/*
* 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 "IntersectionUtilities.h"
#include "LineIntersection.h"
#include "LineUtilities.h"
#include "QuadraticLineSegments.h"
#include "QuadraticUtilities.h"
#include <algorithm> // for swap
static const double tClipLimit = 0.8; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf see Multiple intersections
class QuadraticIntersections {
public:
QuadraticIntersections(const Quadratic& q1, const Quadratic& q2, Intersections& i)
: quad1(q1)
, quad2(q2)
, intersections(i)
, depth(0)
, splits(0)
, coinMinT1(-1) {
}
bool intersect() {
double minT1, minT2, maxT1, maxT2;
if (!bezier_clip(quad2, quad1, minT1, maxT1)) {
return false;
}
if (!bezier_clip(quad1, quad2, minT2, maxT2)) {
return false;
}
quad1Divisions = 1 / subDivisions(quad1);
quad2Divisions = 1 / subDivisions(quad2);
int split;
if (maxT1 - minT1 < maxT2 - minT2) {
intersections.swap();
minT2 = 0;
maxT2 = 1;
split = maxT1 - minT1 > tClipLimit;
} else {
minT1 = 0;
maxT1 = 1;
split = (maxT2 - minT2 > tClipLimit) << 1;
}
return chop(minT1, maxT1, minT2, maxT2, split);
}
protected:
bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
bool t1IsLine = maxT1 - minT1 <= quad1Divisions;
bool t2IsLine = maxT2 - minT2 <= quad2Divisions;
if (t1IsLine | t2IsLine) {
return intersectAsLine(minT1, maxT1, minT2, maxT2, t1IsLine, t2IsLine);
}
Quadratic smaller, larger;
// FIXME: carry last subdivide and reduceOrder result with quad
sub_divide(quad1, minT1, maxT1, intersections.swapped() ? larger : smaller);
sub_divide(quad2, minT2, maxT2, intersections.swapped() ? smaller : larger);
double minT, maxT;
if (!bezier_clip(smaller, larger, minT, maxT)) {
if (approximately_equal(minT, maxT)) {
double smallT, largeT;
_Point q2pt, q1pt;
if (intersections.swapped()) {
largeT = interp(minT2, maxT2, minT);
xy_at_t(quad2, largeT, q2pt.x, q2pt.y);
xy_at_t(quad1, minT1, q1pt.x, q1pt.y);
if (AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)) {
smallT = minT1;
} else {
xy_at_t(quad1, maxT1, q1pt.x, q1pt.y); // FIXME: debug code
SkASSERT(AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y));
smallT = maxT1;
}
} else {
smallT = interp(minT1, maxT1, minT);
xy_at_t(quad1, smallT, q1pt.x, q1pt.y);
xy_at_t(quad2, minT2, q2pt.x, q2pt.y);
if (AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)) {
largeT = minT2;
} else {
xy_at_t(quad2, maxT2, q2pt.x, q2pt.y); // FIXME: debug code
SkASSERT(AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y));
largeT = maxT2;
}
}
intersections.add(smallT, largeT);
return true;
}
return false;
}
int split;
if (intersections.swapped()) {
double newMinT1 = interp(minT1, maxT1, minT);
double newMaxT1 = interp(minT1, maxT1, maxT);
split = (newMaxT1 - newMinT1 > (maxT1 - minT1) * tClipLimit) << 1;
#define VERBOSE 0
#if VERBOSE
printf("%s d=%d s=%d new1=(%g,%g) old1=(%g,%g) split=%d\n", __FUNCTION__, depth,
splits, newMinT1, newMaxT1, minT1, maxT1, split);
#endif
minT1 = newMinT1;
