Anisotropic Surface Meshing Using Locally Isometric Embedding

With the development of computer graphics,anisotropic remeshing has always been a difficult problem which is concerned by researchers and technicians.Compared with isotropic meshes,anisotropic meshes often require fewer triangle facets to approx-imate the original surface well.Due to the smaller number of triangles,numerical prob-lems in many fields such as finite elements,geometric processing and physical simula-tion can be solved faster than that of isotropic meshes.In general,anisotropic remeshing is a very complex problem,which has two objec-tives that must be met:the first is the requirement for anisotropy,which is generally to conform to a pre-determined metric;the second is to reduce the approximation error of the anisotropic mesh to the original surface.However,many existing algorithms have difficulty in satisfying both of these points and require many complicated operations to ensure the robustness and stability.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.