/*
* 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;
}
void SkIntersections::cleanUpCoincidence() {
SkASSERT(fUsed == 2);
// both t values are good
bool startMatch = fT[0][0] == 0 && (fT[1][0] == 0 || fT[1][0] == 1);
bool endMatch = fT[0][1] == 1 && (fT[1][1] == 0 || fT[1][1] == 1);
if (startMatch || endMatch) {
removeOne(startMatch);
return;
}
// either t value is good
bool pStartMatch = fT[0][0] == 0 || fT[1][0] == 0 || fT[1][0] == 1;
bool pEndMatch = fT[0][1] == 1 || fT[1][1] == 0 || fT[1][1] == 1;
removeOne(pStartMatch || !pEndMatch);
}
void SkIntersections::cleanUpParallelLines(bool parallel) {
while (fUsed > 2) {
removeOne(1);
}
if (fUsed == 2 && !parallel) {
bool startMatch = fT[0][0] == 0 || fT[1][0] == 0 || fT[1][0] == 1;
bool endMatch = fT[0][1] == 1 || fT[1][1] == 0 || fT[1][1] == 1;
if ((!startMatch && !endMatch) || approximately_equal(fT[0][0], fT[0][1])) {
SkASSERT(startMatch || endMatch);
removeOne(endMatch);
}
}
}
void SkIntersections::computePoints(const SkDLine& line, int used) {
fPt[0] = line.ptAtT(fT[0][0]);
if ((fUsed = used) == 2) {
fPt[1] = line.ptAtT(fT[0][1]);
}
}
int SkIntersections::intersectRay(const SkDLine& a, const SkDLine& b) {
fMax = 2;
SkDVector aLen = a[1] - a[0];
SkDVector bLen = b[1] - b[0];
/* 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 = bLen.fY * aLen.fX - aLen.fY * bLen.fX;
SkDVector ab0 = a[0] - b[0];
double numerA = ab0.fY * bLen.fX - bLen.fY * ab0.fX;
double numerB = ab0.fY * aLen.fX - aLen.fY * ab0.fX;
numerA /= denom;
numerB /= denom;
int used;
if (!approximately_zero(denom)) {
fT[0][0] = numerA;
fT[1][0] = numerB;
used = 1;
} else {
/* 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(aLen.fX * a[0].fY - aLen.fY * a[0].fX,
aLen.fX * b[0].fY - aLen.fY * b[0].fX)) {
return fUsed = 0;
}
// there's no great answer for intersection points for coincident rays, but return something
fT[0][0] = fT[1][0] = 0;
fT[1][0] = fT[1][1] = 1;
used = 2;
}
computePoints(a, used);
return fUsed;
}
// note that this only works if both lines are neither horizontal nor vertical
int SkIntersections::intersect(const SkDLine& a, const SkDLine& b) {
fMax = 3; // note that we clean up so that there is no more than two in the end
// see if end points intersect the opposite line
double t;
for (int iA = 0; iA < 2; ++iA) {
if ((t = b.exactPoint(a[iA])) >= 0) {
insert(iA, t, a[iA]);
}
}
for (int iB = 0; iB < 2; ++iB) {
if ((t = a.exactPoint(b[iB])) >= 0) {
insert(t, iB, b[iB]);
}
}
/* Determine the intersection point of two line segments
Return FALSE if the lines don't intersect
from: http://paulbourke.net/geometry/lineline2d/ */
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 axByLen = axLen * byLen;
double ayBxLen = ayLen * bxLen;
// detect parallel lines the same way here and in SkOpAngle operator <
// so that non-parallel means they are also sortable
bool unparallel = fAllowNear ? NotAlmostEqualUlps(axByLen, ayBxLen)
: NotAlmostDequalUlps(axByLen, ayBxLen);
if (unparallel && fUsed == 0) {
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;
double denom = axByLen - ayBxLen;
if (between(0, numerA, denom) && between(0, numerB, denom)) {
fT[0][0] = numerA / denom;
fT[1][0] = numerB / denom;
computePoints(a, 1);
}
}
if (fAllowNear || !unparallel) {
for (int iA = 0; iA < 2; ++iA) {
if ((t = b.nearPoint(a[iA])) >= 0) {
insert(iA, t, a[iA]);
}
}
for (int iB = 0; iB < 2; ++iB) {
if ((t = a.nearPoint(b[iB])) >= 0) {
insert(t, iB, b[iB]);
}
}
}
cleanUpParallelLines(!unparallel);
SkASSERT(fUsed <= 2);
return fUsed;
}
static int horizontal_coincident(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 0;
}
if (AlmostEqualUlps(min, max) && max - min < fabs(line[0].fX - line[1].fX)) {
return 2;
}
return 1;
}
static double horizontal_intercept(const SkDLine& line, double y) {
return SkPinT((y - line[0].fY) / (line[1].fY - line[0].fY));
}
