Continuity of non-uniform recursive subdivision surfaces  

作　　者：秦开怀 王华维 

机构地区：[1]Department of Computer Science & Technology, Tsinghua University, Beijing 100084, China

出　　处：《Science China(Technological Sciences)》2000年第5期461-472,共12页中国科学（技术科学英文版）

摘　　要：Since Doo-Sabin and Catmull-Clark surfaces were proposed in 1978, eigenstructure, convergence and continuity analyses of stationary subdivision have been performed very well, but it has been very difficult to prove the convergence and continuity of non-uniform recursive subdivision surfaces (NURSSes, for short) of arbitrary topology. In fact, so far a problem whether or not there exists the limit surface as well as G1 continuity of a non-uniform Catmull-Clark subdivision has not been solved yet. Here the concept of equivalent knot spacing is introduced. A new technique for eigenanaly-sis, convergence and continuity analyses of non-uniform Catmull-Clark surfaces is proposed such that the convergence and G1 continuity of NURSSes at extraordinary points are proved. In addition, slightly improved rules for NURSSes are developed. This offers us one more alternative for modeling free-form surfaces of arbitrary topologies with geometric features such as cusps, sharp edges, creases and darts, while elsewhere maintaining the same order of continuity as B-spline surfaces.

关 键 词：CATMULL-CLARK NON-UNIFORM RECURSIVE SUBDIVISION surface CONVERGENCE continuity. 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]