Guaranteed quality isotropic surface remeshing based on uniformization

Surface remeshing plays a significant role in computer graphics and visualization. Numerous surface remeshing methods have been developed to produce high quality meshes. Generally, the mesh quality is improved in terms of vertex sampling, regularity, triangle size and triangle shape. Many of such surface remeshing methods are based on Delaunay refinement. In particular, some surface remeshing methods generate high quality meshes by performing the planar Delaunay refinement on the conformal uniformization domain. However, most of these methods can only handle topological disks. Even though some methods can cope with high-genus surfaces, they require partitioning a high-genus surface into multiple simply connected segments, and remesh each segment in the parameterized domain. In this work, we propose a novel surface remeshing method based on uniformization theorem using dynamic discrete Yamabe flow and Delaunay refinement, which is capable of handling surfaces with complicated topologies, without the need of partitioning. The proposed method has the following merits: Dimension deduction, it converts all 3D surface remeshing to 2D planar meshing; Theoretic rigor, the existence of the constant curvature measures and the lower bound of the corner angles of the generated meshes can be proven. Experimental results demonstrate the efficiency and efficacy of our proposed method.