应用在联合细分曲面的离散PDE光顺方法

Application of discrete PDE fairing method to combined subdivision surface

将离散偏微分方程(PDE)光顺方法应用在联合细分的控制网格光顺过程中,即以插值曲线对应的控制边为界将控制网格分割为不重叠的子网格.针对各个子网格分别求解离散PDE,得到控制网格理想曲率,然后在控制网格法向调整控制顶点位置,使控制网格的实际离散曲率逼近于理想曲率.在不同细分层次上,分别对各个子网格光顺,也就实现了控制网格局部和全局的光顺,同时消除了联合细分极限曲面中存在的凹陷等不光顺现象.除奇异点外,极限曲面均达到G2连续.该方法提高了联合细分曲面的质量,扩宽了联合细分的应用范围.

Discrete partial differential equation （PDE） control mesh of combine subdivision surface. Bounded fairing method is directly applied to fair the by control edges related with curves, control mesh is partitioned into submeshes without overlapping. By solving discrete PDE the ideal curvature of single submesh can be obtained. The adjustment of the control vertexes at their 0ormal will make the actual discrete curvature approach to the ideal curvature. While fairing the submeshes separately at different subdivision level, the local and global fairing of control mesh is achieved, and the typical concave phenomenon in combined subdivision surface is removed. The limited surface reaches G^2 continuity except at extraordinary vertex. The method improves combined subdivision surface＇s quality and extends the use of combined subdivision.