/*
* 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 "SkPathOpsCubic.h"
#include "SkPathOpsLine.h"
#include "SkPathOpsPoint.h"
#include "SkPathOpsQuad.h"
#include "SkPathOpsRect.h"
#include "SkReduceOrder.h"
#include "SkTSort.h"
#if ONE_OFF_DEBUG
static const double tLimits1[2][2] = {{0.3, 0.4}, {0.8, 0.9}};
static const double tLimits2[2][2] = {{-0.8, -0.9}, {-0.8, -0.9}};
#endif
#define DEBUG_QUAD_PART ONE_OFF_DEBUG && 1
#define DEBUG_QUAD_PART_SHOW_SIMPLE DEBUG_QUAD_PART && 0
#define SWAP_TOP_DEBUG 0
static const int kCubicToQuadSubdivisionDepth = 8; // slots reserved for cubic to quads subdivision
static int quadPart(const SkDCubic& cubic, double tStart, double tEnd, SkReduceOrder* reducer) {
SkDCubic part = cubic.subDivide(tStart, tEnd);
SkDQuad quad = part.toQuad();
// FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an
// extremely shallow quadratic?
int order = reducer->reduce(quad);
#if DEBUG_QUAD_PART
SkDebugf("%s cubic=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
" t=(%1.9g,%1.9g)\n", __FUNCTION__, cubic[0].fX, cubic[0].fY,
cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY,
cubic[3].fX, cubic[3].fY, tStart, tEnd);
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n"
" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
part[0].fX, part[0].fY, part[1].fX, part[1].fY, part[2].fX, part[2].fY,
part[3].fX, part[3].fY, quad[0].fX, quad[0].fY,
quad[1].fX, quad[1].fY, quad[2].fX, quad[2].fY);
#if DEBUG_QUAD_PART_SHOW_SIMPLE
SkDebugf("%s simple=(%1.9g,%1.9g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY);
if (order > 1) {
SkDebugf(" %1.9g,%1.9g", reducer->fQuad[1].fX, reducer->fQuad[1].fY);
}
if (order > 2) {
SkDebugf(" %1.9g,%1.9g", reducer->fQuad[2].fX, reducer->fQuad[2].fY);
}
SkDebugf(")\n");
SkASSERT(order < 4 && order > 0);
#endif
#endif
return order;
}
static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2,
int order2, SkIntersections& i) {
if (order1 == 3 && order2 == 3) {
i.intersect(simple1, simple2);
} else if (order1 <= 2 && order2 <= 2) {
i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2);
} else if (order1 == 3 && order2 <= 2) {
i.intersect(simple1, (const SkDLine&) simple2);
} else {
SkASSERT(order1 <= 2 && order2 == 3);
i.intersect(simple2, (const SkDLine&) simple1);
i.swapPts();
}
}
// this flavor centers potential intersections recursively. In contrast, '2' may inadvertently
// chase intersections near quadratic ends, requiring odd hacks to find them.
static void intersect(const SkDCubic& cubic1, double t1s, double t1e, const SkDCubic& cubic2,
double t2s, double t2e, double precisionScale, SkIntersections& i) {
i.upDepth();
SkDCubic c1 = cubic1.subDivide(t1s, t1e);
SkDCubic c2 = cubic2.subDivide(t2s, t2e);
SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts1;
// OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection)
c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1);
SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts2;
c2.toQuadraticTs(c2.calcPrecision() * precisionScale, &ts2);
double t1Start = t1s;
int ts1Count = ts1.count();
for (int i1 = 0; i1 <= ts1Count; ++i1) {
const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1;
const double t1 = t1s + (t1e - t1s) * tEnd1;
SkReduceOrder s1;
int o1 = quadPart(cubic1, t1Start, t1, &s1);
double t2Start = t2s;
int ts2Count = ts2.count();
for (int i2 = 0; i2 <= ts2Count; ++i2) {
const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1;
const double t2 = t2s + (t2e - t2s) * tEnd2;
if (&cubic1 == &cubic2 && t1Start >= t2Start) {
t2Start = t2;
continue;
}
SkReduceOrder s2;
int o2 = quadPart(cubic2, t2Start, t2, &s2);
#if ONE_OFF_DEBUG
char tab[] = " ";
if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1
&& tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) {
SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab,
__FUNCTION__, t1Start, t1, t2Start, t2);
SkIntersections xlocals;
xlocals.allowNear(false);
intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals);
SkDebugf(" xlocals.fUsed=%d\n", xlocals.used());
}
#endif
SkIntersections locals;
locals.allowNear(false);
intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals);
int tCount = locals.used();
for (int tIdx = 0; tIdx < tCount; ++tIdx) {
double to1 = t1Start + (t1 - t1Start) * locals[0][tIdx];
double to2 = t2Start + (t2 - t2Start) * locals[1][tIdx];
// if the computed t is not sufficiently precise, iterate
SkDPoint p1 = cubic1.ptAtT(to1);
SkDPoint p2 = cubic2.ptAtT(to2);
if (p1.approximatelyEqual(p2)) {
// FIXME: local edge may be coincident -- experiment with not propagating coincidence to caller
// SkASSERT(!locals.isCoincident(tIdx));
if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) {
if (i.swapped()) { // FIXME: insert should respect swap
i.insert(to2, to1, p1);
} else {
i.insert(to1, to2, p1);
}
}
} else {
/*for random cubics, 16 below catches 99.997% of the intersections. To test for the remaining 0.003%
look for nearly coincident curves. and check each 1/16th section.
