Curve interpolation based on Catmull-Clark subdivision scheme  

作　　者：ZHANG Jingqiao and WANG Guojin(State Key Laboratory of CAD&CG, Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, China) 

出　　处：《Progress in Natural Science:Materials International》2003年第2期142-148,共7页自然科学进展·国际材料（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 60173034);the Major State Basic Research Development Program of China (Gtant No. G1998030600)

摘　　要：An efficient algorithm for curve interpolation is proposed. The algorithm can produce a subdivision surface that can interpolate the predefined cubic B-spline curves by applying the Catmull-Clark scheme to a polygonal mesh containing 'symmetric zonal meshes', which possesses some special properties. Many kinds of curve interpolation problems can be dealt with by this algorithm, such as interpolating single open curve or closed curve, a mesh of nonintersecting or intersecting curve. The interpolating surface is C2 everywhere excepting at a finite number of points. At the same time, sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of initial mesh, I. e. the surface is only C along the cubic B-spline curve that is defined by the tagged edges. Because of being simple and easy to implement, this method can be used for product shape design and graphic software development.An efficient algorithm for curve interpolation is proposed. The algorithm can produce a subdivision surface that can interpolate the predefined cubic B-spline curves by applying the Catmull-Clark scheme to a polygonal mesh containing 'symmetric zonal meshes', which possesses some special properties. Many kinds of curve interpolation problems can be dealt with by this algorithm, such as interpolating single open curve or closed curve, a mesh of nonintersecting or intersecting curve. The interpolating surface is C2 everywhere excepting at a finite number of points. At the same time, sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of initial mesh, i.e. the surface is only C0 along the cubic B-spline curve that is defined by the tagged edges. Because of being simple and easy to implement, this method can be used for product shape design and graphic software development.

关 键 词：curve interpolation B-SPLINE subdivision scheme. 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]