = numerA; |
| fT[1][0] = numerB; |
| fPt[0] = a.xyAtT(numerA); |
| return computePoints(a, 1); |
| } |
| /* 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(axLen * a[0].fY - ayLen * a[0].fX, |
| axLen * b[0].fY - ayLen * b[0].fX)) { |
| return fUsed = 0; |
| } |
| const double* aPtr; |
| const double* bPtr; |
| if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) { |
| aPtr = &a[0].fX; |
| bPtr = &b[0].fX; |
| } else { |
| aPtr = &a[0].fY; |
| bPtr = &b[0].fY; |
| } |
| double a0 = aPtr[0]; |
| double a1 = aPtr[2]; |
| double b0 = bPtr[0]; |
| double b1 = bPtr[2]; |
| // OPTIMIZATION: restructure to reject before the divide |
| // e.g., if ((a0 - b0) * (a0 - a1) < 0 || abs(a0 - b0) > abs(a0 - a1)) |
| // (except efficient) |
| double aDenom = a0 - a1; |
| if (approximately_zero(aDenom)) { |
| if (!between(b0, a0, b1)) { |
| return fUsed = 0; |
| } |
| fT[0][0] = fT[0][1] = 0; |
| } else { |
| double at0 = (a0 - b0) / aDenom; |
| double at1 = (a0 - b1) / aDenom; |
| if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) { |
| return fUsed = 0; |
| } |
| fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0); |
| fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0); |
| } |
| double bDenom = b0 - b1; |
| if (approximately_zero(bDenom)) { |
| fT[1][0] = fT[1][1] = 0; |
| } else { |
| int bIn = aDenom * bDenom < 0; |
| fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / bDenom, 1.0), 0.0); |
| fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / bDenom, 1.0), 0.0); |
| } |
| bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON; |
| SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second); |
| return computePoints(a, 1 + second); |
| } |
| |
| int SkIntersections::horizontal(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 fUsed = 0; |
| } |
| if (AlmostEqualUlps(min, max)) { |
| fT[0][0] = 0; |
| fT[0][1] = 1; |
| return fUsed = 2; |
| } |
| fT[0][0] = (y - line[0].fY) / (line[1].fY - line[0].fY); |
| return fUsed = 1; |
| } |
| |
| int SkIntersections::horizontal(const SkDLine& line, double left, double right, |
| double y, bool flipped) { |
| int result = horizontal(line, y); |
| switch (result) { |
| case 0: |
| break; |
| case 1: { |
| double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX); |
| if (!precisely_between(left, xIntercept, right)) { |
| return fUsed = 0; |
| } |
| fT[1][0] = (xIntercept - left) / (right - left); |
| break; |
| } |
| case 2: |
| double a0 = line[0].fX; |
| double a1 = line[1].fX; |
| double b0 = flipped ? right : left; |
| double b1 = flipped ? left : right; |
| // FIXME: share common code below |
| double at0 = (a0 - b0) / (a0 - a1); |
| double at1 = (a0 - b1) / (a0 - a1); |
| if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) { |
| return fUsed = 0; |
| } |
| fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0); |
| fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0); |
| int bIn = (a0 - a1) * (b0 - b1) < 0; |
| fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), 1.0), 0.0); |
| fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), 1.0), 0.0); |
| bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON; |
| SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second); |
| return computePoints(line, 1 + second); |
| } |
| 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]; |
| } |
| } |
| return computePoints(line, result); |
| } |
| |
| int SkIntersections::vertical(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 fUsed = 0; |
| } |
| if (AlmostEqualUlps(min, max)) { |
| fT[0][0] = 0; |
| fT[0][1] = 1; |
| return fUsed = 2; |
| } |
| fT[0][0] = (x - line[0].fX) / (line[1].fX - line[0].fX); |
| return fUsed = 1; |
| } |
| |
| int SkIntersections::vertical(const SkDLine& line, double top, double bottom, |
| double x, bool flipped) { |
| int result = vertical(line, x); |
| switch (result) { |
| case 0: |
| break; |
| case 1: { |
| double yIntercept = line[0].fY + fT[0][0] * (line[1].fY - line[0].fY); |
| if (!precisely_between(top, yIntercept, bottom)) { |
| return fUsed = 0; |
| } |
| fT[1][0] = (yIntercept - top) / (bottom - top); |
| break; |
| } |
| case 2: |
| double a0 = line[0].fY; |
| double a1 = line[1].fY; |
| double b0 = flipped ? bottom : top; |
| double b1 = flipped ? top : bottom; |
| // FIXME: share common code above |
| double at0 = (a0 - b0) / (a0 - a1); |
| double at1 = (a0 - b1) / (a0 - a1); |
| if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) { |
| return fUsed = 0; |
| } |
| fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0); |
| fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0); |
| int bIn = (a0 - a1) * (b0 - b1) < 0; |
| fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), 1.0), 0.0); |
| fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), 1.0), 0.0); |
| bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON; |
| SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second); |
| return computePoints(line, 1 + second); |
| } |
| 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]; |
| } |
| } |
| return computePoints(line, result); |
| } |
| |
| // 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]); |
| } |