// 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.
static bool intersectEnd(const Cubic& cubic1, bool start, const Cubic& cubic2, const _Rect& bounds2,
Intersections& i) {
// bool selfIntersect = cubic1 == cubic2;
_Line line;
int t1Index = start ? 0 : 3;
line[0] = cubic1[t1Index];
// don't bother if the two cubics are connnected
#if 0
if (!selfIntersect && (line[0].approximatelyEqual(cubic2[0])
|| line[0].approximatelyEqual(cubic2[3]))) {
return false;
}
#endif
bool result = false;
SkTDArray<double> tVals; // OPTIMIZE: replace with hard-sized array
for (int index = 0; index < 4; ++index) {
if (index == t1Index) {
continue;
}
_Vector dxy1 = cubic1[index] - line[0];
dxy1 /= gPrecisionUnit;
line[1] = line[0] + dxy1;
_Rect lineBounds;
lineBounds.setBounds(line);
if (!bounds2.intersects(lineBounds)) {
continue;
}
Intersections local;
if (!intersect(cubic2, line, local)) {
continue;
}
for (int idx2 = 0; idx2 < local.used(); ++idx2) {
double foundT = local.fT[0][idx2];
if (approximately_less_than_zero(foundT)
|| approximately_greater_than_one(foundT)) {
continue;
}
if (local.fPt[idx2].approximatelyEqual(line[0])) {
if (i.swapped()) { // FIXME: insert should respect swap
i.insert(foundT, start ? 0 : 1, line[0]);
} else {
i.insert(start ? 0 : 1, foundT, line[0]);
}
result = true;
} else {
*tVals.append() = local.fT[0][idx2];
}
}
}
if (tVals.count() == 0) {
return result;
}
QSort<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 = i.used();
result |= intersect3(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
if (lastUsed == i.used()) {
tMin2 = SkTMax(tVals[tIdx] - (1.0 / gPrecisionUnit), 0.0);
tMax2 = SkTMin(tVals[tLast] + (1.0 / gPrecisionUnit), 1.0);
result |= intersect3(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
}
tIdx = tLast + 1;
} while (tIdx < tVals.count());
return result;
}
// this flavor centers potential intersections recursively. In contrast, '2' may inadvertently
// chase intersections near quadratic ends, requiring odd hacks to find them.
static bool intersect3(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
double t2s, double t2e, double precisionScale, Intersections& i) {
i.upDepth();
bool result = false;
Cubic c1, c2;
sub_divide(cubic1, t1s, t1e, c1);
sub_divide(cubic2, t2s, t2e, c2);
SkTDArray<double> ts1;
// OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection)
cubic_to_quadratics(c1, calcPrecision(c1) * precisionScale, ts1);
SkTDArray<double> ts2;
cubic_to_quadratics(c2, calcPrecision(c2) * 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;
Quadratic 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;
}
Quadratic 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) {
Cubic cSub1, cSub2;
sub_divide(cubic1, t1Start, t1, cSub1);
sub_divide(cubic2, t2Start, t2, cSub2);
SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab, __FUNCTION__,
t1Start, t1, t2Start, t2);
Intersections xlocals;
intersectWithOrder(s1, o1, s2, o2, xlocals);
SkDebugf(" xlocals.fUsed=%d\n", xlocals.used());
}
#endif
Intersections locals;
intersectWithOrder(s1, o1, s2, o2, locals);
double coStart[2] = { -1 };
_Point coPoint;
int tCount = locals.used();
for (int tIdx = 0; tIdx < tCount; ++tIdx) {
double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
// if the computed t is not sufficiently precise, iterate
_Point p1 = xy_at_t(cubic1, to1);
_Point p2 = xy_at_t(cubic2, to2);
if (p1.approximatelyEqual(p2)) {
if (locals.fIsCoincident[0] & 1 << tIdx) {
if (coStart[0] < 0) {
coStart[0] = to1;
coStart[1] = to2;
coPoint = p1;
} else {
i.insertCoincidentPair(coStart[0], to1, coStart[1], to2, coPoint, p1);
coStart[0] = -1;
}
result = true;
} else 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);
}
result = true;
}
} else {
double offset = precisionScale / 16; // FIME: const is arbitrary -- test & refine
#if 1
double c1Bottom = tIdx == 0 ? 0 :
(t1Start + (t1 - t1Start) * locals.fT[0][tIdx - 1] + to1) / 2;
double c1Min = SkTMax(c1Bottom, to1 - offset);
double c1Top = tIdx == tCount - 1 ? 1 :
(t1Start + (t1 - t1Start) * locals.fT[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
intersect3(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.fT[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.fT[1][tIdx - 1] + to2) / 2;
double c2Top = tIdx == tCount - 1 ? to2 :
(t2Start + (t2 - t2Start) * locals.fT[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
intersect3(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.fT[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
intersect3(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.fT[0][i.used() - 1] : -1);
#endif
}
#else
double c1Bottom = tIdx == 0 ? 0 :
(t1Start + (t1 - t1Start) * locals.fT[0][tIdx - 1] + to1) / 2;
