/*
* 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 "SkOpAngle.h"
#include "SkOpSegment.h"
#include "SkPathOpsCurve.h"
#include "SkTSort.h"
/* Angles are sorted counterclockwise. The smallest angle has a positive x and the smallest
positive y. The largest angle has a positive x and a zero y. */
#if DEBUG_ANGLE
static bool CompareResult(const char* func, SkString* bugOut, SkString* bugPart, int append,
bool compare) {
SkDebugf("%s %c %d\n", bugOut->c_str(), compare ? 'T' : 'F', append);
SkDebugf("%sPart %s\n", func, bugPart[0].c_str());
SkDebugf("%sPart %s\n", func, bugPart[1].c_str());
SkDebugf("%sPart %s\n", func, bugPart[2].c_str());
return compare;
}
#define COMPARE_RESULT(append, compare) CompareResult(__FUNCTION__, &bugOut, bugPart, append, \
compare)
#else
#define COMPARE_RESULT(append, compare) compare
#endif
/* quarter angle values for sector
31 x > 0, y == 0 horizontal line (to the right)
0 x > 0, y == epsilon quad/cubic horizontal tangent eventually going +y
1 x > 0, y > 0, x > y nearer horizontal angle
2 x + e == y quad/cubic 45 going horiz
3 x > 0, y > 0, x == y 45 angle
4 x == y + e quad/cubic 45 going vert
5 x > 0, y > 0, x < y nearer vertical angle
6 x == epsilon, y > 0 quad/cubic vertical tangent eventually going +x
7 x == 0, y > 0 vertical line (to the top)
8 7 6
9 | 5
10 | 4
11 | 3
12 \ | / 2
13 | 1
14 | 0
15 --------------+------------- 31
16 | 30
17 | 29
18 / | \ 28
19 | 27
20 | 26
21 | 25
22 23 24
*/
// return true if lh < this < rh
bool SkOpAngle::after(SkOpAngle* test) {
SkOpAngle* lh = test;
SkOpAngle* rh = lh->fNext;
SkASSERT(lh != rh);
fPart.fCurve = fOriginalCurvePart;
lh->fPart.fCurve = lh->fOriginalCurvePart;
lh->fPart.fCurve.offset(lh->segment()->verb(), fPart.fCurve[0] - lh->fPart.fCurve[0]);
rh->fPart.fCurve = rh->fOriginalCurvePart;
rh->fPart.fCurve.offset(rh->segment()->verb(), fPart.fCurve[0] - rh->fPart.fCurve[0]);
#if DEBUG_ANGLE
SkString bugOut;
bugOut.printf("%s [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g"
" < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g"
" < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g ", __FUNCTION__,
lh->segment()->debugID(), lh->debugID(), lh->fSectorStart, lh->fSectorEnd,
lh->fStart->t(), lh->fEnd->t(),
segment()->debugID(), debugID(), fSectorStart, fSectorEnd, fStart->t(), fEnd->t(),
rh->segment()->debugID(), rh->debugID(), rh->fSectorStart, rh->fSectorEnd,
rh->fStart->t(), rh->fEnd->t());
SkString bugPart[3] = { lh->debugPart(), this->debugPart(), rh->debugPart() };
#endif
if (lh->fComputeSector && !lh->computeSector()) {
return COMPARE_RESULT(1, true);
}
if (fComputeSector && !this->computeSector()) {
return COMPARE_RESULT(2, true);
}
if (rh->fComputeSector && !rh->computeSector()) {
return COMPARE_RESULT(3, true);
}
#if DEBUG_ANGLE // reset bugOut with computed sectors
bugOut.printf("%s [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g"
" < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g"
" < [%d/%d] %d/%d tStart=%1.9g tEnd=%1.9g ", __FUNCTION__,
lh->segment()->debugID(), lh->debugID(), lh->fSectorStart, lh->fSectorEnd,
lh->fStart->t(), lh->fEnd->t(),
segment()->debugID(), debugID(), fSectorStart, fSectorEnd, fStart->t(), fEnd->t(),
rh->segment()->debugID(), rh->debugID(), rh->fSectorStart, rh->fSectorEnd,
rh->fStart->t(), rh->fEnd->t());
#endif
bool ltrOverlap = (lh->fSectorMask | rh->fSectorMask) & fSectorMask;
bool lrOverlap = lh->fSectorMask & rh->fSectorMask;
int lrOrder; // set to -1 if either order works
if (!lrOverlap) { // no lh/rh sector overlap
if (!ltrOverlap) { // no lh/this/rh sector overlap
return COMPARE_RESULT(4, (lh->fSectorEnd > rh->fSectorStart)
^ (fSectorStart > lh->fSectorEnd) ^ (fSectorStart > rh->fSectorStart));
}
int lrGap = (rh->fSectorStart - lh->fSectorStart + 32) & 0x1f;
/* A tiny change can move the start +/- 4. The order can only be determined if
lr gap is not 12 to 20 or -12 to -20.