int SkIntersections::horizontal(const SkDLine& line, double y) {
fMax = 2;
int horizontalType = horizontal_coincident(line, y);
if (horizontalType == 1) {
fT[0][0] = horizontal_intercept(line, y);
} else if (horizontalType == 2) {
fT[0][0] = 0;
fT[0][1] = 1;
}
return fUsed = horizontalType;
}
int SkIntersections::horizontal(const SkDLine& line, double left, double right,
double y, bool flipped) {
fMax = 2;
// see if end points intersect the opposite line
double t;
const SkDPoint leftPt = { left, y };
if ((t = line.exactPoint(leftPt)) >= 0) {
insert(t, (double) flipped, leftPt);
}
if (left != right) {
const SkDPoint rightPt = { right, y };
if ((t = line.exactPoint(rightPt)) >= 0) {
insert(t, (double) !flipped, rightPt);
}
for (int index = 0; index < 2; ++index) {
if ((t = SkDLine::ExactPointH(line[index], left, right, y)) >= 0) {
insert((double) index, flipped ? 1 - t : t, line[index]);
}
}
}
int result = horizontal_coincident(line, y);
if (result == 1 && fUsed == 0) {
fT[0][0] = horizontal_intercept(line, y);
double xIntercept = line[0].fX + fT[0][0] * (line[1].fX - line[0].fX);
if (between(left, xIntercept, right)) {
fT[1][0] = (xIntercept - left) / (right - left);
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];
}
}
fPt[0].fX = xIntercept;
fPt[0].fY = y;
fUsed = 1;
}
}
if (fAllowNear || result == 2) {
if ((t = line.nearPoint(leftPt)) >= 0) {
insert(t, (double) flipped, leftPt);
}
if (left != right) {
const SkDPoint rightPt = { right, y };
if ((t = line.nearPoint(rightPt)) >= 0) {
insert(t, (double) !flipped, rightPt);
}
for (int index = 0; index < 2; ++index) {
if ((t = SkDLine::NearPointH(line[index], left, right, y)) >= 0) {
insert((double) index, flipped ? 1 - t : t, line[index]);
}
}
}
}
cleanUpParallelLines(result == 2);
return fUsed;
}
static int vertical_coincident(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 0;
}
if (AlmostEqualUlps(min, max)) {
return 2;
}
return 1;
}
static double vertical_intercept(const SkDLine& line, double x) {
return SkPinT((x - line[0].fX) / (line[1].fX - line[0].fX));
}
int SkIntersections::vertical(const SkDLine& line, double x) {
fMax = 2;
int verticalType = vertical_coincident(line, x);
if (verticalType == 1) {
fT[0][0] = vertical_intercept(line, x);
} else if (verticalType == 2) {
fT[0][0] = 0;
fT[0][1] = 1;
}
return fUsed = verticalType;
}
int SkIntersections::vertical(const SkDLine& line, double top, double bottom,
double x, bool flipped) {
fMax = 2;
// see if end points intersect the opposite line
double t;
SkDPoint topPt = { x, top };
if ((t = line.exactPoint(topPt)) >= 0) {
insert(t, (double) flipped, topPt);
}
if (top != bottom) {
SkDPoint bottomPt = { x, bottom };
if ((t = line.exactPoint(bottomPt)) >= 0) {
insert(t, (double) !flipped, bottomPt);
}
for (int index = 0; index < 2; ++index) {
if ((t = SkDLine::ExactPointV(line[index], top, bottom, x)) >= 0) {
insert((double) index, flipped ? 1 - t : t, line[index]);
}
}
}
int result = vertical_coincident(line, x);
if (result == 1 && fUsed == 0) {
fT[0][0] = vertical_intercept(line, x);
double yIntercept = line[0].fY + fT[0][0] * (line[1].fY - line[0].fY);
if (between(top, yIntercept, bottom)) {
fT[1][0] = (yIntercept - top) / (bottom - top);
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];
}
}
fPt[0].fX = x;
fPt[0].fY = yIntercept;
fUsed = 1;
}
}
if (fAllowNear || result == 2) {
if ((t = line.nearPoint(topPt)) >= 0) {
insert(t, (double) flipped, topPt);
}
if (top != bottom) {
SkDPoint bottomPt = { x, bottom };
if ((t = line.nearPoint(bottomPt)) >= 0) {
insert(t, (double) !flipped, bottomPt);
}
for (int index = 0; index < 2; ++index) {
if ((t = SkDLine::NearPointV(line[index], top, bottom, x)) >= 0) {
insert((double) index, flipped ? 1 - t : t, line[index]);
}
}
}
}
cleanUpParallelLines(result == 2);
return fUsed;
}
// 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]);
}