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.

基于Voronoi图的2流形表面分区 ${\mathrm{[R}}^3$是几何处理领域中的一项基本操作。但是，当输入对象是薄板模型或包含细分支时，传统的受限Voronoi图（RVD）无法诱导与原始表面共形的流形结构。严等。（2014）是第一个提出本地化RVD（LRVD）算法来处理此问题的人。他们的算法基于面部级别的聚类技术，然后进行一系列的二等分裁剪操作。当输入模型具有长而细的三角形时，它可能会失败。在本文中，我们提出了一种用于在具有薄板甚至管状零件的模型上计算RVD的更为优雅/鲁棒的算法。我们的想法受到这样一个事实的启发：所需的RVD必须保证每个站点都在一个与磁盘拓扑相同的单个区域中占主导地位。因此，当站点在不连贯的子区域中占主导地位时，我们将识别那些无主区域并使用简单快速的本地Voronoi分区操作将它们重新划分为附近的站点。对于控制管状零件的每个部位，我们建议再添加两个部位，以使三个部位几乎是旋转对称的。与最先进的方法相比，我们的方法易于实施，并且对于具有挑战性的案例更强大。