平面三次NURBS曲线的自动光顺算法

Automatic Fairing Algorithm for Planar Cubic NURBS Curves

针对平面三次 NU RBS曲线的光顺问题 ,基于节点插入、节点消去和重新确定权因子等技术 ,给出了平面三次 NURBS曲线的一种光顺算法 .算法根据给定的光顺准则 ,自动选择需要光顺的节点 。

The algorithm is based on knot removal, knot insertion, and weight modification of the NURBS. These knots and weights are selected automatically by means of a fairness criterion. The proposed algorithm includes Farin's algorithm as a special case. The advantages of the new algorithm compared with Kjellander's algorithm are: 1) It is automatic, no user interaction is required. 2) It is local, each time the algorithm is applied, at most three control vertices are affected. 3) It is ensured that the fairing curve will be exactly C 3 at the offensive knot location. 4) It preserves the local convexity property of the initial curve.