The Voronoi diagram is a certain geometric data structure which has numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and useful, with several different and important algorithms. However, this theory has been quite steady during the last few decades in the sense that no essentially new algorithms have entered the game. In addition, most of the known algorithms are serial in nature and hence cast inherent difficulties on the possibility to compute the diagram in parallel. In this paper we present the projector algorithm: a new and simple algorithm which enables the (combinatorial) computation of 2D Voronoi diagrams. The algorithm is significantly different from previous ones and some of the involved concepts in it are in the spirit of linear programming and optics. Parallel implementation is naturally supported since each Voronoi cell can be computed independently of the other cells. A new combinatorial structure for representing the cells (and any convex polytope) is described along the way and the computation of the induced Delaunay graph is obtained almost automatically.

翻译：Voronoi图是一种特定的几何数据结构，在众多科学与技术领域具有广泛应用。针对点集计算二维欧几里得Voronoi图的算法理论丰富且实用，包含数种不同且重要的算法。然而，近几十年来该理论始终较为稳定，本质上的新算法并未出现。此外，现有算法大多本质上是串行的，因此对并行计算该图结构造成了固有困难。本文提出投影算法：一种可实现二维Voronoi图（组合）计算的新型简洁算法。该算法与以往算法显著不同，其所涉及的部分概念源于线性规划与光学思想。由于每个Voronoi单元可独立于其他单元进行计算，因此并行实现自然得到支持。文中还描述了一种用于表示单元（及任意凸多面体）的新型组合结构，并近乎自动地实现了由此导出的Delaunay图的计算。