-31 ..-21 1
-20 ..-12 -1
-11 .. -1 0
0 shouldn't get here
11 .. 1 1
12 .. 20 -1
21 .. 31 0
*/
lrOrder = lrGap > 20 ? 0 : lrGap > 11 ? -1 : 1;
} else {
lrOrder = (int) lh->orderable(rh);
if (!ltrOverlap) {
return COMPARE_RESULT(5, !lrOrder);
}
}
int ltOrder;
SkASSERT((lh->fSectorMask & fSectorMask) || (rh->fSectorMask & fSectorMask));
if (lh->fSectorMask & fSectorMask) {
ltOrder = (int) lh->orderable(this);
} else {
int ltGap = (fSectorStart - lh->fSectorStart + 32) & 0x1f;
ltOrder = ltGap > 20 ? 0 : ltGap > 11 ? -1 : 1;
}
int trOrder;
if (rh->fSectorMask & fSectorMask) {
trOrder = (int) orderable(rh);
} else {
int trGap = (rh->fSectorStart - fSectorStart + 32) & 0x1f;
trOrder = trGap > 20 ? 0 : trGap > 11 ? -1 : 1;
}
this->alignmentSameSide(lh, <Order);
this->alignmentSameSide(rh, &trOrder);
if (lrOrder >= 0 && ltOrder >= 0 && trOrder >= 0) {
return COMPARE_RESULT(7, lrOrder ? (ltOrder & trOrder) : (ltOrder | trOrder));
}
SkASSERT(lrOrder >= 0 || ltOrder >= 0 || trOrder >= 0);
// There's not enough information to sort. Get the pairs of angles in opposite planes.
// If an order is < 0, the pair is already in an opposite plane. Check the remaining pairs.
// FIXME : once all variants are understood, rewrite this more simply
if (ltOrder == 0 && lrOrder == 0) {
SkASSERT(trOrder < 0);
// FIXME : once this is verified to work, remove one opposite angle call
SkDEBUGCODE(bool lrOpposite = lh->oppositePlanes(rh));
bool ltOpposite = lh->oppositePlanes(this);
SkOPASSERT(lrOpposite != ltOpposite);
return COMPARE_RESULT(8, ltOpposite);
} else if (ltOrder == 1 && trOrder == 0) {
SkASSERT(lrOrder < 0);
bool trOpposite = oppositePlanes(rh);
return COMPARE_RESULT(9, trOpposite);
} else if (lrOrder == 1 && trOrder == 1) {
SkASSERT(ltOrder < 0);
// SkDEBUGCODE(bool trOpposite = oppositePlanes(rh));
bool lrOpposite = lh->oppositePlanes(rh);
// SkASSERT(lrOpposite != trOpposite);
return COMPARE_RESULT(10, lrOpposite);
}
if (lrOrder < 0) {
if (ltOrder < 0) {
return COMPARE_RESULT(11, trOrder);
}
return COMPARE_RESULT(12, ltOrder);
}
return COMPARE_RESULT(13, !lrOrder);
}
// given a line, see if the opposite curve's convex hull is all on one side
// returns -1=not on one side 0=this CW of test 1=this CCW of test
int SkOpAngle::allOnOneSide(const SkOpAngle* test) {
SkASSERT(!fPart.isCurve());
SkASSERT(test->fPart.isCurve());
SkDPoint origin = fPart.fCurve[0];
SkDVector line = fPart.fCurve[1] - origin;
double crosses[3];
SkPath::Verb testVerb = test->segment()->verb();
int iMax = SkPathOpsVerbToPoints(testVerb);
// SkASSERT(origin == test.fCurveHalf[0]);
const SkDCurve& testCurve = test->fPart.fCurve;
for (int index = 1; index <= iMax; ++index) {
double xy1 = line.fX * (testCurve[index].fY - origin.fY);
double xy2 = line.fY * (testCurve[index].fX - origin.fX);
crosses[index - 1] = AlmostBequalUlps(xy1, xy2) ? 0 : xy1 - xy2;
}
if (crosses[0] * crosses[1] < 0) {
return -1;
}
if (SkPath::kCubic_Verb == testVerb) {
if (crosses[0] * crosses[2] < 0 || crosses[1] * crosses[2] < 0) {
return -1;
}
}
if (crosses[0]) {
return crosses[0] < 0;
}
if (crosses[1]) {
return crosses[1] < 0;
}
if (SkPath::kCubic_Verb == testVerb && crosses[2]) {
return crosses[2] < 0;
}
fUnorderable = true;
return -1;
}
// To sort the angles, all curves are translated to have the same starting point.
// If the curve's control point in its original position is on one side of a compared line,
// and translated is on the opposite side, reverse the previously computed order.
