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/*
* 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;
}
// OPTIMIZATION Given: dy = line[1].fY - line[0].fY
// and: xIntercept / (y - line[0].fY) == (line[1].fX - line[0].fX) / dy
// then: xIntercept * dy == (line[1].fX - line[0].fX) * (y - line[0].fY)
// Assuming that dy is always > 0, the line segment intercepts if:
// left * dy <= xIntercept * dy <= right * dy
// thus: left * dy <= (line[1].fX - line[0].fX) * (y - line[0].fY) <= 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 SkIntersections::horizontal(const SkDLine& line, double left, double right, double y) {
int result = horizontal(line, y);
if (result != 1) {
SkASSERT(0);
return result;
}
double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX);
if (!precisely_between(left, xIntercept, right)) {
return fUsed = 0;
}
return result;
}
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]);
}