Uniform Voronoi tessellation of digital manifolds: a GPU-based algorithm with applications to remeshing

We present here a GPU-friendly algorithm for uniform Voronoi tessellation (UVT) of a digital manifold, which, in particular, may be conceived as the voxelized representation of a 2-manifold surface. Its pipeline integrates several novel ideas, such as local directional field, which is used to estimate field energy, and when combined with Voronoi energy, provides an estimate of the uniformity of tessellation in each iteration. For selection of seeds needed to initialize field computation and Voronoi tessellation, an efficient strategy of functional partitioning is used to partition the digital manifold into a collection of functional components. Over successive iterations, the seeds are updated to effectuate energy optimization, and thus to gradually converge towards a uniform tessellation. As its application in 3D modeling, we have also shown how the energy-optimizing tessellation iteratively transforms a 2-manifold surface (e.g., a triangulated mesh) into an isotropic mesh while preserving the surface details. As our algorithm works entirely in voxel space, it is readily implementable in GPU for all associated computations. Experimental results on different datasets have been presented to demonstrate its efficiency and robustness.