Catmull-Clark细分曲面的正则性  

On Regularity of Catmull-Clark Subdivision Surfaces

作　　者：王晶[1,2] 蔺宏伟[1,2] 王潇[1,2] 卢兴江[1,2] 

机构地区：[1]浙江大学数学科学学院,杭州310027 [2]浙江大学CAD&CG国家重点实验室,杭州310058

出　　处：《计算机辅助设计与图形学学报》2016年第9期1401-1409,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61272300;61379072)

摘　　要：针对Catmull-Clark(C-C)细分曲面的正则性进行研究,得到简单易用的判别C-C细分曲面正则性的充分条件.首先给出网格点差分向量的3种定义:前向差分向量,中心差分向量和后向差分向量;然后推导出C-C细分曲面的差分向量的细分格式;进一步,通过特征分析建立了C-C细分极限曲面的切向量与初始控制网格差分向量之间的关系;最后得到判别C-C细分极限曲面正则性的一个充分条件.由于该判别条件表达为初始控制网格差分向量之间的几何关系,因此这个条件具有明显的几何意义.实验结果表明,文中的判别条件易于验证.The regularity of the Catmull-Clark（C-C） subdivision surfaces is studied in this paper, aiming to deduce a simple and easy to use sufficient condition for discriminating the regularity of a C-C subdivision surface. Specifically, we first present the definitions of three types of difference vectors on the mesh, i.e., forward difference vector, central difference vector, and backward difference vector; and then, develop the subdivision formats of the difference vectors; moreover, the relationship between the tangent vectors of a C-C subdivision surface and the deference vectors of its initial control mesh is established by eigen analysis; finally, a sufficient condition for the regularity of a C-C subdivision surface is deduced. Because the condition is represented as the geometric relationship between the difference vectors on the initial control mesh, it has clear geometric meanings. Experiments show that the sufficient condition is easy to validate.

关 键 词：C-C细分曲面 初始控制网格 差分向量 正则性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]