45a8fc6a8b
git-svn-id: http://skia.googlecode.com/svn/trunk@7738 2bbb7eff-a529-9590-31e7-b0007b416f81
339 lines
12 KiB
C++
339 lines
12 KiB
C++
/*
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* Copyright 2012 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "CurveIntersection.h"
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#include "Intersections.h"
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#include "LineIntersection.h"
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#include "LineUtilities.h"
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/* Determine the intersection point of two lines. This assumes the lines are not parallel,
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and that that the lines are infinite.
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From http://en.wikipedia.org/wiki/Line-line_intersection
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*/
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void lineIntersect(const _Line& a, const _Line& b, _Point& p) {
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double axLen = a[1].x - a[0].x;
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double ayLen = a[1].y - a[0].y;
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double bxLen = b[1].x - b[0].x;
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double byLen = b[1].y - b[0].y;
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double denom = byLen * axLen - ayLen * bxLen;
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SkASSERT(denom);
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double term1 = a[1].x * a[0].y - a[1].y * a[0].x;
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double term2 = b[1].x * b[0].y - b[1].y * b[0].x;
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p.x = (term1 * bxLen - axLen * term2) / denom;
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p.y = (term1 * byLen - ayLen * term2) / denom;
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}
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static int computePoints(const _Line& a, int used, Intersections& i) {
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i.fPt[0] = xy_at_t(a, i.fT[0][0]);
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if ((i.fUsed = used) == 2) {
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i.fPt[1] = xy_at_t(a, i.fT[0][1]);
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}
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return i.fUsed;
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}
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/*
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Determine the intersection point of two line segments
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Return FALSE if the lines don't intersect
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from: http://paulbourke.net/geometry/lineline2d/
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*/
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int intersect(const _Line& a, const _Line& b, Intersections& i) {
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double axLen = a[1].x - a[0].x;
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double ayLen = a[1].y - a[0].y;
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double bxLen = b[1].x - b[0].x;
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double byLen = b[1].y - b[0].y;
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/* Slopes match when denom goes to zero:
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axLen / ayLen == bxLen / byLen
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(ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
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byLen * axLen == ayLen * bxLen
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byLen * axLen - ayLen * bxLen == 0 ( == denom )
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*/
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double denom = byLen * axLen - ayLen * bxLen;
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double ab0y = a[0].y - b[0].y;
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double ab0x = a[0].x - b[0].x;
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double numerA = ab0y * bxLen - byLen * ab0x;
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double numerB = ab0y * axLen - ayLen * ab0x;
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bool mayNotOverlap = (numerA < 0 && denom > numerA) || (numerA > 0 && denom < numerA)
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|| (numerB < 0 && denom > numerB) || (numerB > 0 && denom < numerB);
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numerA /= denom;
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numerB /= denom;
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if ((!approximately_zero(denom) || (!approximately_zero_inverse(numerA)
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&& !approximately_zero_inverse(numerB))) && !sk_double_isnan(numerA)
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&& !sk_double_isnan(numerB)) {
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if (mayNotOverlap) {
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return 0;
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}
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i.fT[0][0] = numerA;
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i.fT[1][0] = numerB;
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i.fPt[0] = xy_at_t(a, numerA);
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return computePoints(a, 1, i);
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}
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/* See if the axis intercepts match:
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ay - ax * ayLen / axLen == by - bx * ayLen / axLen
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axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen)
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axLen * ay - ax * ayLen == axLen * by - bx * ayLen
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*/
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// FIXME: need to use AlmostEqualUlps variant instead
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if (!approximately_equal_squared(axLen * a[0].y - ayLen * a[0].x,
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axLen * b[0].y - ayLen * b[0].x)) {
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return 0;
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}
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const double* aPtr;
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const double* bPtr;
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if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) {
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aPtr = &a[0].x;
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bPtr = &b[0].x;
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} else {
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aPtr = &a[0].y;
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bPtr = &b[0].y;
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}
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double a0 = aPtr[0];
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double a1 = aPtr[2];
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double b0 = bPtr[0];
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double b1 = bPtr[2];
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// OPTIMIZATION: restructure to reject before the divide
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// e.g., if ((a0 - b0) * (a0 - a1) < 0 || abs(a0 - b0) > abs(a0 - a1))
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// (except efficient)
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double aDenom = a0 - a1;
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if (approximately_zero(aDenom)) {
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if (!between(b0, a0, b1)) {
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return 0;
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}
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i.fT[0][0] = i.fT[0][1] = 0;
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} else {
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double at0 = (a0 - b0) / aDenom;
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double at1 = (a0 - b1) / aDenom;
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if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
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return 0;
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}
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i.fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
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i.fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
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}
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double bDenom = b0 - b1;