void SkOpAngle::alignmentSameSide(const SkOpAngle* test, int* order) const {
if (*order < 0) {
return;
}
if (fPart.isCurve()) {
// This should support all curve types, but only bug that requires this has lines
// Turning on for curves causes existing tests to fail
return;
}
if (test->fPart.isCurve()) {
return;
}
const SkDPoint& xOrigin = test->fPart.fCurve.fLine[0];
const SkDPoint& oOrigin = test->fOriginalCurvePart.fLine[0];
if (xOrigin == oOrigin) {
return;
}
int iMax = SkPathOpsVerbToPoints(this->segment()->verb());
SkDVector xLine = test->fPart.fCurve.fLine[1] - xOrigin;
SkDVector oLine = test->fOriginalCurvePart.fLine[1] - oOrigin;
for (int index = 1; index <= iMax; ++index) {
const SkDPoint& testPt = fPart.fCurve[index];
double xCross = oLine.crossCheck(testPt - xOrigin);
double oCross = xLine.crossCheck(testPt - oOrigin);
if (oCross * xCross < 0) {
*order ^= 1;
break;
}
}
}
bool SkOpAngle::checkCrossesZero() const {
int start = SkTMin(fSectorStart, fSectorEnd);
int end = SkTMax(fSectorStart, fSectorEnd);
bool crossesZero = end - start > 16;
return crossesZero;
}
bool SkOpAngle::checkParallel(SkOpAngle* rh) {
SkDVector scratch[2];
const SkDVector* sweep, * tweep;
if (this->fPart.isOrdered()) {
sweep = this->fPart.fSweep;
} else {
scratch[0] = this->fPart.fCurve[1] - this->fPart.fCurve[0];
sweep = &scratch[0];
}
if (rh->fPart.isOrdered()) {
tweep = rh->fPart.fSweep;
} else {
scratch[1] = rh->fPart.fCurve[1] - rh->fPart.fCurve[0];
tweep = &scratch[1];
}
double s0xt0 = sweep->crossCheck(*tweep);
if (tangentsDiverge(rh, s0xt0)) {
return s0xt0 < 0;
}
// compute the perpendicular to the endpoints and see where it intersects the opposite curve
// if the intersections within the t range, do a cross check on those
bool inside;
if (!fEnd->contains(rh->fEnd)) {
if (this->endToSide(rh, &inside)) {
return inside;
}
if (rh->endToSide(this, &inside)) {
return !inside;
}
}
if (this->midToSide(rh, &inside)) {
return inside;
}
if (rh->midToSide(this, &inside)) {
return !inside;
}
// compute the cross check from the mid T values (last resort)
SkDVector m0 = segment()->dPtAtT(this->midT()) - this->fPart.fCurve[0];
SkDVector m1 = rh->segment()->dPtAtT(rh->midT()) - rh->fPart.fCurve[0];
double m0xm1 = m0.crossCheck(m1);
if (m0xm1 == 0) {
this->fUnorderable = true;
rh->fUnorderable = true;
return true;
}
return m0xm1 < 0;
}
// the original angle is too short to get meaningful sector information
// lengthen it until it is long enough to be meaningful or leave it unset if lengthening it
// would cause it to intersect one of the adjacent angles
bool SkOpAngle::computeSector() {
if (fComputedSector) {
return !fUnorderable;
}
fComputedSector = true;
bool stepUp = fStart->t() < fEnd->t();
SkOpSpanBase* checkEnd = fEnd;
if (checkEnd->final() && stepUp) {
fUnorderable = true;
return false;
}
do {
// advance end
const SkOpSegment* other = checkEnd->segment();
const SkOpSpanBase* oSpan = other->head();
do {
if (oSpan->segment() != segment()) {
continue;
}
if (oSpan == checkEnd) {
continue;
}
if (!approximately_equal(oSpan->t(), checkEnd->t())) {
continue;
}
goto recomputeSector;
} while (!oSpan->final() && (oSpan = oSpan->upCast()->next()));
checkEnd = stepUp ? !checkEnd->final()
? checkEnd->upCast()->next() : nullptr
: checkEnd->prev();
} while (checkEnd);
recomputeSector:
SkOpSpanBase* computedEnd = stepUp ? checkEnd ? checkEnd->prev() : fEnd->segment()->head()
: checkEnd ? checkEnd->upCast()->next() : fEnd->segment()->tail();
if (checkEnd == fEnd || computedEnd == fEnd || computedEnd == fStart) {
fUnorderable = true;
return false;
}
if (stepUp != (fStart->t() < computedEnd->t())) {
fUnorderable = true;
return false;
}
SkOpSpanBase* saveEnd = fEnd;
fComputedEnd = fEnd = computedEnd;
setSpans();
setSector();
fEnd = saveEnd;
return !fUnorderable;
}
int SkOpAngle::convexHullOverlaps(const SkOpAngle* rh) {
const SkDVector* sweep = this->fPart.fSweep;
const SkDVector* tweep = rh->fPart.fSweep;
double s0xs1 = sweep[0].crossCheck(sweep[1]);
double s0xt0 = sweep[0].crossCheck(tweep[0]);
