| /* |
| * 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 "CurveIntersection.h" |
| #include "Intersections.h" |
| #include "LineIntersection.h" |
| #include "LineUtilities.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 |
| */ |
| void lineIntersect(const _Line& a, const _Line& b, _Point& p) { |
| double axLen = a[1].x - a[0].x; |
| double ayLen = a[1].y - a[0].y; |
| double bxLen = b[1].x - b[0].x; |
| double byLen = b[1].y - b[0].y; |
| double denom = byLen * axLen - ayLen * bxLen; |
| SkASSERT(denom); |
| double term1 = a[1].x * a[0].y - a[1].y * a[0].x; |
| double term2 = b[1].x * b[0].y - b[1].y * b[0].x; |
| p.x = (term1 * bxLen - axLen * term2) / denom; |
| p.y = (term1 * byLen - ayLen * term2) / denom; |
| } |
| |
| static int computePoints(const _Line& a, int used, Intersections& i) { |
| i.fPt[0] = xy_at_t(a, i.fT[0][0]); |
| if ((i.fUsed = used) == 2) { |
| i.fPt[1] = xy_at_t(a, i.fT[0][1]); |
| } |
| return i.fUsed; |
| } |
| |
| /* |
| Determine the intersection point of two line segments |
| Return FALSE if the lines don't intersect |
| from: http://paulbourke.net/geometry/lineline2d/ |
| */ |
| |
| int intersect(const _Line& a, const _Line& b, Intersections& i) { |
| double axLen = a[1].x - a[0].x; |
| double ayLen = a[1].y - a[0].y; |
| double bxLen = b[1].x - b[0].x; |
| double byLen = b[1].y - b[0].y; |
| /* 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].y - b[0].y; |
| double ab0x = a[0].x - b[0].x; |
| 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 0; |
| } |
| i.fT[0][0] = numerA; |
| i.fT[1][0] = numerB; |
| i.fPt[0] = xy_at_t(a, numerA); |
| return computePoints(a, 1, i); |
| } |
| /* 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 |
| */ |
| // FIXME: need to use AlmostEqualUlps variant instead |
| if (!approximately_equal_squared(axLen * a[0].y - ayLen * a[0].x, |
| axLen * b[0].y - ayLen * b[0].x)) { |
| return 0; |
| } |
| const double* aPtr; |
| const double* bPtr; |
| if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) { |
| aPtr = &a[0].x; |
| bPtr = &b[0].x; |
| } else { |
| aPtr = &a[0].y; |
| bPtr = &b[0].y; |
| } |
| 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 0; |
| } |
| i.fT[0][0] = i.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 0; |
| } |
| i.fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0); |
| i.fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0); |
| } |
| double bDenom = b0 - b1; |
| if (approximately_zero(bDenom)) { |
| i.fT[1][0] = i.fT[1][1] = 0; |
| } else { |
| int bIn = aDenom * bDenom < 0; |
| i.fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / bDenom, 1.0), 0.0); |
| i.fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / bDenom, 1.0), 0.0); |
| } |
| bool second = fabs(i.fT[0][0] - i.fT[0][1]) > FLT_EPSILON; |
| SkASSERT((fabs(i.fT[1][0] - i.fT[1][1]) <= FLT_EPSILON) ^ second); |
| return computePoints(a, 1 + second, i); |
| } |
| |
| int horizontalIntersect(const _Line& line, double y, double tRange[2]) { |
| double min = line[0].y; |
| double max = line[1].y; |
| if (min > max) { |
| SkTSwap(min, max); |
| } |
| if (min > y || max < y) { |
| return 0; |
| } |
| if (AlmostEqualUlps(min, max)) { |
| tRange[0] = 0; |
| tRange[1] = 1; |
| return 2; |
| } |
| tRange[0] = (y - line[0].y) / (line[1].y - line[0].y); |
| return 1; |
| } |
| |
| // OPTIMIZATION Given: dy = line[1].y - line[0].y |
| // and: xIntercept / (y - line[0].y) == (line[1].x - line[0].x) / dy |
| // then: xIntercept * dy == (line[1].x - line[0].x) * (y - line[0].y) |
| // Assuming that dy is always > 0, the line segment intercepts if: |
| // left * dy <= xIntercept * dy <= right * dy |
| // thus: left * dy <= (line[1].x - line[0].x) * (y - line[0].y) <= right * dy |
| // (clever as this is, it does not give us the t value, so may be useful only |
| // as a quick reject -- and maybe not then; it takes 3 muls, 3 adds, 2 cmps) |
| int horizontalLineIntersect(const _Line& line, double left, double right, |
| double y, double tRange[2]) { |
| int result = horizontalIntersect(line, y, tRange); |
| if (result != 1) { |
| // FIXME: this is incorrect if result == 2 |
| return result; |
| } |
| double xIntercept = line[0].x + tRange[0] * (line[1].x - line[0].x); |
| if (xIntercept > right || xIntercept < left) { |
| return 0; |
| } |
| return result; |
| } |
| |
| int horizontalIntersect(const _Line& line, double left, double right, |
| double y, bool flipped, Intersections& intersections) { |
| int result = horizontalIntersect(line, y, intersections.fT[0]); |
| switch (result) { |
| case 0: |
| break; |
| case 1: { |
| double xIntercept = line[0].x + intersections.fT[0][0] |
| * (line[1].x - line[0].x); |
| if (xIntercept > right || xIntercept < left) { |
| return 0; |
| } |
| intersections.fT[1][0] = (xIntercept - left) / (right - left); |
| break; |
| } |
