基于局部等距嵌入的各向异性曲面网格生成

Anisotropic surface meshing using locally isometric embedding

提出了一种新颖的各向异性曲面网格生成方法.不同于之前依赖于全局共形嵌入或高维等距嵌入的方法,该算法以局部等距嵌入的思想为基础.为了实现等距嵌入的目标,我们将原始曲面分割成圆锥曲面集,对曲面片逐一进行处理.首先,利用双射参数化将圆锥曲面嵌入到平面,然后,在参数域进行各向异性网格生成,最后,将圆锥曲面映回原始曲面.为了处理不同圆锥曲面之间的缝合问题,我们使当前圆锥曲面包含之前未处理的边界,使得边界附近的三角面片可以在当前迭代中处理.大量实验验证了本文算法的鲁棒性.相较于之前的各向异性网格生成算法,本文的算法能够更加鲁棒地处理高亏格网格,且能够得到与输入网格逼近误差更小的结果.

A novel method for anisotropic surface meshing was proposed.Different from the previous methods using globally conformal embeddings or high-dimensional isometric embeddings,our algorithm is based on the idea of locally isometric embedding.In order to achieve isometric embeddings,the input surface was partitioned into a set of cone patches that are remeshed one by one.First,a patch was parameterized bijectively into a plane,then an anisotropic mesh was generated in the parameterized domain,and finally,the remeshed patch was mapped back to the input surface.To deal with the stitching problem between different patches,the cone patch was made containing the previously unprocessed boundary.Therefore,the triangles near the boundary could be remeshed.The robustness of our method was demonstrated on various complex meshes.Compared to the existing methods,our method is more robust,and contains a smaller approximation error to the input mesh.