2D约束Delaunay剖分生成表面模型的表面网格

Surface mesh generation for surface models by 2D conforming delaunay triangulation

提出一种生成表面模型的表面非结构化网格的方法.该方法仅假定表面模型的每个面片在取定适当的投影平面时可看成是一个单值函数.对表面模型的每个面片,首先在其相应的投影面上进行二维约束Delaunay剖分,然后对网格顶点进行插值.由于采用联动剖分的策略使得单独生成的各个表面网格在共同边界处匹配.与通常的生成表面网格的网格前沿法相比,本方法无需预先对域的边界进行离散,边界的离散体现在约束Delaunay剖分中恢复限定线段的边界细分过程中,减少了用户干预.通过合理地指定2D约束Delaunay三角化时网格单元尺寸分布函数,可以有效控制表面网格对表面模型的逼近精度和实现自适应的表面网格.实验结果证明了本算法的有效性.

An approach to the generation of unstructured surface meshes for surface models was presented. The only assumption is that each patch of input surface model can be treated as a single-valued function by properly specifying the projection plane. To mesh a patch of the surface model, 2D conforming Delaunay triangulation was employed on the corresponding projection plane followed by cooperate-triangulation strategy, the generated surface mesh interpolating the vertices of mesh. Because of adopting was matched at common boundary although the mesh of each patch was generated separately. Compared with advancing-front method,boundary discretization need not to be performed in advanced, the same effect was achieved when the boundary is recovered by means of boundary subdivision scheme in the conforming Delaunay triangulation procedure. By assigning element size distribution function reasonably in conforming Delaunay triangulation procedure, the generated surface mesh was a nice approximation of the underlying surface model, and self-adaptive surface mesh can be achieved. The capability of the method is demonstrated for several 3D surface models.