Robustly computing restricted Voronoi diagrams (RVD) on thin-plate models

摘要

Voronoi diagram based partitioning of a 2-manifold surface in R~3 is a fundamental operation in the field of geometry processing. However, when the input object is a thin-plate model or contains thin branches, the traditional restricted Voronoi diagrams (RVD) cannot induce a manifold structure that is conformal to the original surface. Yan et al. (2014) are the first who proposed a localized RVD (LRVD) algorithm to handle this issue. Their algorithm is based on a face-level clustering technique, followed by a sequence of bisector clipping operations. It may fail when the input model has long and thin triangles. In this paper, we propose a more elegant/robust algorithm for computing RVDs on models with thin plates or even tubular parts. Our idea is inspired by such a fact: the desired RVD must guarantee that each site dominates a single region that is topologically identical to a disk. Therefore, when a site dominates disconnected subregions, we identify those ownerless regions and re-partition them to the nearby sites using a simple and fast local Voronoi partitioning operation. For each site that dominates a tubular part, we suggest add two more sites such that the three sites are almost rotational symmetric. Our approach is easy to implement and more robust to challenging cases than the state-of-the-art approach.