Estimating Subdivision Depth of Catmull-Clark Surfaces

作     者：Hua-WeiWang Kai-HuaiQin 

作者机构：DepartmentofComputerScienceandTechnologyTsinghuaUniversityBeijing100083P.R.China 

出 版 物：《Journal of Computer Science & Technology》 (计算机科学技术学报（英文版）)

年 卷 期：2004年第19卷第5期

页      面：657-664页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 080203[工学-机械设计及理论] 0835[工学-软件工程] 0802[工学-机械工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：国家自然科学基金 高等学校博士学科点专项科研项目 面向21世纪教育振兴行动计划(985计划) 

主　　题：Catmull-Clark surface subdivision depth control polyhedron approximation error 

摘      要：In this paper, both general and exponential bounds of the distance between a uniform Catmull-Clark surface and its control polyhedron are derived. The exponential bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Based on the exponential bound, we can predict the depth of subdivision within a user-specified error tolerance. This is quite useful and important for pre-computing the subdivision depth of subdivision surfaces in many engineering applications such as surface/surface intersection, mesh generation, numerical control machining and surface rendering.