三维模型四面体化是一种重要的有限元网格生成技术.介绍了一种特征保持的四面体网格生成及优化算法.首先使用三维模型主成分分析进行预处理,然后用体心立方构建初始四面体,接着通过拉普拉斯坐标改变模型边界切点的移动方式保持模型的局部特征,最后构造改进的密度能量误差函数优化四面体网格质量.实验结果表明,该方法可行、有效,且能很好地保持模型特征.

Tetrahedralization of 3D models is an important technique in finite element mesh generation. An algorithm of tetrahedral mesh generation and optimization is proposed in this paper. It first uses principal component analysis of 3D models for the preprocessing. Then the initial tetrahedral mesh is built based on the body-centered cubic while the movement of cutting point is improved via Laplacian coordinates for keeping local features. Finally, it optimizes the quality of the tetrahedral mesh by using the function of energy-density error. Experimental results demonstrate that this method is viable, effective, and can preserve the model feature well.

国家自然科学基金(61272298, 61133009);教育部留学回国人员科研启动基金([2009]1590);浙江省自然科学基金(LY14A010032);浙江理工大学521人才资助项目(11430032521301)