double s1xt0 = sweep[1].crossCheck(tweep[0]);
bool tBetweenS = s0xs1 > 0 ? s0xt0 > 0 && s1xt0 < 0 : s0xt0 < 0 && s1xt0 > 0;
double s0xt1 = sweep[0].crossCheck(tweep[1]);
double s1xt1 = sweep[1].crossCheck(tweep[1]);
tBetweenS |= s0xs1 > 0 ? s0xt1 > 0 && s1xt1 < 0 : s0xt1 < 0 && s1xt1 > 0;
double t0xt1 = tweep[0].crossCheck(tweep[1]);
if (tBetweenS) {
return -1;
}
if ((s0xt0 == 0 && s1xt1 == 0) || (s1xt0 == 0 && s0xt1 == 0)) { // s0 to s1 equals t0 to t1
return -1;
}
bool sBetweenT = t0xt1 > 0 ? s0xt0 < 0 && s0xt1 > 0 : s0xt0 > 0 && s0xt1 < 0;
sBetweenT |= t0xt1 > 0 ? s1xt0 < 0 && s1xt1 > 0 : s1xt0 > 0 && s1xt1 < 0;
if (sBetweenT) {
return -1;
}
// if all of the sweeps are in the same half plane, then the order of any pair is enough
if (s0xt0 >= 0 && s0xt1 >= 0 && s1xt0 >= 0 && s1xt1 >= 0) {
return 0;
}
if (s0xt0 <= 0 && s0xt1 <= 0 && s1xt0 <= 0 && s1xt1 <= 0) {
return 1;
}
// if the outside sweeps are greater than 180 degress:
// first assume the inital tangents are the ordering
// if the midpoint direction matches the inital order, that is enough
SkDVector m0 = this->segment()->dPtAtT(this->midT()) - this->fPart.fCurve[0];
SkDVector m1 = rh->segment()->dPtAtT(rh->midT()) - rh->fPart.fCurve[0];
double m0xm1 = m0.crossCheck(m1);
if (s0xt0 > 0 && m0xm1 > 0) {
return 0;
}
if (s0xt0 < 0 && m0xm1 < 0) {
return 1;
}
if (tangentsDiverge(rh, s0xt0)) {
return s0xt0 < 0;
}
return m0xm1 < 0;
}
// OPTIMIZATION: longest can all be either lazily computed here or precomputed in setup
double SkOpAngle::distEndRatio(double dist) const {
double longest = 0;
const SkOpSegment& segment = *this->segment();
int ptCount = SkPathOpsVerbToPoints(segment.verb());
const SkPoint* pts = segment.pts();
for (int idx1 = 0; idx1 <= ptCount - 1; ++idx1) {
for (int idx2 = idx1 + 1; idx2 <= ptCount; ++idx2) {
if (idx1 == idx2) {
continue;
}
SkDVector v;
v.set(pts[idx2] - pts[idx1]);
double lenSq = v.lengthSquared();
longest = SkTMax(longest, lenSq);
}
}
return sqrt(longest) / dist;
}
bool SkOpAngle::endsIntersect(SkOpAngle* rh) {
SkPath::Verb lVerb = this->segment()->verb();
SkPath::Verb rVerb = rh->segment()->verb();
int lPts = SkPathOpsVerbToPoints(lVerb);
int rPts = SkPathOpsVerbToPoints(rVerb);
SkDLine rays[] = {{{this->fPart.fCurve[0], rh->fPart.fCurve[rPts]}},
{{this->fPart.fCurve[0], this->fPart.fCurve[lPts]}}};
if (this->fEnd->contains(rh->fEnd)) {
return checkParallel(rh);
}
double smallTs[2] = {-1, -1};
bool limited[2] = {false, false};
for (int index = 0; index < 2; ++index) {
SkPath::Verb cVerb = index ? rVerb : lVerb;
// if the curve is a line, then the line and the ray intersect only at their crossing
if (cVerb == SkPath::kLine_Verb) {
continue;
}
const SkOpSegment& segment = index ? *rh->segment() : *this->segment();
SkIntersections i;
(*CurveIntersectRay[cVerb])(segment.pts(), segment.weight(), rays[index], &i);
double tStart = index ? rh->fStart->t() : this->fStart->t();
double tEnd = index ? rh->fComputedEnd->t() : this->fComputedEnd->t();
bool testAscends = tStart < (index ? rh->fComputedEnd->t() : this->fComputedEnd->t());
double t = testAscends ? 0 : 1;
for (int idx2 = 0; idx2 < i.used(); ++idx2) {
double testT = i[0][idx2];
if (!approximately_between_orderable(tStart, testT, tEnd)) {
continue;
}
if (approximately_equal_orderable(tStart, testT)) {
continue;
}
smallTs[index] = t = testAscends ? SkTMax(t, testT) : SkTMin(t, testT);
limited[index] = approximately_equal_orderable(t, tEnd);
}
}
bool sRayLonger = false;
SkDVector sCept = {0, 0};
double sCeptT = -1;
int sIndex = -1;
bool useIntersect = false;
for (int index = 0; index < 2; ++index) {
if (smallTs[index] < 0) {
continue;
}
const SkOpSegment& segment = index ? *rh->segment() : *this->segment();
const SkDPoint& dPt = segment.dPtAtT(smallTs[index]);
SkDVector cept = dPt - rays[index][0];
// If this point is on the curve, it should have been detected earlier by ordinary
// curve intersection. This may be hard to determine in general, but for lines,
// the point could be close to or equal to its end, but shouldn't be near the start.
