基于LEPP递变的四面体网格自适应剖分算法

Adaptive Tetrahedral Mesh Generation Based on LEPP Algorithm

为了更合理地进行四面体网格剖分,提出了一种根据待剖分对象形态不同进行网格密度自适应调整的四面体网格剖分方法。该方法首先采用BCC(body-centered cubic)网格初始化网格空间,并根据表面曲率的大小以及距离物体表面的远近,采用LEPP(longest edge propagation path)算法由外至内对初始化后的网格空间进行不同尺度的细分;然后对横跨表面的网格进行调整,以形成对象的表面形态;最后采用以质量函数引导的拉普拉斯平滑与棱边收缩(edge collapse)的方法对网格的质量进行优化来最终得到待剖分对象的四面体网格。结果表明,该方法所生成的网格不仅具有自适应的网格密度,而且网格质量比常用的Advancing Front算法也有所提高。对于基于3维断层图像或表面模型进行有限元建模,该方法不失为一种行之有效的好方法。

A tetrahedral mesh generation method based on which the mesh density could be adjusted with the shape of the object was developed in the paper. The BCC lattice was used to initialize the mesh space. According to the curvature and the distance from the lattice to the surface of the object, the LEPP algorithm is adopted to refine the initialized mesh from the outer to the inner with different scales. Then all the lattices that stride the surface were adjusted to fit the shape of the object. At last the quality function navigated Laplacian smoothing and Edge Collapse methods were used to optimize the quality of the meshed tetrahedral and the meshed model was obtained. Result shows the method improves the configuration of the mesh while the quality of the tetrahedral is also guaranteed. The method is tested to be useful in the finite element modeling based on 3D computer tomography images or surface model.