基于C-C细分的四边形网格上插值光滑Bzier曲面的生成  

Generation of Interpolatory Smooth Bézier Patches over Quadrilateral Mesh Based on C-C Subdivision

作　　者：蒋跃华[1] 陈志杨[2] 李根[1] 张三元[1] 叶修梓[1] 

机构地区：[1]浙江大学计算机科学与技术学院,杭州310027 [2]浙江工业大学软件学院,杭州310014

出　　处：《计算机辅助设计与图形学学报》2009年第1期53-59,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60473106);教育部博士点基金(20060335114);国家“八六三”高技术研究发展计划(2007AA01Z311,2007AA04ZA5)

摘　　要：在任意拓扑的四边形网格上构造光滑的曲面是计算机辅助几何设计中的一个重要问题.基于C-C细分,提出一种从四边形网格上生成插值网格顶点的光滑Bzier曲面片的算法.将输入四边形网格作为C-C细分的初始控制网格,在四边形网格的每张面上对应得到一张Bzier曲面,使Bzier曲面片逼近C-C细分极限曲面.曲面片在与奇异顶点相连的边界上G1连续,其他地方C2连续.为解决C-C细分的收缩问题,给出了基于误差控制的迭代扩张初始控制网格的方法,使从扩张后网格上生成的曲面插值于初始控制网格的顶点.实验结果表明,该算法效率高,生成的曲面具有较好的连续性,适用于对四边化后的网格模型上重建光滑的曲面.Constructing smooth surface over arbitrary topological quadrilateral mesh is an important issue in CAGD. This paper presents an algorithm for generating smoothly connected Bezier patches that interpolate the mesh vertices over a quadrilateral mesh based on C-C subdivision. The input quadrilateral mesh is taken as the initial control mesh of C-C subdivision, and the limit surface of C-C subdivision is converted into Bezier patches. For each facet of the quadrilateral mesh, a Bezier patch is obtained. The Bezier patches are G^1-continuous along boundaries connecting to extraordinary points and C^2-continuous everywhere else. For resolving the shrinking problem of C-C subdivision, a recursive method to expand the initial control mesh is proposed based on the deviation analysis. The final surface generated from the expanded mesh interpolates the vertices of the input quadrilateral mesh. The experimental data show that the presented algorithm is effective and the constructed surface has good smoothness and continuity. It can be well applied to reconstruct smooth surface from quadrilateral mesh.

关 键 词：C-C细分 Bzier曲面片 四边形网格 插值 G1连续 C2连续 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]