if ((index ? lPts : rPts) == 1) {
SkDVector total = rays[index][1] - rays[index][0];
if (cept.lengthSquared() * 2 < total.lengthSquared()) {
continue;
}
}
SkDVector end = rays[index][1] - rays[index][0];
if (cept.fX * end.fX < 0 || cept.fY * end.fY < 0) {
continue;
}
double rayDist = cept.length();
double endDist = end.length();
bool rayLonger = rayDist > endDist;
if (limited[0] && limited[1] && rayLonger) {
useIntersect = true;
sRayLonger = rayLonger;
sCept = cept;
sCeptT = smallTs[index];
sIndex = index;
break;
}
double delta = fabs(rayDist - endDist);
double minX, minY, maxX, maxY;
minX = minY = SK_ScalarInfinity;
maxX = maxY = -SK_ScalarInfinity;
const SkDCurve& curve = index ? rh->fPart.fCurve : this->fPart.fCurve;
int ptCount = index ? rPts : lPts;
for (int idx2 = 0; idx2 <= ptCount; ++idx2) {
minX = SkTMin(minX, curve[idx2].fX);
minY = SkTMin(minY, curve[idx2].fY);
maxX = SkTMax(maxX, curve[idx2].fX);
maxY = SkTMax(maxY, curve[idx2].fY);
}
double maxWidth = SkTMax(maxX - minX, maxY - minY);
delta /= maxWidth;
if (delta > 1e-3 && (useIntersect ^= true)) { // FIXME: move this magic number
sRayLonger = rayLonger;
sCept = cept;
sCeptT = smallTs[index];
sIndex = index;
}
}
if (useIntersect) {
const SkDCurve& curve = sIndex ? rh->fPart.fCurve : this->fPart.fCurve;
const SkOpSegment& segment = sIndex ? *rh->segment() : *this->segment();
double tStart = sIndex ? rh->fStart->t() : fStart->t();
SkDVector mid = segment.dPtAtT(tStart + (sCeptT - tStart) / 2) - curve[0];
double septDir = mid.crossCheck(sCept);
if (!septDir) {
return checkParallel(rh);
}
return sRayLonger ^ (sIndex == 0) ^ (septDir < 0);
} else {
return checkParallel(rh);
}
}
bool SkOpAngle::endToSide(const SkOpAngle* rh, bool* inside) const {
const SkOpSegment* segment = this->segment();
SkPath::Verb verb = segment->verb();
SkDLine rayEnd;
rayEnd[0].set(this->fEnd->pt());
rayEnd[1] = rayEnd[0];
SkDVector slopeAtEnd = (*CurveDSlopeAtT[verb])(segment->pts(), segment->weight(),
this->fEnd->t());
rayEnd[1].fX += slopeAtEnd.fY;
rayEnd[1].fY -= slopeAtEnd.fX;
SkIntersections iEnd;
const SkOpSegment* oppSegment = rh->segment();
SkPath::Verb oppVerb = oppSegment->verb();
(*CurveIntersectRay[oppVerb])(oppSegment->pts(), oppSegment->weight(), rayEnd, &iEnd);
double endDist;
int closestEnd = iEnd.closestTo(rh->fStart->t(), rh->fEnd->t(), rayEnd[0], &endDist);
if (closestEnd < 0) {
return false;
}
if (!endDist) {
return false;
}
SkDPoint start;
start.set(this->fStart->pt());
// OPTIMIZATION: multiple times in the code we find the max scalar
double minX, minY, maxX, maxY;
minX = minY = SK_ScalarInfinity;
maxX = maxY = -SK_ScalarInfinity;
const SkDCurve& curve = rh->fPart.fCurve;
int oppPts = SkPathOpsVerbToPoints(oppVerb);
for (int idx2 = 0; idx2 <= oppPts; ++idx2) {
minX = SkTMin(minX, curve[idx2].fX);
minY = SkTMin(minY, curve[idx2].fY);
maxX = SkTMax(maxX, curve[idx2].fX);
maxY = SkTMax(maxY, curve[idx2].fY);
}
double maxWidth = SkTMax(maxX - minX, maxY - minY);
endDist /= maxWidth;
if (endDist < 5e-12) { // empirically found
return false;
}
const SkDPoint* endPt = &rayEnd[0];
SkDPoint oppPt = iEnd.pt(closestEnd);
SkDVector vLeft = *endPt - start;
SkDVector vRight = oppPt - start;
double dir = vLeft.crossNoNormalCheck(vRight);
if (!dir) {
return false;
}
*inside = dir < 0;
return true;
}
/* y<0 y==0 y>0 x<0 x==0 x>0 xy<0 xy==0 xy>0
0 x x x
1 x x x
2 x x x
3 x x x
4 x x x
5 x x x
6 x x x
7 x x x
8 x x x
9 x x x
10 x x x
11 x x x
12 x x x
13 x x x
14 x x x
15 x x x
*/
int SkOpAngle::findSector(SkPath::Verb verb, double x, double y) const {
double absX = fabs(x);
double absY = fabs(y);
double xy = SkPath::kLine_Verb == verb || !AlmostEqualUlps(absX, absY) ? absX - absY : 0;
// If there are four quadrants and eight octants, and since the Latin for sixteen is sedecim,
// one could coin the term sedecimant for a space divided into 16 sections.
