快速收敛的四边形网格三分细分模式

提出了四边形网格的三分细分模式.对于正则和非正则四边形网格,分别采用不同的细分模板获得新的细分顶点.从双三次B样条中推导出正则四边形网格的三分细分模板,极限曲面C²连续;对细分矩阵进行傅里叶变换,推导出非正则四边形网格的三分细分模板,极限曲面C¹连续.提出的三分细分模式可以解决任意拓扑四边形网格的曲面细分问题.与其他细分模式相比,具有收敛速度快、适用范围广等优点.最后给出了四边形网格细分的实例.

Ternary Subdivision Scheme for Quadrilateral Mesh with Fast Convergence

This paper proposes a ternary stationary subdivision scheme for quadrilateral mesh. For regular and irregular quadrilateral meshes, different subdivision masks are applied to generate new vertices. The number of faces on the refined mesh is about nine times than that of the coarse mesh after every subdivision step. The limit surface generated by the new method is C² continuous for a regular mesh and C¹ continuous for an irregular mesh. Compared with typical subdivision schemes, the proposed scheme has faster convergence speed and the ability to solve arbitrary topological quadrilateral mesh. Some examples are given in the end to illustrate the performance of the new subdivision scheme.