基于三角形和四边形网格上Laplace-Beltrami算子、高斯曲率和平均曲率的离散及其收敛性分析,提出了一种使用四阶几何流构造几何偏微分方程Bézier曲面的方法.使用该方法构造出的Bézier曲面既具有几何偏微分方程曲面的最优性质,同时又满足G1连续性.算法收敛性的数值实验表明该方法是有效的.

Basing on discretizations of Laplace-Beltrami operator and Gaussian curvature over triangular and quadrilateral meshes and their convergence analyses, this paper proposes in this paper a novel approach for constructing geometric partial differential equation (PDE) Bézier surfaces, using several fourth order geometric flows. Both three-sided and four-sided Bézier surface patches are constructed with G1 boundary constraint conditions. Convergence properties of the proposed method are numerically investigated, which justify that the method is effective and mathematically correct.

Supported by the National Natural Science Foundation of China under Grant No.60773165 (国家自然科学基金); the National Basic Research Program of China under Grant No.2004CB318000 (国家重点基础研究发展计划(973)