/* Looking for F' dot F'' == 0
A = b - a
B = c - 2b + a
C = d - 3c + 3b - a
F' = 3Ct^2 + 6Bt + 3A
F'' = 6Ct + 6B
F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
*/
int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3])
{
SkFP coeffX[4], coeffY[4];
int i;
formulate_F1DotF2(&src[0].fX, coeffX);
formulate_F1DotF2(&src[0].fY, coeffY);
for (i = 0; i < 4; i++)
coeffX[i] = SkFPAdd(coeffX[i],coeffY[i]);
SkScalar t[3];
int count = solve_cubic_polynomial(coeffX, t);
int maxCount = 0;
// now remove extrema where the curvature is zero (mins)
// !!!! need a test for this !!!!
for (i = 0; i < count; i++)
{
// if (not_min_curvature())
if (t[i] > kMinTValueForChopping && t[i] < SK_Scalar1 - kMinTValueForChopping)
tValues[maxCount++] = t[i];
}
return maxCount;
}
/* from SkGeometry.cpp
Looking for F' dot F'' == 0
A = b - a
B = c - 2b + a
C = d - 3c + 3b - a
F' = 3Ct^2 + 6Bt + 3A
F'' = 6Ct + 6B
F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
*/
int SkDCubic::findMaxCurvature(double tValues[]) const {
double coeffX[4], coeffY[4];
int i;
formulate_F1DotF2(&fPts[0].fX, coeffX);
formulate_F1DotF2(&fPts[0].fY, coeffY);
for (i = 0; i < 4; i++) {
coeffX[i] = coeffX[i] + coeffY[i];
}
return RootsValidT(coeffX[0], coeffX[1], coeffX[2], coeffX[3], tValues);
}
/* from SkGeometry.cpp
Looking for F' dot F'' == 0
A = b - a
B = c - 2b + a
C = d - 3c + 3b - a
F' = 3Ct^2 + 6Bt + 3A
F'' = 6Ct + 6B
F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
*/
int find_cubic_max_curvature(const Cubic& src, double tValues[])
{
double coeffX[4], coeffY[4];
int i;
formulate_F1DotF2(&src[0].x, coeffX);
formulate_F1DotF2(&src[0].y, coeffY);
for (i = 0; i < 4; i++) {
coeffX[i] = coeffX[i] + coeffY[i];
}
return cubicRootsValidT(coeffX[0], coeffX[1], coeffX[2], coeffX[3], tValues);
}