| case 2: |
| #if 0 // sorting edges fails to preserve original direction |
| double lineL = line[0].x; |
| double lineR = line[1].x; |
| if (lineL > lineR) { |
| SkTSwap(lineL, lineR); |
| } |
| double overlapL = SkTMax(left, lineL); |
| double overlapR = SkTMin(right, lineR); |
| if (overlapL > overlapR) { |
| return 0; |
| } |
| if (overlapL == overlapR) { |
| result = 1; |
| } |
| intersections.fT[0][0] = (overlapL - line[0].x) / (line[1].x - line[0].x); |
| intersections.fT[1][0] = (overlapL - left) / (right - left); |
| if (result > 1) { |
| intersections.fT[0][1] = (overlapR - line[0].x) / (line[1].x - line[0].x); |
| intersections.fT[1][1] = (overlapR - left) / (right - left); |
| } |
| #else |
| double a0 = line[0].x; |
| double a1 = line[1].x; |
| 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 0; |
| } |
| intersections.fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0); |
| intersections.fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0); |
| int bIn = (a0 - a1) * (b0 - b1) < 0; |
| intersections.fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), |
| 1.0), 0.0); |
| intersections.fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), |
| 1.0), 0.0); |
| bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1]) |
| > FLT_EPSILON; |
| SkASSERT((fabs(intersections.fT[1][0] - intersections.fT[1][1]) |
| <= FLT_EPSILON) ^ second); |
| return computePoints(line, 1 + second, intersections); |
| #endif |
| break; |
| } |
| if (flipped) { |
| // OPTIMIZATION: instead of swapping, pass original line, use [1].x - [0].x |
| for (int index = 0; index < result; ++index) { |
| intersections.fT[1][index] = 1 - intersections.fT[1][index]; |
| } |
| } |
| return computePoints(line, result, intersections); |
| } |
| |
| static int verticalIntersect(const _Line& line, double x, double tRange[2]) { |
| double min = line[0].x; |
| double max = line[1].x; |
| if (min > max) { |
| SkTSwap(min, max); |
| } |
| if (min > x || max < x) { |
| return 0; |
| } |
| if (AlmostEqualUlps(min, max)) { |
| tRange[0] = 0; |
| tRange[1] = 1; |
| return 2; |
| } |
| tRange[0] = (x - line[0].x) / (line[1].x - line[0].x); |
| return 1; |
| } |
| |
| int verticalIntersect(const _Line& line, double top, double bottom, |
| double x, bool flipped, Intersections& intersections) { |
| int result = verticalIntersect(line, x, intersections.fT[0]); |
| switch (result) { |
| case 0: |
| break; |
| case 1: { |
| double yIntercept = line[0].y + intersections.fT[0][0] |
| * (line[1].y - line[0].y); |
| if (yIntercept > bottom || yIntercept < top) { |
| return 0; |
| } |
| intersections.fT[1][0] = (yIntercept - top) / (bottom - top); |
| break; |
| } |
| case 2: |
| #if 0 // sorting edges fails to preserve original direction |
| double lineT = line[0].y; |
| double lineB = line[1].y; |
| if (lineT > lineB) { |
| SkTSwap(lineT, lineB); |
| } |
| double overlapT = SkTMax(top, lineT); |
| double overlapB = SkTMin(bottom, lineB); |
| if (overlapT > overlapB) { |
| return 0; |
| } |
| if (overlapT == overlapB) { |
| result = 1; |
| } |
| intersections.fT[0][0] = (overlapT - line[0].y) / (line[1].y - line[0].y); |
| intersections.fT[1][0] = (overlapT - top) / (bottom - top); |
| if (result > 1) { |
| intersections.fT[0][1] = (overlapB - line[0].y) / (line[1].y - line[0].y); |
| intersections.fT[1][1] = (overlapB - top) / (bottom - top); |
| } |
| #else |
| double a0 = line[0].y; |
| double a1 = line[1].y; |
| 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 0; |
| } |
| intersections.fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0); |
| intersections.fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0); |
| int bIn = (a0 - a1) * (b0 - b1) < 0; |
| intersections.fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1), |
| 1.0), 0.0); |
| intersections.fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1), |
| 1.0), 0.0); |
| bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1]) |
| > FLT_EPSILON; |
| SkASSERT((fabs(intersections.fT[1][0] - intersections.fT[1][1]) |
| <= FLT_EPSILON) ^ second); |
| return computePoints(line, 1 + second, intersections); |
| #endif |
| break; |
| } |
| if (flipped) { |
| // OPTIMIZATION: instead of swapping, pass original line, use [1].y - [0].y |
| for (int index = 0; index < result; ++index) { |
| intersections.fT[1][index] = 1 - intersections.fT[1][index]; |
| } |
| } |
| return computePoints(line, result, intersections); |
| } |
| |
| // from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py |
| // 4 subs, 2 muls, 1 cmp |
| static bool ccw(const _Point& A, const _Point& B, const _Point& C) { |
| return (C.y - A.y) * (B.x - A.x) > (B.y - A.y) * (C.x - A.x); |
| } |
| |
| // 16 subs, 8 muls, 6 cmps |
| bool testIntersect(const _Line& a, const _Line& 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]); |
| } |