*/
double offset = precisionScale / 16; // FIXME: const is arbitrary: test, refine
double c1Bottom = tIdx == 0 ? 0 :
(t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2;
double c1Min = SkTMax(c1Bottom, to1 - offset);
double c1Top = tIdx == tCount - 1 ? 1 :
(t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2;
double c1Max = SkTMin(c1Top, to1 + offset);
double c2Min = SkTMax(0., to2 - offset);
double c2Max = SkTMin(1., to2 + offset);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
__FUNCTION__,
c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
&& c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
&& to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
&& c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
&& to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
" 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1.,
to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
" c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
c1Max, c2Min, c2Max);
#endif
intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
#endif
if (tCount > 1) {
c1Min = SkTMax(0., to1 - offset);
c1Max = SkTMin(1., to1 + offset);
double c2Bottom = tIdx == 0 ? to2 :
(t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2;
double c2Top = tIdx == tCount - 1 ? to2 :
(t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2;
if (c2Bottom > c2Top) {
SkTSwap(c2Bottom, c2Top);
}
if (c2Bottom == to2) {
c2Bottom = 0;
}
if (c2Top == to2) {
c2Top = 1;
}
c2Min = SkTMax(c2Bottom, to2 - offset);
c2Max = SkTMin(c2Top, to2 + offset);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
__FUNCTION__,
c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
&& c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
&& to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
&& c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
&& to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
" 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
" c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
c1Max, c2Min, c2Max);
#endif
intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
#endif
c1Min = SkTMax(c1Bottom, to1 - offset);
c1Max = SkTMin(c1Top, to1 + offset);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
__FUNCTION__,
c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
&& c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
&& to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
&& c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
&& to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
" 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
" c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
c1Max, c2Min, c2Max);
#endif
intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
#if ONE_OFF_DEBUG
SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
#endif
}
// intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
// FIXME: if no intersection is found, either quadratics intersected where
// cubics did not, or the intersection was missed. In the former case, expect
// the quadratics to be nearly parallel at the point of intersection, and check
// for that.
}
}
t2Start = t2;
}
t1Start = t1;
}
i.downDepth();
}
// if two ends intersect, check middle for coincidence
bool SkIntersections::cubicCheckCoincidence(const SkDCubic& c1, const SkDCubic& c2) {
if (fUsed < 2) {
return false;
}
int last = fUsed - 1;
double tRange1 = fT[0][last] - fT[0][0];
double tRange2 = fT[1][last] - fT[1][0];
for (int index = 1; index < 5; ++index) {
double testT1 = fT[0][0] + tRange1 * index / 5;
double testT2 = fT[1][0] + tRange2 * index / 5;
SkDPoint testPt1 = c1.ptAtT(testT1);
SkDPoint testPt2 = c2.ptAtT(testT2);
if (!testPt1.approximatelyEqual(testPt2)) {
return false;
}
}
if (fUsed > 2) {
fPt[1] = fPt[last];
fT[0][1] = fT[0][last];
fT[1][1] = fT[1][last];
fUsed = 2;
}
fIsCoincident[0] = fIsCoincident[1] = 0x03;
return true;
}
#define LINE_FRACTION 0.1
// intersect the end of the cubic with the other. Try lines from the end to control and opposite
// end to determine range of t on opposite cubic.