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if (approximately_zero(bDenom)) {
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i.fT[1][0] = i.fT[1][1] = 0;
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} else {
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int bIn = aDenom * bDenom < 0;
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i.fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / bDenom, 1.0), 0.0);
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i.fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / bDenom, 1.0), 0.0);
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}
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bool second = fabs(i.fT[0][0] - i.fT[0][1]) > FLT_EPSILON;
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SkASSERT((fabs(i.fT[1][0] - i.fT[1][1]) <= FLT_EPSILON) ^ second);
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return computePoints(a, 1 + second, i);
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}
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int horizontalIntersect(const _Line& line, double y, double tRange[2]) {
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double min = line[0].y;
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double max = line[1].y;
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if (min > max) {
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SkTSwap(min, max);
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}
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if (min > y || max < y) {
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return 0;
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}
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if (AlmostEqualUlps(min, max)) {
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tRange[0] = 0;
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tRange[1] = 1;
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return 2;
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}
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tRange[0] = (y - line[0].y) / (line[1].y - line[0].y);
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return 1;
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}
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// OPTIMIZATION Given: dy = line[1].y - line[0].y
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// and: xIntercept / (y - line[0].y) == (line[1].x - line[0].x) / dy
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// then: xIntercept * dy == (line[1].x - line[0].x) * (y - line[0].y)
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// Assuming that dy is always > 0, the line segment intercepts if:
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// left * dy <= xIntercept * dy <= right * dy
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// thus: left * dy <= (line[1].x - line[0].x) * (y - line[0].y) <= right * dy
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// (clever as this is, it does not give us the t value, so may be useful only
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// as a quick reject -- and maybe not then; it takes 3 muls, 3 adds, 2 cmps)
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int horizontalLineIntersect(const _Line& line, double left, double right,
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double y, double tRange[2]) {
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int result = horizontalIntersect(line, y, tRange);
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if (result != 1) {
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// FIXME: this is incorrect if result == 2
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return result;
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}
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double xIntercept = line[0].x + tRange[0] * (line[1].x - line[0].x);
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if (xIntercept > right || xIntercept < left) {
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return 0;
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}
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return result;
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}
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int horizontalIntersect(const _Line& line, double left, double right,
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double y, bool flipped, Intersections& intersections) {
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int result = horizontalIntersect(line, y, intersections.fT[0]);
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switch (result) {
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case 0:
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break;
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case 1: {
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double xIntercept = line[0].x + intersections.fT[0][0]
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* (line[1].x - line[0].x);
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if (xIntercept > right || xIntercept < left) {
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return 0;
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}
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intersections.fT[1][0] = (xIntercept - left) / (right - left);
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break;
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}
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case 2:
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#if 0 // sorting edges fails to preserve original direction
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double lineL = line[0].x;
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double lineR = line[1].x;
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if (lineL > lineR) {
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SkTSwap(lineL, lineR);
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}
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double overlapL = SkTMax(left, lineL);
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double overlapR = SkTMin(right, lineR);
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if (overlapL > overlapR) {
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return 0;
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}
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if (overlapL == overlapR) {
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result = 1;
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}
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intersections.fT[0][0] = (overlapL - line[0].x) / (line[1].x - line[0].x);
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intersections.fT[1][0] = (overlapL - left) / (right - left);
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if (result > 1) {
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intersections.fT[0][1] = (overlapR - line[0].x) / (line[1].x - line[0].x);
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intersections.fT[1][1] = (overlapR - left) / (right - left);
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}
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#else
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double a0 = line[0].x;
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double a1 = line[1].x;
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double b0 = flipped ? right : left;
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double b1 = flipped ? left : right;
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// FIXME: share common code below
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double at0 = (a0 - b0) / (a0 - a1);
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double at1 = (a0 - b1) / (a0 - a1);
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if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
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return 0;
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}
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intersections.fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
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intersections.fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
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int bIn = (a0 - a1) * (b0 - b1) < 0;
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intersections.fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1),
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1.0), 0.0);
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intersections.fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1),
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1.0), 0.0);
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bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1])
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> FLT_EPSILON;
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SkASSERT((fabs(intersections.fT[1][0] - intersections.fT[1][1])
