Ternary Subdivision Scheme for Quadrilateral Mesh with Fast Convergence
快速收敛的四边形网格三分细分模式

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.