SkDCubic SkDCubic::subDivide(double t1, double t2) const {
if (t1 == 0 || t2 == 1) {
if (t1 == 0 && t2 == 1) {
return *this;
}
SkDCubicPair pair = chopAt(t1 == 0 ? t2 : t1);
SkDCubic dst = t1 == 0 ? pair.first() : pair.second();
return dst;
}
SkDCubic dst;
double ax = dst[0].fX = interp_cubic_coords(&fPts[0].fX, t1);
double ay = dst[0].fY = interp_cubic_coords(&fPts[0].fY, t1);
double ex = interp_cubic_coords(&fPts[0].fX, (t1*2+t2)/3);
double ey = interp_cubic_coords(&fPts[0].fY, (t1*2+t2)/3);
double fx = interp_cubic_coords(&fPts[0].fX, (t1+t2*2)/3);
double fy = interp_cubic_coords(&fPts[0].fY, (t1+t2*2)/3);
double dx = dst[3].fX = interp_cubic_coords(&fPts[0].fX, t2);
double dy = dst[3].fY = interp_cubic_coords(&fPts[0].fY, t2);
double mx = ex * 27 - ax * 8 - dx;
double my = ey * 27 - ay * 8 - dy;
double nx = fx * 27 - ax - dx * 8;
double ny = fy * 27 - ay - dy * 8;
/* bx = */ dst[1].fX = (mx * 2 - nx) / 18;
/* by = */ dst[1].fY = (my * 2 - ny) / 18;
/* cx = */ dst[2].fX = (nx * 2 - mx) / 18;
/* cy = */ dst[2].fY = (ny * 2 - my) / 18;
// FIXME: call align() ?
return dst;
}
// flavor that returns T values only, deferring computing the quads until they are needed
// FIXME: when called from recursive intersect 2, this could take the original cubic
// and do a more precise job when calling chop at and sub divide by computing the fractional ts.
// it would still take the prechopped cubic for reduce order and find cubic inflections
void SkDCubic::toQuadraticTs(double precision, SkTDArray<double>* ts) const {
SkReduceOrder reducer;
int order = reducer.reduce(*this, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
if (order < 3) {
return;
}
double inflectT[5];
int inflections = findInflections(inflectT);
SkASSERT(inflections <= 2);
if (!endsAreExtremaInXOrY()) {
inflections += findMaxCurvature(&inflectT[inflections]);
SkASSERT(inflections <= 5);
}
QSort<double>(inflectT, &inflectT[inflections - 1]);
// OPTIMIZATION: is this filtering common enough that it needs to be pulled out into its
// own subroutine?
while (inflections && approximately_less_than_zero(inflectT[0])) {
memmove(inflectT, &inflectT[1], sizeof(inflectT[0]) * --inflections);
}
int start = 0;
do {
int next = start + 1;
if (next >= inflections) {
break;
}
if (!approximately_equal(inflectT[start], inflectT[next])) {
++start;
continue;
}
memmove(&inflectT[start], &inflectT[next], sizeof(inflectT[0]) * (--inflections - start));
} while (true);
while (inflections && approximately_greater_than_one(inflectT[inflections - 1])) {
--inflections;
}
SkDCubicPair pair;
if (inflections == 1) {
pair = chopAt(inflectT[0]);
int orderP1 = reducer.reduce(pair.first(), SkReduceOrder::kNo_Quadratics,
SkReduceOrder::kFill_Style);
if (orderP1 < 2) {
--inflections;
} else {
int orderP2 = reducer.reduce(pair.second(), SkReduceOrder::kNo_Quadratics,
SkReduceOrder::kFill_Style);
if (orderP2 < 2) {
--inflections;
}
}
}
if (inflections == 0 && add_simple_ts(*this, precision, ts)) {
return;
}
if (inflections == 1) {
pair = chopAt(inflectT[0]);
addTs(pair.first(), precision, 0, inflectT[0], ts);
addTs(pair.second(), precision, inflectT[0], 1, ts);
return;
}
if (inflections > 1) {
SkDCubic part = subDivide(0, inflectT[0]);
addTs(part, precision, 0, inflectT[0], ts);
int last = inflections - 1;
for (int idx = 0; idx < last; ++idx) {
part = subDivide(inflectT[idx], inflectT[idx + 1]);
addTs(part, precision, inflectT[idx], inflectT[idx + 1], ts);
}
part = subDivide(inflectT[last], 1);
addTs(part, precision, inflectT[last], 1, ts);
return;
}
addTs(*this, precision, 0, 1, ts);
}