bool SkIntersections::cubicExactEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2) {
int t1Index = start ? 0 : 3;
double testT = (double) !start;
bool swap = swapped();
// quad/quad at this point checks to see if exact matches have already been found
// cubic/cubic can't reject so easily since cubics can intersect same point more than once
SkDLine tmpLine;
tmpLine[0] = tmpLine[1] = cubic2[t1Index];
tmpLine[1].fX += cubic2[2 - start].fY - cubic2[t1Index].fY;
tmpLine[1].fY -= cubic2[2 - start].fX - cubic2[t1Index].fX;
SkIntersections impTs;
impTs.allowNear(false);
impTs.intersectRay(cubic1, tmpLine);
for (int index = 0; index < impTs.used(); ++index) {
SkDPoint realPt = impTs.pt(index);
if (!tmpLine[0].approximatelyEqual(realPt)) {
continue;
}
if (swap) {
cubicInsert(testT, impTs[0][index], tmpLine[0], cubic2, cubic1);
} else {
cubicInsert(impTs[0][index], testT, tmpLine[0], cubic1, cubic2);
}
return true;
}
return false;
}
void SkIntersections::cubicInsert(double one, double two, const SkDPoint& pt,
const SkDCubic& cubic1, const SkDCubic& cubic2) {
for (int index = 0; index < fUsed; ++index) {
if (fT[0][index] == one) {
double oldTwo = fT[1][index];
if (oldTwo == two) {
return;
}
SkDPoint mid = cubic2.ptAtT((oldTwo + two) / 2);
if (mid.approximatelyEqual(fPt[index])) {
return;
}
}
if (fT[1][index] == two) {
SkDPoint mid = cubic1.ptAtT((fT[0][index] + two) / 2);
if (mid.approximatelyEqual(fPt[index])) {
return;
}
}
}
insert(one, two, pt);
}
void SkIntersections::cubicNearEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2,
const SkDRect& bounds2) {
SkDLine line;
int t1Index = start ? 0 : 3;
double testT = (double) !start;
// don't bother if the two cubics are connnected
static const int kPointsInCubic = 4; // FIXME: move to DCubic, replace '4' with this
static const int kMaxLineCubicIntersections = 3;
SkSTArray<(kMaxLineCubicIntersections - 1) * kMaxLineCubicIntersections, double, true> tVals;
line[0] = cubic1[t1Index];
// this variant looks for intersections with the end point and lines parallel to other points
for (int index = 0; index < kPointsInCubic; ++index) {
if (index == t1Index) {
continue;
}
SkDVector dxy1 = cubic1[index] - line[0];
dxy1 /= SkDCubic::gPrecisionUnit;
line[1] = line[0] + dxy1;
SkDRect lineBounds;
lineBounds.setBounds(line);
if (!bounds2.intersects(&lineBounds)) {
continue;
}
SkIntersections local;
if (!local.intersect(cubic2, line)) {
continue;
}
for (int idx2 = 0; idx2 < local.used(); ++idx2) {
double foundT = local[0][idx2];
if (approximately_less_than_zero(foundT)
|| approximately_greater_than_one(foundT)) {
continue;
}
if (local.pt(idx2).approximatelyEqual(line[0])) {
if (swapped()) { // FIXME: insert should respect swap
insert(foundT, testT, line[0]);
} else {
insert(testT, foundT, line[0]);
}
} else {
tVals.push_back(foundT);
}
}
}
if (tVals.count() == 0) {
return;
}
SkTQSort<double>(tVals.begin(), tVals.end() - 1);
double tMin1 = start ? 0 : 1 - LINE_FRACTION;
double tMax1 = start ? LINE_FRACTION : 1;
int tIdx = 0;
do {
int tLast = tIdx;
while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) {
++tLast;
}
double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0);
double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0);
int lastUsed = used();
if (start ? tMax1 < tMin2 : tMax2 < tMin1) {
::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
}
if (lastUsed == used()) {
tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0);
tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0);
if (start ? tMax1 < tMin2 : tMax2 < tMin1) {
