void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc,
SkVector* tangent, SkVector* curvature) {
SkASSERT(src);
SkASSERT(t >= 0 && t <= SK_Scalar1);
if (loc) {
loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t));
}
if (tangent) {
// The derivative equation returns a zero tangent vector when t is 0 or 1, and the
// adjacent control point is equal to the end point. In this case, use the
// next control point or the end points to compute the tangent.
if ((t == 0 && src[0] == src[1]) || (t == 1 && src[2] == src[3])) {
if (t == 0) {
*tangent = src[2] - src[0];
} else {
*tangent = src[3] - src[1];
}
if (!tangent->fX && !tangent->fY) {
*tangent = src[3] - src[0];
}
} else {
tangent->set(eval_cubic_derivative(&src[0].fX, t),
eval_cubic_derivative(&src[0].fY, t));
}
}
if (curvature) {
curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t),
eval_cubic_2ndDerivative(&src[0].fY, t));
}
}
void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc, SkVector* tangent, SkVector* curvature)
{
SkASSERT(src);
SkASSERT(t >= 0 && t <= SK_Scalar1);
if (loc)
loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t));
if (tangent)
tangent->set(eval_cubic_derivative(&src[0].fX, t),
eval_cubic_derivative(&src[0].fY, t));
if (curvature)
curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t),
eval_cubic_2ndDerivative(&src[0].fY, t));
}
SkScalar SkUnitCubicInterp(SkScalar value, SkScalar bx, SkScalar by,
SkScalar cx, SkScalar cy) {
// pin to the unit-square, and convert to 2.14
Dot14 x = pin_and_convert(value);
if (x == 0) return 0;
if (x == Dot14_ONE) return SK_Scalar1;
Dot14 b = pin_and_convert(bx);
Dot14 c = pin_and_convert(cx);
// Now compute our coefficients from the control points
// t -> 3b
// t^2 -> 3c - 6b
// t^3 -> 3b - 3c + 1
Dot14 A = 3*b;
Dot14 B = 3*(c - 2*b);
Dot14 C = 3*(b - c) + Dot14_ONE;
// Now search for a t value given x
Dot14 t = Dot14_HALF;
Dot14 dt = Dot14_HALF;
for (int i = 0; i < 13; i++) {
dt >>= 1;
Dot14 guess = eval_cubic(t, A, B, C);
if (x < guess) {
t -= dt;
} else {
t += dt;
}
}
// Now we have t, so compute the coeff for Y and evaluate
b = pin_and_convert(by);
c = pin_and_convert(cy);
A = 3*b;
B = 3*(c - 2*b);
C = 3*(b - c) + Dot14_ONE;
return SkFixedToScalar(eval_cubic(t, A, B, C) << 2);
}
