Catmull-Clark细分曲面等距面生成算法

Offset Algorithm of Catmull-Clark Subdivision Surface

针对带边界的Catmull-Clar细分曲面,根据内部顶点极限位置计算方法,给出了边界顶点极限点及法矢量的计算公式。利用控制网格顶点与其在细分曲面上位置的对应关系,将细分曲面的等距转化为解线性方程组的求解,并采用改进的基于四边形网格的Jacobi迭代法解线性方程组,得到等距后的控制网格。实例表明:采用该算法可以快速高效地生成细分曲面的等距面。

For Catmull-Clark subdivision surface with boundary,this paper gives computation formula for limiting point and its corresponding normal vector of boundary vertex.The main problem is to convert the offset problem to a problem for solving linear equation system using the corresponding relation of the vertex in control mesh and its limiting position.An improved Jacobi iteration method based on quadrangle mesh is used to solve the system of linear equations.Examples show that this method can generate offset surface fast and effectively.