Direct sampling on surfaces for high quality remeshing

Isotropic point distribution is crucial in remeshing process to generate a high-quality mesh. In this paper, we present a novel algorithm of isotropic sampling on two-manifold mesh surface. Our main contribution lies in the successful generalization of a 2D fast Poisson disk sampling algorithm, which makes it able to sample directly 3D mesh surfaces, including feature edges. We adopt geodesic distance as the distance metric for sampling algorithm in 3D to better capture the geometry information. Given a density function over the surface, we derive a close analytic form of the available boundary, which makes our algorithm support efficient adaptive sampling. To further improve the isotropy of point distribution, Lloyd relaxation is performed locally to optimize the location of sampling points. The whole process guarantees that new vertices lie on the original surface. Mutual tessellation is utilized to reconstruct the connectivity of new vertices, which guarantees the fidelity and validity of topology. Experiments show that our algorithm is able to remesh an arbitrary closed manifold into a high-quality mesh with large minimal angles and small number of irregular vertices.