【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.更多还原

【Abstract】 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.更多还原