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G1连续几何偏微分方程Bézier曲面的构造
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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)


Construction of Geometric PDE Bézier Surface with G1 Continuity
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    摘要:

    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.

    Abstract:

    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.

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徐国良,李 明. G1连续几何偏微分方程Bézier曲面的构造.软件学报,2008,19(zk):161-172

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  • 收稿日期:2008-05-03
  • 最后修改日期:2008-11-14
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