Anisotropic surface meshing using locally isometric embedding

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.