Smooth curve

• Classical Idea
  Use polynomials \(\displaystyle p(t)=\sum_{i=0}^{d}\,\left(\sum_{j=0}^{N-1} c_i^j \, p_j\right)\,t^i\)

• Or formulated using basis functions \(\displaystyle p(t)=\sum_{i=0}^{N-1} \,\alpha_i(t)\;p_i\)
• • \((\alpha_i)\) polynomial basis function of degree \(d\)

• - Which polynomials/degree choose ?