double c1Min = SkTMax(c1Bottom, to1 - offset);
double c1Top = tIdx == tCount - 1 ? 1 :
(t1Start + (t1 - t1Start) * locals.fT[0][tIdx + 1] + to1) / 2;
double c1Max = SkTMin(c1Top, to1 + offset);
double c2Bottom = tIdx == 0 ? to2 :
(t2Start + (t2 - t2Start) * locals.fT[1][tIdx - 1] + to2) / 2;
double c2Top = tIdx == tCount - 1 ? to2 :
(t2Start + (t2 - t2Start) * locals.fT[1][tIdx + 1] + to2) / 2;
if (c2Bottom > c2Top) {
SkTSwap(c2Bottom, c2Top);
}
if (c2Bottom == to2) {
c2Bottom = 0;
}
if (c2Top == to2) {
c2Top = 1;
}
double c2Min = SkTMax(c2Bottom, to2 - offset);
double c2Max = SkTMin(c2Top, to2 + offset);
#if ONE_OFF_DEBUG
SkDebugf("%s contains1=%d/%d contains2=%d/%d\n", __FUNCTION__,
c1Min <= 0.210357794 && 0.210357794 <= c1Max
&& c2Min <= 0.223476406 && 0.223476406 <= c2Max,
to1 - offset <= 0.210357794 && 0.210357794 <= to1 + offset
&& to2 - offset <= 0.223476406 && 0.223476406 <= to2 + offset,
c1Min <= 0.211324707 && 0.211324707 <= c1Max
&& c2Min <= 0.211327209 && 0.211327209 <= c2Max,
to1 - offset <= 0.211324707 && 0.211324707 <= to1 + offset
&& to2 - offset <= 0.211327209 && 0.211327209 <= to2 + offset);
SkDebugf("%s 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",
__FUNCTION__, c1Bottom, c1Top, c2Bottom, c2Top,
to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
SkDebugf("%s to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
" c2Max=%1.9g\n", __FUNCTION__, to1, to2, c1Min, c1Max, c2Min, c2Max);
#endif
#endif
intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
// TODO: 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.
}
}
SkASSERT(coStart[0] == -1);
t2Start = t2;
}
t1Start = t1;
}
i.downDepth();
return result;
}
// this flavor approximates the cubics with quads to find the intersecting ts
// OPTIMIZE: if this strategy proves successful, the quad approximations, or the ts used
// to create the approximations, could be stored in the cubic segment
// FIXME: this strategy needs to intersect the convex hull on either end with the opposite to
// account for inset quadratics that cause the endpoint intersection to avoid detection
// the segments can be very short -- the length of the maximum quadratic error (precision)
// FIXME: this needs to recurse on itself, taking a range of T values and computing the new
// t range ala is linear inner. The range can be figured by taking the dx/dy and determining
// the fraction that matches the precision. That fraction is the change in t for the smaller cubic.
static bool intersect2(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
double t2s, double t2e, double precisionScale, Intersections& i) {
Cubic c1, c2;
sub_divide(cubic1, t1s, t1e, c1);
sub_divide(cubic2, t2s, t2e, c2);
SkTDArray<double> ts1;
cubic_to_quadratics(c1, calcPrecision(c1) * precisionScale, ts1);
SkTDArray<double> ts2;
cubic_to_quadratics(c2, calcPrecision(c2) * 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;
Cubic part1;
sub_divide(cubic1, t1Start, t1, part1);
Quadratic q1;
demote_cubic_to_quad(part1, q1);
// start here;
// should reduceOrder be looser in this use case if quartic is going to blow up on an
// extremely shallow quadratic?
Quadratic s1;
int o1 = reduceOrder(q1, 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;
Cubic part2;
sub_divide(cubic2, t2Start, t2, part2);
Quadratic q2;
demote_cubic_to_quad(part2, q2);
Quadratic s2;
double o2 = reduceOrder(q2, s2);
Intersections locals;
if (o1 == 3 && o2 == 3) {
intersect2(q1, q2, locals);
} else if (o1 <= 2 && o2 <= 2) {
locals.fUsed = intersect((const _Line&) s1, (const _Line&) s2, locals.fT[0],
locals.fT[1]);
} else if (o1 == 3 && o2 <= 2) {
intersect(q1, (const _Line&) s2, locals);
} else {
SkASSERT(o1 <= 2 && o2 == 3);
intersect(q2, (const _Line&) s1, locals);
for (int s = 0; s < locals.fUsed; ++s) {
SkTSwap(locals.fT[0][s], locals.fT[1][s]);
}
}
for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx];
double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx];
// if the computed t is not sufficiently precise, iterate
_Point p1, p2;
xy_at_t(cubic1, to1, p1.x, p1.y);
xy_at_t(cubic2, to2, p2.x, p2.y);
if (p1.approximatelyEqual(p2)) {
i.insert(i.swapped() ? to2 : to1, i.swapped() ? to1 : to2);
} else {
double dt1, dt2;
computeDelta(cubic1, to1, (t1e - t1s), cubic2, to2, (t2e - t2s), dt1, dt2);
double scale = precisionScale;
if (dt1 > 0.125 || dt2 > 0.125) {
scale /= 2;
SkDebugf("%s scale=%1.9g\n", __FUNCTION__, scale);
}
#if SK_DEBUG
++debugDepth;
assert(debugDepth < 10);
#endif
i.swap();
intersect2(cubic2, SkTMax(to2 - dt2, 0.), SkTMin(to2 + dt2, 1.),
cubic1, SkTMax(to1 - dt1, 0.), SkTMin(to1 + dt1, 1.), scale, i);
i.swap();
#if SK_DEBUG
--debugDepth;
#endif
}
}
t2Start = t2;
}
t1Start = t1;
}
return i.intersected();
}