// from SkGeometry.cpp (and Numeric Solutions, 5.6)
int SkDCubic::RootsValidT(double A, double B, double C, double D, double t[3]) {
double s[3];
int realRoots = RootsReal(A, B, C, D, s);
int foundRoots = SkDQuad::AddValidTs(s, realRoots, t);
for (int index = 0; index < realRoots; ++index) {
double tValue = s[index];
if (!approximately_one_or_less(tValue) && between(1, tValue, 1.00005)) {
for (int idx2 = 0; idx2 < foundRoots; ++idx2) {
if (approximately_equal(t[idx2], 1)) {
goto nextRoot;
}
}
SkASSERT(foundRoots < 3);
t[foundRoots++] = 1;
} else if (!approximately_zero_or_more(tValue) && between(-0.00005, tValue, 0)) {
for (int idx2 = 0; idx2 < foundRoots; ++idx2) {
if (approximately_equal(t[idx2], 0)) {
goto nextRoot;
}
}
SkASSERT(foundRoots < 3);
t[foundRoots++] = 0;
}
nextRoot:
;
}
return foundRoots;
}
// from SkGeometry.cpp (and Numeric Solutions, 5.6)
int SkDCubic::RootsValidT(double A, double B, double C, double D, double t[3]) {
double s[3];
int realRoots = RootsReal(A, B, C, D, s);
int foundRoots = SkDQuad::AddValidTs(s, realRoots, t);
return foundRoots;
}
// note: caller expects multiple results to be sorted smaller first
// note: http://en.wikipedia.org/wiki/Loss_of_significance has an interesting
// analysis of the quadratic equation, suggesting why the following looks at
// the sign of B -- and further suggesting that the greatest loss of precision
// is in b squared less two a c
int SkDQuad::RootsValidT(double A, double B, double C, double t[2]) {
double s[2];
int realRoots = RootsReal(A, B, C, s);
int foundRoots = AddValidTs(s, realRoots, t);
return foundRoots;
}
