Smooth curve

Objective: Generate a smooth interpolating space-time curve

• Classical Idea
  Use polynomials curves

\(\left\{\begin{array}{l} \displaystyle p(t)=\sum_{i=0}^{N-1} \,\alpha_i(t)\;p_i \\ \displaystyle \alpha_i(t) = \sum_{j=0}^{d} c_i^j\,t^i \end{array} \right.\)

• \((\alpha_i)\) polynomial basis function of degree \(d\)

• • Which polynomials/degree choose ?