maxT1 = newMaxT1;
} else {
double newMinT2 = interp(minT2, maxT2, minT);
double newMaxT2 = interp(minT2, maxT2, maxT);
split = newMaxT2 - newMinT2 > (maxT2 - minT2) * tClipLimit;
#if VERBOSE
printf("%s d=%d s=%d new2=(%g,%g) old2=(%g,%g) split=%d\n", __FUNCTION__, depth,
splits, newMinT2, newMaxT2, minT2, maxT2, split);
#endif
minT2 = newMinT2;
maxT2 = newMaxT2;
}
return chop(minT1, maxT1, minT2, maxT2, split);
}
bool intersectAsLine(double minT1, double maxT1, double minT2, double maxT2,
bool treat1AsLine, bool treat2AsLine)
{
_Line line1, line2;
if (intersections.swapped()) {
SkTSwap(treat1AsLine, treat2AsLine);
SkTSwap(minT1, minT2);
SkTSwap(maxT1, maxT2);
}
if (coinMinT1 >= 0) {
bool earlyExit;
if ((earlyExit = coinMaxT1 == minT1)) {
coinMaxT1 = maxT1;
}
if (coinMaxT2 == minT2) {
coinMaxT2 = maxT2;
return true;
}
if (earlyExit) {
return true;
}
coinMinT1 = -1;
}
// do line/quadratic or even line/line intersection instead
if (treat1AsLine) {
xy_at_t(quad1, minT1, line1[0].x, line1[0].y);
xy_at_t(quad1, maxT1, line1[1].x, line1[1].y);
}
if (treat2AsLine) {
xy_at_t(quad2, minT2, line2[0].x, line2[0].y);
xy_at_t(quad2, maxT2, line2[1].x, line2[1].y);
}
int pts;
double smallT1, largeT1, smallT2, largeT2;
if (treat1AsLine & treat2AsLine) {
double t1[2], t2[2];
pts = ::intersect(line1, line2, t1, t2);
if (pts == 2) {
smallT1 = interp(minT1, maxT1, t1[0]);
largeT1 = interp(minT2, maxT2, t2[0]);
smallT2 = interp(minT1, maxT1, t1[1]);
largeT2 = interp(minT2, maxT2, t2[1]);
intersections.addCoincident(smallT1, smallT2, largeT1, largeT2);
} else {
smallT1 = interp(minT1, maxT1, t1[0]);
largeT1 = interp(minT2, maxT2, t2[0]);
intersections.add(smallT1, largeT1);
}
} else {
Intersections lq;
pts = ::intersect(treat1AsLine ? quad2 : quad1,
treat1AsLine ? line1 : line2, lq);
if (pts == 2) { // if the line and edge are coincident treat differently
_Point midQuad, midLine;
double midQuadT = (lq.fT[0][0] + lq.fT[0][1]) / 2;
xy_at_t(treat1AsLine ? quad2 : quad1, midQuadT, midQuad.x, midQuad.y);
double lineT = t_at(treat1AsLine ? line1 : line2, midQuad);
xy_at_t(treat1AsLine ? line1 : line2, lineT, midLine.x, midLine.y);
if (AlmostEqualUlps(midQuad.x, midLine.x)
&& AlmostEqualUlps(midQuad.y, midLine.y)) {
smallT1 = lq.fT[0][0];
largeT1 = lq.fT[1][0];
smallT2 = lq.fT[0][1];
largeT2 = lq.fT[1][1];
if (treat2AsLine) {
smallT1 = interp(minT1, maxT1, smallT1);
smallT2 = interp(minT1, maxT1, smallT2);
} else {
largeT1 = interp(minT2, maxT2, largeT1);
largeT2 = interp(minT2, maxT2, largeT2);
}
intersections.addCoincident(smallT1, smallT2, largeT1, largeT2);
goto setCoinMinMax;
}
}
for (int index = 0; index < pts; ++index) {
smallT1 = lq.fT[0][index];
largeT1 = lq.fT[1][index];
if (treat2AsLine) {
smallT1 = interp(minT1, maxT1, smallT1);
} else {
largeT1 = interp(minT2, maxT2, largeT1);
}
intersections.add(smallT1, largeT1);
}
}
if (pts > 0) {
setCoinMinMax:
coinMinT1 = minT1;
coinMaxT1 = maxT1;
coinMinT2 = minT2;