// http://english.stackexchange.com/questions/133688/word-for-something-partitioned-into-16-parts
static const int sedecimant[3][3][3] = {
// y<0 y==0 y>0
// x<0 x==0 x>0 x<0 x==0 x>0 x<0 x==0 x>0
{{ 4, 3, 2}, { 7, -1, 15}, {10, 11, 12}}, // abs(x) < abs(y)
{{ 5, -1, 1}, {-1, -1, -1}, { 9, -1, 13}}, // abs(x) == abs(y)
{{ 6, 3, 0}, { 7, -1, 15}, { 8, 11, 14}}, // abs(x) > abs(y)
};
int sector = sedecimant[(xy >= 0) + (xy > 0)][(y >= 0) + (y > 0)][(x >= 0) + (x > 0)] * 2 + 1;
// SkASSERT(SkPath::kLine_Verb == verb || sector >= 0);
return sector;
}
SkOpGlobalState* SkOpAngle::globalState() const {
return this->segment()->globalState();
}
// OPTIMIZE: if this loops to only one other angle, after first compare fails, insert on other side
// OPTIMIZE: return where insertion succeeded. Then, start next insertion on opposite side
bool SkOpAngle::insert(SkOpAngle* angle) {
if (angle->fNext) {
if (loopCount() >= angle->loopCount()) {
if (!merge(angle)) {
return true;
}
} else if (fNext) {
if (!angle->merge(this)) {
return true;
}
} else {
angle->insert(this);
}
return true;
}
bool singleton = nullptr == fNext;
if (singleton) {
fNext = this;
}
SkOpAngle* next = fNext;
if (next->fNext == this) {
if (singleton || angle->after(this)) {
this->fNext = angle;
angle->fNext = next;
} else {
next->fNext = angle;
angle->fNext = this;
}
debugValidateNext();
return true;
}
SkOpAngle* last = this;
bool flipAmbiguity = false;
do {
SkASSERT(last->fNext == next);
if (angle->after(last) ^ (angle->tangentsAmbiguous() & flipAmbiguity)) {
last->fNext = angle;
angle->fNext = next;
debugValidateNext();
return true;
}
last = next;
if (last == this) {
FAIL_IF(flipAmbiguity);
// We're in a loop. If a sort was ambiguous, flip it to end the loop.
flipAmbiguity = true;
}
next = next->fNext;
} while (true);
return true;
}
SkOpSpanBase* SkOpAngle::lastMarked() const {
if (fLastMarked) {
if (fLastMarked->chased()) {
return nullptr;
}
fLastMarked->setChased(true);
}
return fLastMarked;
}
bool SkOpAngle::loopContains(const SkOpAngle* angle) const {
if (!fNext) {
return false;
}
const SkOpAngle* first = this;
const SkOpAngle* loop = this;
const SkOpSegment* tSegment = angle->fStart->segment();
double tStart = angle->fStart->t();
double tEnd = angle->fEnd->t();
do {
const SkOpSegment* lSegment = loop->fStart->segment();
if (lSegment != tSegment) {
continue;
}
double lStart = loop->fStart->t();
if (lStart != tEnd) {
continue;
}
double lEnd = loop->fEnd->t();
if (lEnd == tStart) {
return true;
}
} while ((loop = loop->fNext) != first);
return false;
}
int SkOpAngle::loopCount() const {
int count = 0;
const SkOpAngle* first = this;
const SkOpAngle* next = this;
do {
next = next->fNext;
++count;
} while (next && next != first);
return count;
}
bool SkOpAngle::merge(SkOpAngle* angle) {
SkASSERT(fNext);
SkASSERT(angle->fNext);
SkOpAngle* working = angle;
do {
if (this == working) {
return false;
}
working = working->fNext;
} while (working != angle);
do {
SkOpAngle* next = working->fNext;
working->fNext = nullptr;
insert(working);
working = next;
} while (working != angle);
// it's likely that a pair of the angles are unorderable
debugValidateNext();
return true;
}
double SkOpAngle::midT() const {
return (fStart->t() + fEnd->t()) / 2;
}
bool SkOpAngle::midToSide(const SkOpAngle* rh, bool* inside) const {
const SkOpSegment* segment = this->segment();
SkPath::Verb verb = segment->verb();
const SkPoint& startPt = this->fStart->pt();
const SkPoint& endPt = this->fEnd->pt();
SkDPoint dStartPt;
dStartPt.set(startPt);
SkDLine rayMid;
rayMid[0].fX = (startPt.fX + endPt.fX) / 2;
rayMid[0].fY = (startPt.fY + endPt.fY) / 2;
rayMid[1].fX = rayMid[0].fX + (endPt.fY - startPt.fY);
rayMid[1].fY = rayMid[0].fY - (endPt.fX - startPt.fX);
SkIntersections iMid;
(*CurveIntersectRay[verb])(segment->pts(), segment->weight(), rayMid, &iMid);
int iOutside = iMid.mostOutside(this->fStart->t(), this->fEnd->t(), dStartPt);
if (iOutside < 0) {
return false;
}
const SkOpSegment* oppSegment = rh->segment();
SkPath::Verb oppVerb = oppSegment->verb();
SkIntersections oppMid;