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<= FLT_EPSILON) ^ second);
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return computePoints(line, 1 + second, intersections);
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#endif
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break;
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}
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if (flipped) {
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// OPTIMIZATION: instead of swapping, pass original line, use [1].x - [0].x
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for (int index = 0; index < result; ++index) {
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intersections.fT[1][index] = 1 - intersections.fT[1][index];
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}
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}
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return computePoints(line, result, intersections);
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}
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static int verticalIntersect(const _Line& line, double x, double tRange[2]) {
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double min = line[0].x;
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double max = line[1].x;
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if (min > max) {
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SkTSwap(min, max);
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}
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if (min > x || max < x) {
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return 0;
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}
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if (AlmostEqualUlps(min, max)) {
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tRange[0] = 0;
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tRange[1] = 1;
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return 2;
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}
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tRange[0] = (x - line[0].x) / (line[1].x - line[0].x);
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return 1;
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}
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int verticalIntersect(const _Line& line, double top, double bottom,
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double x, bool flipped, Intersections& intersections) {
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int result = verticalIntersect(line, x, intersections.fT[0]);
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switch (result) {
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case 0:
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break;
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case 1: {
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double yIntercept = line[0].y + intersections.fT[0][0]
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* (line[1].y - line[0].y);
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if (yIntercept > bottom || yIntercept < top) {
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return 0;
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}
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intersections.fT[1][0] = (yIntercept - top) / (bottom - top);
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break;
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}
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case 2:
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#if 0 // sorting edges fails to preserve original direction
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double lineT = line[0].y;
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double lineB = line[1].y;
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if (lineT > lineB) {
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SkTSwap(lineT, lineB);
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}
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double overlapT = SkTMax(top, lineT);
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double overlapB = SkTMin(bottom, lineB);
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if (overlapT > overlapB) {
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return 0;
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}
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if (overlapT == overlapB) {
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result = 1;
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}
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intersections.fT[0][0] = (overlapT - line[0].y) / (line[1].y - line[0].y);
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intersections.fT[1][0] = (overlapT - top) / (bottom - top);
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if (result > 1) {
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intersections.fT[0][1] = (overlapB - line[0].y) / (line[1].y - line[0].y);
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intersections.fT[1][1] = (overlapB - top) / (bottom - top);
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}
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#else
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double a0 = line[0].y;
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double a1 = line[1].y;
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double b0 = flipped ? bottom : top;
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double b1 = flipped ? top : bottom;
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// FIXME: share common code above
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double at0 = (a0 - b0) / (a0 - a1);
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double at1 = (a0 - b1) / (a0 - a1);
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if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
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return 0;
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}
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intersections.fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
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intersections.fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
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int bIn = (a0 - a1) * (b0 - b1) < 0;
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intersections.fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / (b0 - b1),
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1.0), 0.0);
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intersections.fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / (b0 - b1),
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1.0), 0.0);
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bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1])
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> FLT_EPSILON;
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SkASSERT((fabs(intersections.fT[1][0] - intersections.fT[1][1])
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<= FLT_EPSILON) ^ second);
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return computePoints(line, 1 + second, intersections);
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#endif
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break;
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}
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if (flipped) {
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// OPTIMIZATION: instead of swapping, pass original line, use [1].y - [0].y
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for (int index = 0; index < result; ++index) {
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intersections.fT[1][index] = 1 - intersections.fT[1][index];
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}
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}
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return computePoints(line, result, intersections);
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}
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// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py
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// 4 subs, 2 muls, 1 cmp
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static bool ccw(const _Point& A, const _Point& B, const _Point& C) {
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return (C.y - A.y) * (B.x - A.x) > (B.y - A.y) * (C.x - A.x);
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}
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// 16 subs, 8 muls, 6 cmps
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bool testIntersect(const _Line& a, const _Line& b) {
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return ccw(a[0], b[0], b[1]) != ccw(a[1], b[0], b[1])
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&& ccw(a[0], a[1], b[0]) != ccw(a[0], a[1], b[1]);
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}
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