::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
}
}
tIdx = tLast + 1;
} while (tIdx < tVals.count());
return;
}
const double CLOSE_ENOUGH = 0.001;
static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) {
return false;
}
pt = cubic.ptAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2);
return true;
}
static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
int last = i.used() - 1;
if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) {
return false;
}
pt = cubic.ptAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2);
return true;
}
static bool only_end_pts_in_common(const SkDCubic& c1, const SkDCubic& c2) {
// the idea here is to see at minimum do a quick reject by rotating all points
// to either side of the line formed by connecting the endpoints
// if the opposite curves points are on the line or on the other side, the
// curves at most intersect at the endpoints
for (int oddMan = 0; oddMan < 4; ++oddMan) {
const SkDPoint* endPt[3];
for (int opp = 1; opp < 4; ++opp) {
int end = oddMan ^ opp; // choose a value not equal to oddMan
endPt[opp - 1] = &c1[end];
}
for (int triTest = 0; triTest < 3; ++triTest) {
double origX = endPt[triTest]->fX;
double origY = endPt[triTest]->fY;
int oppTest = triTest + 1;
if (3 == oppTest) {
oppTest = 0;
}
double adj = endPt[oppTest]->fX - origX;
double opp = endPt[oppTest]->fY - origY;
if (adj == 0 && opp == 0) { // if the other point equals the test point, ignore it
continue;
}
double sign = (c1[oddMan].fY - origY) * adj - (c1[oddMan].fX - origX) * opp;
if (approximately_zero(sign)) {
goto tryNextHalfPlane;
}
for (int n = 0; n < 4; ++n) {
double test = (c2[n].fY - origY) * adj - (c2[n].fX - origX) * opp;
if (test * sign > 0 && !precisely_zero(test)) {
goto tryNextHalfPlane;
}
}
}
return true;
tryNextHalfPlane:
;
}
return false;
}
int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) {
if (fMax == 0) {
fMax = 9;
}
bool selfIntersect = &c1 == &c2;
if (selfIntersect) {
if (c1[0].approximatelyEqual(c1[3])) {
insert(0, 1, c1[0]);
return fUsed;
}
} else {
// OPTIMIZATION: set exact end bits here to avoid cubic exact end later
for (int i1 = 0; i1 < 4; i1 += 3) {
for (int i2 = 0; i2 < 4; i2 += 3) {
if (c1[i1].approximatelyEqual(c2[i2])) {
insert(i1 >> 1, i2 >> 1, c1[i1]);
}
}
}
}
SkASSERT(fUsed < 4);
if (!selfIntersect) {
if (only_end_pts_in_common(c1, c2)) {
return fUsed;
}
if (only_end_pts_in_common(c2, c1)) {
return fUsed;
}
}
// quad/quad does linear test here -- cubic does not
// cubics which are really lines should have been detected in reduce step earlier
int exactEndBits = 0;
if (selfIntersect) {
if (fUsed) {
return fUsed;
}
} else {
exactEndBits |= cubicExactEnd(c1, false, c2) << 0;
exactEndBits |= cubicExactEnd(c1, true, c2) << 1;
swap();
exactEndBits |= cubicExactEnd(c2, false, c1) << 2;
exactEndBits |= cubicExactEnd(c2, true, c1) << 3;
swap();
}
if (cubicCheckCoincidence(c1, c2)) {
SkASSERT(!selfIntersect);
return fUsed;
}
// FIXME: pass in cached bounds from caller
SkDRect c2Bounds;
c2Bounds.setBounds(c2);
if (!(exactEndBits & 4)) {
cubicNearEnd(c1, false, c2, c2Bounds);
}
if (!(exactEndBits & 8)) {
if (selfIntersect && fUsed) {
return fUsed;
}
cubicNearEnd(c1, true, c2, c2Bounds);
if (selfIntersect && fUsed && ((approximately_less_than_zero(fT[0][0])
&& approximately_less_than_zero(fT[1][0]))
|| (approximately_greater_than_one(fT[0][0])
&& approximately_greater_than_one(fT[1][0])))) {
SkASSERT(fUsed == 1);
fUsed = 0;
return fUsed;
}
}
if (!selfIntersect) {
SkDRect c1Bounds;
c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ?