(*CurveIntersectRay[oppVerb])(oppSegment->pts(), oppSegment->weight(), rayMid, &oppMid);
int oppOutside = oppMid.mostOutside(rh->fStart->t(), rh->fEnd->t(), dStartPt);
if (oppOutside < 0) {
return false;
}
SkDVector iSide = iMid.pt(iOutside) - dStartPt;
SkDVector oppSide = oppMid.pt(oppOutside) - dStartPt;
double dir = iSide.crossCheck(oppSide);
if (!dir) {
return false;
}
*inside = dir < 0;
return true;
}
bool SkOpAngle::oppositePlanes(const SkOpAngle* rh) const {
int startSpan = SkTAbs(rh->fSectorStart - fSectorStart);
return startSpan >= 8;
}
bool SkOpAngle::orderable(SkOpAngle* rh) {
int result;
if (!fPart.isCurve()) {
if (!rh->fPart.isCurve()) {
double leftX = fTangentHalf.dx();
double leftY = fTangentHalf.dy();
double rightX = rh->fTangentHalf.dx();
double rightY = rh->fTangentHalf.dy();
double x_ry = leftX * rightY;
double rx_y = rightX * leftY;
if (x_ry == rx_y) {
if (leftX * rightX < 0 || leftY * rightY < 0) {
return true; // exactly 180 degrees apart
}
goto unorderable;
}
SkASSERT(x_ry != rx_y); // indicates an undetected coincidence -- worth finding earlier
return x_ry < rx_y;
}
if ((result = this->allOnOneSide(rh)) >= 0) {
return result;
}
if (fUnorderable || approximately_zero(rh->fSide)) {
goto unorderable;
}
} else if (!rh->fPart.isCurve()) {
if ((result = rh->allOnOneSide(this)) >= 0) {
return !result;
}
if (rh->fUnorderable || approximately_zero(fSide)) {
goto unorderable;
}
} else if ((result = this->convexHullOverlaps(rh)) >= 0) {
return result;
}
return this->endsIntersect(rh);
unorderable:
fUnorderable = true;
rh->fUnorderable = true;
return true;
}
// OPTIMIZE: if this shows up in a profile, add a previous pointer
// as is, this should be rarely called
SkOpAngle* SkOpAngle::previous() const {
SkOpAngle* last = fNext;
do {
SkOpAngle* next = last->fNext;
if (next == this) {
return last;
}
last = next;
} while (true);
}
SkOpSegment* SkOpAngle::segment() const {
return fStart->segment();
}
void SkOpAngle::set(SkOpSpanBase* start, SkOpSpanBase* end) {
fStart = start;
fComputedEnd = fEnd = end;
SkASSERT(start != end);
fNext = nullptr;
fComputeSector = fComputedSector = fCheckCoincidence = fTangentsAmbiguous = false;
setSpans();
setSector();
SkDEBUGCODE(fID = start ? start->globalState()->nextAngleID() : -1);
}
void SkOpAngle::setSpans() {
fUnorderable = false;
fLastMarked = nullptr;
if (!fStart) {
fUnorderable = true;
return;
}
const SkOpSegment* segment = fStart->segment();
const SkPoint* pts = segment->pts();
SkDEBUGCODE(fPart.fCurve.fVerb = SkPath::kCubic_Verb); // required for SkDCurve debug check
SkDEBUGCODE(fPart.fCurve[2].fX = fPart.fCurve[2].fY = fPart.fCurve[3].fX = fPart.fCurve[3].fY
= SK_ScalarNaN); // make the non-line part uninitialized
SkDEBUGCODE(fPart.fCurve.fVerb = segment->verb()); // set the curve type for real
segment->subDivide(fStart, fEnd, &fPart.fCurve); // set at least the line part if not more
fOriginalCurvePart = fPart.fCurve;
const SkPath::Verb verb = segment->verb();
fPart.setCurveHullSweep(verb);
if (SkPath::kLine_Verb != verb && !fPart.isCurve()) {
SkDLine lineHalf;
fPart.fCurve[1] = fPart.fCurve[SkPathOpsVerbToPoints(verb)];
fOriginalCurvePart[1] = fPart.fCurve[1];
lineHalf[0].set(fPart.fCurve[0].asSkPoint());
lineHalf[1].set(fPart.fCurve[1].asSkPoint());
fTangentHalf.lineEndPoints(lineHalf);
fSide = 0;
}
switch (verb) {
case SkPath::kLine_Verb: {
SkASSERT(fStart != fEnd);
const SkPoint& cP1 = pts[fStart->t() < fEnd->t()];
SkDLine lineHalf;
lineHalf[0].set(fStart->pt());
lineHalf[1].set(cP1);
fTangentHalf.lineEndPoints(lineHalf);
fSide = 0;
} return;
case SkPath::kQuad_Verb:
case SkPath::kConic_Verb: {
SkLineParameters tangentPart;
(void) tangentPart.quadEndPoints(fPart.fCurve.fQuad);
fSide = -tangentPart.pointDistance(fPart.fCurve[2]); // not normalized -- compare sign only
} break;
case SkPath::kCubic_Verb: {
SkLineParameters tangentPart;
(void) tangentPart.cubicPart(fPart.fCurve.fCubic);
fSide = -tangentPart.pointDistance(fPart.fCurve[3]);
double testTs[4];
// OPTIMIZATION: keep inflections precomputed with cubic segment?