coinMaxT2 = maxT2;
}
return pts > 0;
}
bool chop(double minT1, double maxT1, double minT2, double maxT2, int split) {
++depth;
intersections.swap();
if (split) {
++splits;
if (split & 2) {
double middle1 = (maxT1 + minT1) / 2;
intersect(minT1, middle1, minT2, maxT2);
intersect(middle1, maxT1, minT2, maxT2);
} else {
double middle2 = (maxT2 + minT2) / 2;
intersect(minT1, maxT1, minT2, middle2);
intersect(minT1, maxT1, middle2, maxT2);
}
--splits;
intersections.swap();
--depth;
return intersections.intersected();
}
bool result = intersect(minT1, maxT1, minT2, maxT2);
intersections.swap();
--depth;
return result;
}
private:
const Quadratic& quad1;
const Quadratic& quad2;
Intersections& intersections;
int depth;
int splits;
double quad1Divisions; // line segments to approximate original within error
double quad2Divisions;
double coinMinT1; // range of Ts where approximate line intersected curve
double coinMaxT1;
double coinMinT2;
double coinMaxT2;
};
#include "LineParameters.h"
static void hackToFixPartialCoincidence(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
// look to see if non-coincident data basically has unsortable tangents
// look to see if a point between non-coincident data is on the curve
int cIndex;
for (int uIndex = 0; uIndex < i.fUsed; ) {
double bestDist1 = 1;
double bestDist2 = 1;
int closest1 = -1;
int closest2 = -1;
for (cIndex = 0; cIndex < i.fCoincidentUsed; ++cIndex) {
double dist = fabs(i.fT[0][uIndex] - i.fCoincidentT[0][cIndex]);
if (bestDist1 > dist) {
bestDist1 = dist;
closest1 = cIndex;
}
dist = fabs(i.fT[1][uIndex] - i.fCoincidentT[1][cIndex]);
if (bestDist2 > dist) {
bestDist2 = dist;
closest2 = cIndex;
}
}
_Line ends;
_Point mid;
double t1 = i.fT[0][uIndex];
xy_at_t(q1, t1, ends[0].x, ends[0].y);
xy_at_t(q1, i.fCoincidentT[0][closest1], ends[1].x, ends[1].y);
double midT = (t1 + i.fCoincidentT[0][closest1]) / 2;
xy_at_t(q1, midT, mid.x, mid.y);
LineParameters params;
params.lineEndPoints(ends);
double midDist = params.pointDistance(mid);
// Note that we prefer to always measure t error, which does not scale,
// instead of point error, which is scale dependent. FIXME
if (!approximately_zero(midDist)) {
++uIndex;
continue;
}
double t2 = i.fT[1][uIndex];
xy_at_t(q2, t2, ends[0].x, ends[0].y);
xy_at_t(q2, i.fCoincidentT[1][closest2], ends[1].x, ends[1].y);
midT = (t2 + i.fCoincidentT[1][closest2]) / 2;
xy_at_t(q2, midT, mid.x, mid.y);
params.lineEndPoints(ends);
midDist = params.pointDistance(mid);
if (!approximately_zero(midDist)) {
++uIndex;
continue;
}
// if both midpoints are close to the line, lengthen coincident span
int cEnd = closest1 ^ 1; // assume coincidence always travels in pairs
if (!between(i.fCoincidentT[0][cEnd], t1, i.fCoincidentT[0][closest1])) {
i.fCoincidentT[0][closest1] = t1;
}
cEnd = closest2 ^ 1;
if (!between(i.fCoincidentT[0][cEnd], t2, i.fCoincidentT[0][closest2])) {
i.fCoincidentT[0][closest2] = t2;
}
int remaining = --i.fUsed - uIndex;
