/**
* A variation of Hermite where a velocity is given only for the first point. It interpolates P0
* at t=0 and P1 at t=1. P(t) = (t^2 - 2*t + 1) * P0 + (-t^2 + 2*t) * P1 + (t^2 - t) * T0
*
* @param P0
* @param T0
* @param P1
* @param t
* @return
*/
private static Vector3f quadraticHermite(Vector3f P0, Vector3f T0, Vector3f P1, float t) {
float t2 = t * t;
Vector3f P = new Vector3f();
P.scaleAdd(t2 - 2 * t + 1, P0, P);
P.scaleAdd(-t2 + 2 * t, P1, P);
P.scaleAdd(t2 - t, T0, P);
return P;
}
/**
* Hermite interpolation of the points P0 to P1 at time t=0 to t=1 with the specified velocities
* T0 and T1.
*
* @param P0
* @param T0
* @param P1
* @param T1
* @param t
* @return
*/
private static Vector3f cubicHermite(
Vector3f P0, Vector3f T0, Vector3f P1, Vector3f T1, float t) {
float t2 = t * t;
float t3 = t2 * t;
Vector3f P = new Vector3f();
P.scaleAdd(2 * t3 - 3 * t2 + 1, P0, P);
P.scaleAdd(t3 - 2 * t2 + t, T0, P);
P.scaleAdd(-2 * t3 + 3 * t2, P1, P);
P.scaleAdd(t3 - t2, T1, P);
return P;
}