swap();
if (!(exactEndBits & 1)) {
cubicNearEnd(c2, false, c1, c1Bounds);
}
if (!(exactEndBits & 2)) {
cubicNearEnd(c2, true, c1, c1Bounds);
}
swap();
}
if (cubicCheckCoincidence(c1, c2)) {
SkASSERT(!selfIntersect);
return fUsed;
}
SkIntersections i;
i.fAllowNear = false;
i.fMax = 9;
::intersect(c1, 0, 1, c2, 0, 1, 1, i);
int compCount = i.used();
if (compCount) {
int exactCount = used();
if (exactCount == 0) {
*this = i;
} else {
// at least one is exact or near, and at least one was computed. Eliminate duplicates
for (int exIdx = 0; exIdx < exactCount; ++exIdx) {
for (int cpIdx = 0; cpIdx < compCount; ) {
if (fT[0][0] == i[0][0] && fT[1][0] == i[1][0]) {
i.removeOne(cpIdx);
--compCount;
continue;
}
double tAvg = (fT[0][exIdx] + i[0][cpIdx]) / 2;
SkDPoint pt = c1.ptAtT(tAvg);
if (!pt.approximatelyEqual(fPt[exIdx])) {
++cpIdx;
continue;
}
tAvg = (fT[1][exIdx] + i[1][cpIdx]) / 2;
pt = c2.ptAtT(tAvg);
if (!pt.approximatelyEqual(fPt[exIdx])) {
++cpIdx;
continue;
}
i.removeOne(cpIdx);
--compCount;
}
}
// if mid t evaluates to nearly the same point, skip the t
for (int cpIdx = 0; cpIdx < compCount - 1; ) {
double tAvg = (fT[0][cpIdx] + i[0][cpIdx + 1]) / 2;
SkDPoint pt = c1.ptAtT(tAvg);
if (!pt.approximatelyEqual(fPt[cpIdx])) {
++cpIdx;
continue;
}
tAvg = (fT[1][cpIdx] + i[1][cpIdx + 1]) / 2;
pt = c2.ptAtT(tAvg);
if (!pt.approximatelyEqual(fPt[cpIdx])) {
++cpIdx;
continue;
}
i.removeOne(cpIdx);
--compCount;
}
// in addition to adding below missing function, think about how to say
append(i);
}
}
// If an end point and a second point very close to the end is returned, the second
// point may have been detected because the approximate quads
// intersected at the end and close to it. Verify that the second point is valid.
if (fUsed <= 1) {
return fUsed;
}
SkDPoint pt[2];
if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1])
&& pt[0].approximatelyEqual(pt[1])) {
removeOne(1);
}
if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1])
&& pt[0].approximatelyEqual(pt[1])) {
removeOne(used() - 2);
}
// vet the pairs of t values to see if the mid value is also on the curve. If so, mark
// the span as coincident
if (fUsed >= 2 && !coincidentUsed()) {
int last = fUsed - 1;
int match = 0;
for (int index = 0; index < last; ++index) {
double mid1 = (fT[0][index] + fT[0][index + 1]) / 2;
double mid2 = (fT[1][index] + fT[1][index + 1]) / 2;
pt[0] = c1.ptAtT(mid1);
pt[1] = c2.ptAtT(mid2);
if (pt[0].approximatelyEqual(pt[1])) {
match |= 1 << index;
}
}
if (match) {
#if DEBUG_CONCIDENT
if (((match + 1) & match) != 0) {
SkDebugf("%s coincident hole\n", __FUNCTION__);
}
#endif
// for now, assume that everything from start to finish is coincident
if (fUsed > 2) {
fPt[1] = fPt[last];
fT[0][1] = fT[0][last];
fT[1][1] = fT[1][last];
fIsCoincident[0] = 0x03;
fIsCoincident[1] = 0x03;
fUsed = 2;
}
}
}
return fUsed;
}
// Up promote the quad to a cubic.
// OPTIMIZATION If this is a common use case, optimize by duplicating
// the intersect 3 loop to avoid the promotion / demotion code
int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) {
fMax = 6;
SkDCubic up = quad.toCubic();
(void) intersect(cubic, up);
return used();
}
/* http://www.ag.jku.at/compass/compasssample.pdf
( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen
Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth@math.uio.no
SINTEF Applied Mathematics http://www.sintef.no )
describes a method to find the self intersection of a cubic by taking the gradient of the implicit
form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/
int SkIntersections::intersect(const SkDCubic& c) {
fMax = 1;
// check to see if x or y end points are the extrema. Are other quick rejects possible?
if (c.endsAreExtremaInXOrY()) {
return false;
}
// OPTIMIZATION: could quick reject if neither end point tangent ray intersected the line
// segment formed by the opposite end point to the control point
(void) intersect(c, c);
if (used() > 0) {
if (approximately_equal_double(fT[0][0], fT[1][0])) {
fUsed = 0;
} else {
SkASSERT(used() == 1);
if (fT[0][0] > fT[1][0]) {
swapPts();
}
}
}
return used();
}