有理三次Bezier样条的曲线修正方法

Modification of Curves with Rational Cubic Bezier Splines

提出了一种新的用于曲线修正的方法:对于初始的G2分段有理三次Bezier样条曲线,首先根据需要给出约束边界,对于与约束边界相交的曲线段,将被其所在的曲线族中的一条与约束边界相切或过约束边界顶点的曲线所取代,最后依据曲率恢复其G2连续性.修正后的曲线不穿过约束边界,且继续保持原有的几何连续性.数值实验表明,该方法简单、快速、有效.

A new method for modification of curves is described in this paper. To modify an initial G^2 rational cubic Bezier curve, we give constrained boundaries, replace the curve segment intersecting the boundaries with one of its curve family, which is either tangent to the boundaries or passes their vertexes, and restore G^2 continuity according to the curvature. The modified curve does not intersect the boundaries and keeps geometric continuity. Numerical examples are given, showing that the method is simple, fast and efficient.