int testCount = SkDCubic::FindInflections(pts, testTs);
double startT = fStart->t();
double endT = fEnd->t();
double limitT = endT;
int index;
for (index = 0; index < testCount; ++index) {
if (!::between(startT, testTs[index], limitT)) {
testTs[index] = -1;
}
}
testTs[testCount++] = startT;
testTs[testCount++] = endT;
SkTQSort<double>(testTs, &testTs[testCount - 1]);
double bestSide = 0;
int testCases = (testCount << 1) - 1;
index = 0;
while (testTs[index] < 0) {
++index;
}
index <<= 1;
for (; index < testCases; ++index) {
int testIndex = index >> 1;
double testT = testTs[testIndex];
if (index & 1) {
testT = (testT + testTs[testIndex + 1]) / 2;
}
// OPTIMIZE: could avoid call for t == startT, endT
SkDPoint pt = dcubic_xy_at_t(pts, segment->weight(), testT);
SkLineParameters tangentPart;
tangentPart.cubicEndPoints(fPart.fCurve.fCubic);
double testSide = tangentPart.pointDistance(pt);
if (fabs(bestSide) < fabs(testSide)) {
bestSide = testSide;
}
}
fSide = -bestSide; // compare sign only
} break;
default:
SkASSERT(0);
}
}
void SkOpAngle::setSector() {
if (!fStart) {
fUnorderable = true;
return;
}
const SkOpSegment* segment = fStart->segment();
SkPath::Verb verb = segment->verb();
fSectorStart = this->findSector(verb, fPart.fSweep[0].fX, fPart.fSweep[0].fY);
if (fSectorStart < 0) {
goto deferTilLater;
}
if (!fPart.isCurve()) { // if it's a line or line-like, note that both sectors are the same
SkASSERT(fSectorStart >= 0);
fSectorEnd = fSectorStart;
fSectorMask = 1 << fSectorStart;
return;
}
SkASSERT(SkPath::kLine_Verb != verb);
fSectorEnd = this->findSector(verb, fPart.fSweep[1].fX, fPart.fSweep[1].fY);
if (fSectorEnd < 0) {
deferTilLater:
fSectorStart = fSectorEnd = -1;
fSectorMask = 0;
fComputeSector = true; // can't determine sector until segment length can be found
return;
}
if (fSectorEnd == fSectorStart
&& (fSectorStart & 3) != 3) { // if the sector has no span, it can't be an exact angle
fSectorMask = 1 << fSectorStart;
return;
}
bool crossesZero = this->checkCrossesZero();
int start = SkTMin(fSectorStart, fSectorEnd);
bool curveBendsCCW = (fSectorStart == start) ^ crossesZero;
// bump the start and end of the sector span if they are on exact compass points
if ((fSectorStart & 3) == 3) {
fSectorStart = (fSectorStart + (curveBendsCCW ? 1 : 31)) & 0x1f;
}
if ((fSectorEnd & 3) == 3) {
fSectorEnd = (fSectorEnd + (curveBendsCCW ? 31 : 1)) & 0x1f;
}
crossesZero = this->checkCrossesZero();
start = SkTMin(fSectorStart, fSectorEnd);
int end = SkTMax(fSectorStart, fSectorEnd);
if (!crossesZero) {
fSectorMask = (unsigned) -1 >> (31 - end + start) << start;
} else {
fSectorMask = (unsigned) -1 >> (31 - start) | ((unsigned) -1 << end);
}
}
SkOpSpan* SkOpAngle::starter() {
return fStart->starter(fEnd);
}
bool SkOpAngle::tangentsDiverge(const SkOpAngle* rh, double s0xt0) {
if (s0xt0 == 0) {
return false;
}
// if the ctrl tangents are not nearly parallel, use them
// solve for opposite direction displacement scale factor == m
// initial dir = v1.cross(v2) == v2.x * v1.y - v2.y * v1.x
// displacement of q1[1] : dq1 = { -m * v1.y, m * v1.x } + q1[1]
// straight angle when : v2.x * (dq1.y - q1[0].y) == v2.y * (dq1.x - q1[0].x)
// v2.x * (m * v1.x + v1.y) == v2.y * (-m * v1.y + v1.x)
// - m * (v2.x * v1.x + v2.y * v1.y) == v2.x * v1.y - v2.y * v1.x
// m = (v2.y * v1.x - v2.x * v1.y) / (v2.x * v1.x + v2.y * v1.y)
// m = v1.cross(v2) / v1.dot(v2)
const SkDVector* sweep = fPart.fSweep;
const SkDVector* tweep = rh->fPart.fSweep;
double s0dt0 = sweep[0].dot(tweep[0]);
if (!s0dt0) {
return true;
}
SkASSERT(s0dt0 != 0);
double m = s0xt0 / s0dt0;
double sDist = sweep[0].length() * m;
double tDist = tweep[0].length() * m;
bool useS = fabs(sDist) < fabs(tDist);
double mFactor = fabs(useS ? this->distEndRatio(sDist) : rh->distEndRatio(tDist));
fTangentsAmbiguous = mFactor >= 50 && mFactor < 200;
return mFactor < 50; // empirically found limit
}