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Diffstat (limited to 'chromium/third_party/skia/experimental/Intersection/LineIntersection.cpp')
| -rw-r--r-- | chromium/third_party/skia/experimental/Intersection/LineIntersection.cpp | 338 |
1 files changed, 338 insertions, 0 deletions
diff --git a/chromium/third_party/skia/experimental/Intersection/LineIntersection.cpp b/chromium/third_party/skia/experimental/Intersection/LineIntersection.cpp new file mode 100644 index 00000000000..ca6a8e40817 --- /dev/null +++ b/chromium/third_party/skia/experimental/Intersection/LineIntersection.cpp @@ -0,0 +1,338 @@ +/* + * 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]); +} |