Smooth curve
Objective: Generate a smooth interpolating space-time curve
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Classical Idea
Use polynomials curves
\(\left\{\begin{array}{l} \displaystyle p(t)=\sum_{i=0}^{N-1} \,\alpha_i(t)\;p_i \\ \displaystyle \alpha_i(t) =
\sum_{j=0}^{d} c_{ij}\,t^i \end{array} \right.\)
- \((\alpha_i)\) polynomial basis function of degree \(d\)
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- Which polynomials/degree choose ?