if (remaining > 0) {
memmove(&i.fT[0][uIndex], &i.fT[0][uIndex + 1], sizeof(i.fT[0][0]) * remaining);
memmove(&i.fT[1][uIndex], &i.fT[1][uIndex + 1], sizeof(i.fT[1][0]) * remaining);
}
}
// if coincident data is subjectively a tiny span, replace it with a single point
for (cIndex = 0; cIndex < i.fCoincidentUsed; ) {
double start1 = i.fCoincidentT[0][cIndex];
double end1 = i.fCoincidentT[0][cIndex + 1];
_Line ends1;
xy_at_t(q1, start1, ends1[0].x, ends1[0].y);
xy_at_t(q1, end1, ends1[1].x, ends1[1].y);
if (!AlmostEqualUlps(ends1[0].x, ends1[1].x) || AlmostEqualUlps(ends1[0].y, ends1[1].y)) {
cIndex += 2;
continue;
}
double start2 = i.fCoincidentT[1][cIndex];
double end2 = i.fCoincidentT[1][cIndex + 1];
_Line ends2;
xy_at_t(q2, start2, ends2[0].x, ends2[0].y);
xy_at_t(q2, end2, ends2[1].x, ends2[1].y);
// again, approximately should be used with T values, not points FIXME
if (!AlmostEqualUlps(ends2[0].x, ends2[1].x) || AlmostEqualUlps(ends2[0].y, ends2[1].y)) {
cIndex += 2;
continue;
}
if (approximately_less_than_zero(start1) || approximately_less_than_zero(end1)) {
start1 = 0;
} else if (approximately_greater_than_one(start1) || approximately_greater_than_one(end1)) {
start1 = 1;
} else {
start1 = (start1 + end1) / 2;
}
if (approximately_less_than_zero(start2) || approximately_less_than_zero(end2)) {
start2 = 0;
} else if (approximately_greater_than_one(start2) || approximately_greater_than_one(end2)) {
start2 = 1;
} else {
start2 = (start2 + end2) / 2;
}
i.insert(start1, start2);
i.fCoincidentUsed -= 2;
int remaining = i.fCoincidentUsed - cIndex;
if (remaining > 0) {
memmove(&i.fCoincidentT[0][cIndex], &i.fCoincidentT[0][cIndex + 2], sizeof(i.fCoincidentT[0][0]) * remaining);
memmove(&i.fCoincidentT[1][cIndex], &i.fCoincidentT[1][cIndex + 2], sizeof(i.fCoincidentT[1][0]) * remaining);
}
}
}
bool intersect(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
if (implicit_matches(q1, q2)) {
// FIXME: compute T values
// compute the intersections of the ends to find the coincident span
bool useVertical = fabs(q1[0].x - q1[2].x) < fabs(q1[0].y - q1[2].y);
double t;
if ((t = axialIntersect(q1, q2[0], useVertical)) >= 0) {
i.addCoincident(t, 0);
}
if ((t = axialIntersect(q1, q2[2], useVertical)) >= 0) {
i.addCoincident(t, 1);
}
useVertical = fabs(q2[0].x - q2[2].x) < fabs(q2[0].y - q2[2].y);
if ((t = axialIntersect(q2, q1[0], useVertical)) >= 0) {
i.addCoincident(0, t);
}
if ((t = axialIntersect(q2, q1[2], useVertical)) >= 0) {
i.addCoincident(1, t);
}
SkASSERT(i.fCoincidentUsed <= 2);
return i.fCoincidentUsed > 0;
}
QuadraticIntersections q(q1, q2, i);
bool result = q.intersect();
// FIXME: partial coincidence detection is currently poor. For now, try
// to fix up the data after the fact. In the future, revisit the error
// term to try to avoid this kind of result in the first place.
if (i.fUsed && i.fCoincidentUsed) {
hackToFixPartialCoincidence(q1, q2, i);
}
return result;
}