A Search-and-Merge Algorithm for Generating Various Voronoi Diagrams Based on Spatial Chromatic Model

Abstract

As a type of spatial tessellation model, the Voronoi diagram (VD) is widely used in many fields, and it is also an important spatial structure for the study of computational geometry.  In this study, we proposed a new search-and-merge (S&M) Voronoi generation algorithm which is based on the spatial chromatic model. The advantage of the S&M algorithm is that it can quickly generate various VDs by retrieving and merging cells from databases without having to develop specific algorithms for each VD. The S&M Voronoi algorithm can be particularly applied in cases where a variety of Voronoi diagrams are frequently required for computation and analysis, such as the location-based spatial analysis. In addition, the proposed S&M method can also generate some new types of spatial tessellations that are different from VDs.

Keywords: Voronoi diagram, spatial chromatic model, spatial tessellation, Computational Geometry