Energy Optimization Fairing Algorithm of Non-uniform Cubic Parametric Splines

In 1996, Poliakoff presented a useful fairing algorithm. Her algorithm generalizes Kjellander algorithm to non-uniform cubic parametric splines. However, she neglects to change corresponding tangent vector of the bad point. Sometimes the bad tangent vector could seriously affect fairing results. In order to solve this problem, a novel fairing algorithm is proposed in this paper. By the algorithm, the bad point's position and tangent vector is changed at the same time. An explicit formula of fairing algorithm is accordingly derived. The new algorithm possesses energy optimality, and it also shows that Poliakoff algorithm is a special case of the algorithm. Numerical examples show that the new algorithm is quite valid and promising in the future application.