Robust and GPU-friendly Isotropic Meshing Based on Narrow-banded Euclidean Distance Transformation

Abstract

In this paper, we propose a simple-yet-effective method for isotropic meshing via Euclidean distance transformation based Centroidal Voronoi Tessellation (CVT). The proposed approach aims at improving the performance as well as robustness of computing CVT on curved domains while simultaneously maintaining the high-quality of the output meshes. In contrast to the conventional extrinsic methods which compute CVTs in the entire volume bounded by the input model, our idea is to restrict the computation in a 3D shell space with user-controlled thickness. Taking the voxels which contain the surface samples as the sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is fully parallel and memory-efficient, and it can construct the shell space with resolution up to 2048<sup>3</sup> at interactive speed. Since the shell space is able to bridge holes and gaps up to a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm works well on models with such defects, whereas the conventional remeshing methods often fail.