G^1连续的细分几何偏微分方程曲面设计  

Designing of Subdivision Geometric Partial Differential Equation Surfaces with G^1 Continuity

作　　者：潘青[1] 徐国良[2] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081 [2]中国科学院数学与系统科学研究院计算数学与科学工程计算研究所,北京100190

出　　处：《计算机辅助设计与图形学学报》2011年第12期1994-1999,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11171103);国家自然科学基金重点项目(10990013);国家自然科学基金创新群体项目(11021101);湖南师范大学青年优秀人才培养计划(ET10901)

摘　　要：几何偏微分方程方法是一项构造高质量曲面的强大技术.曲面细分自出现以来由于其对拓扑结构的灵活性就一直活跃在CAD领域.文中将这2种不同的方法结合在一个统一的框架下,高效而令人满意地设计了带有G1边界条件的几何偏微分方程细分曲面.所考虑的3个四阶几何偏微分方程为曲面扩散流、拟曲面扩散流和Willmore流,这些方程采用混合有限元方法来求解,并成功地设计了基于四边形的Catmull-Clark细分的四阶几何偏微分方程曲面的有限元方法.Numerical solutions to the geometric partial differential equations（PDE） are useful tools for constructing high-quality surfaces.Meanwhile,subdivision surfaces had been widely used in computer aided design because of its flexibility in topology structure.In this paper,we combine the PDE methods and the subdivision surfaces to efficiently design subdivision surfaces with G1 boundary condition in a unified framework.Three forth-order geometric partial differential equations are considered,including surface diffusion flow,quasi surface diffusion flow and Willmore flow.These equations are solved by the mixed finite element method.It is shown that by applying our proposed method,the finite element method of forth-order geometric PDE surfaces based on the quadrilateral Catmull-Clark＇s subdivision can be successively designed.

关 键 词：四阶几何流 CATMULL-CLARK细分 曲面设计 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]