- Compute \(p(t)\) as a cubic spline interpolation
-
- - Given keyframes \((p_i,t_i)_{i\in[0,N-1]}\)
- - Given time \(t\in[t_1,t_{N-2}]\)
- 1. Find \(i\) such that \(t\in[t_{i},t_{i+1}]\)
- 2. Compute \(\;\;\displaystyle d_i=\mu\,\frac{p_{i+1}-p_{i-1}}{t_{i+1}-t_{i-1}}\), and \(\displaystyle
d_{i+1}=\mu\,\frac{p_{i+2}-p_{i}}{t_{i+2}-t_{i}}\)
- 3. Compute \(\;\;p(t) = (2s^3-3s^2+1) \, p_i + (s^3-2s^2+s) \, d_i +(-2s^3 +3s^2)\, p_{i+1}+(s^3-s^2)\,d_{i+1}\)
-
- with \(\displaystyle s=\frac{t-t_{i}}{t_{i+1}-t_i}\).