Denomination-based Quasi-isotropic Remeshing using Curvature Map and Voronoi Tessellation

We propose a novel algorithm for quasi-isotropic remeshing when edge-length denomination is given as input. It is designed by the prudence of fitting triangles on the surface based on curvature—higher the curvature, lower will be the triangle size (as per the given denomination), and vice versa. By virtue of this, we have a better control of the remeshing quality, measured in terms of different parameters such as Hausdorff error, average vertex degree, and the like. The proposed pipeline comprises mesh voxelization, discrete curvature estimation, centroidal Voronoi tessellation based on curvature map and energy optimization, and finally the conventional step of Delaunay triangulation. Upon testing on various datasets, it is found to exhibit encouraging results with isotropic triangles getting fitted in regions of uniform curvature, while some occasional anisotropy occurring across regions of changing curvature. We have furnished related results and statistics to adjudge its merit, and have pointed out its further scope in mesh remodeling.