非均匀三次参数样条曲线的能量最优光顺算法

1996年，Poliakoff提出了一种具有广泛应用背景的的光顺算法，该算法将Kjellander算法推广到非均匀三次参数样条曲线的情形，但忽视了对坏点切向量的修改，而坏点切向量有时会严重影响光顺效果．据此，提出了同时修改坏点位置和切向量算法，导出了光顺算法的显式公式，并且证明了该算法是能量最优的；还指出Poliakoff算法是文中算法的一种特例．大量的数值例子表明，文中算法具有很好的光顺效果，具有良好的应用前景．

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.