Interpolating triangular meshes by Loop subdivision scheme  

作　　者：DENG ChongYang WANG GuoZhao 

机构地区：[1]Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University Hangzhou 310018, China [2]Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Science China(Information Sciences)》2010年第9期1765-1773,共9页中国科学（信息科学）（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.10926058,60904070,60673032,60773179);the National Basic Research Program of China(Grant No.2004CB318000);the Scientific Start-up Foundation of Hangzhou Dianzi University(Grant No.KYS075608073)

摘　　要：Using the limit point formula of the Loop subdivision scheme, we propose a very simple and efficient method for constructing interpolation surface of triangular meshes by Loop subdivision scheme. The excellent properties of the method are： （1） Locality： the perturbation of a given vertex only influences the surface shape near this vertex. （2） Efficiency： the locations of new points can be computed with explicit formulae. （3） Easiness in implementation： only the geometric rule of the first step should be modified. （4） Freedom： for each edge, there is one degree of freedom to adjust the shape of the interpolation surface. （5） Easiness in generalization： it is easy to generalize our method to other approximation subdivision schemes with explicit formulae to compute limit point.Using the limit point formula of the Loop subdivision scheme, we propose a very simple and efficient method for constructing interpolation surface of triangular meshes by Loop subdivision scheme. The excellent properties of the method are： （1） Locality： the perturbation of a given vertex only influences the surface shape near this vertex. （2） Efficiency： the locations of new points can be computed with explicit formulae. （3） Easiness in implementation： only the geometric rule of the first step should be modified. （4） Freedom： for each edge, there is one degree of freedom to adjust the shape of the interpolation surface. （5） Easiness in generalization： it is easy to generalize our method to other approximation subdivision schemes with explicit formulae to compute limit point.

关 键 词：computer aided geometric design subdivision surface approximating subdivision scheme Loop surface surface interpolating 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TP391.72[自动化与计算机技术—计算机科学与技术]