用C-C细分法和流形方法构造G2连续的自由型曲面

通过改进Cotrina等利用流形方法构造n边曲面片的算法,以C-C细分网格奇异点的5一环作为控制网构造出了带有均匀三次B样条边界的n边曲面片,使得该曲面片和C-C细分曲面G^2拼接．在此基础上,讨论了C-C细分曲面中n边域的构造和填充,从而为基于任意拓扑网格构造低次G^2连续曲面的问题给出了一个有效的解决方案,实现了用流形方法构造的曲面和C-C细分曲面的融合．最后,给出了几个具体算例．

Modeling G2 Continuous Free-Form Surfaces by C-C Subdivision Method and Manifold Method

By improving the algorithm to construct n-sided patches given by J. Cotrina et al, a n-sided patch is constructed with uniformly cubic B-spline boundary, whose control mesh is the mesh formed by 5-ring of an extraordinary point in C-C subdivision mesh. The patch can G2 continuously joint with a C-C subdivision surface. On this basis, the question on how to form and fill n-sided holes in C-C subdivision surfaces is discussed. A method is given to solve the problem in modeling low-degree G2 continuous free-form surfaces based on arbitrary topology meshes. The blend is realized between surfaces constructed by manifolds and C-C subdivision surfaces. Finally, several examples are presented.