Dynamic Construction of Spherical Raster Voronoi Diagrams Based on Ordered Dilation

Abstract

The Voronoi diagram on the Earth’s surface is a significant data model, characterized by natural proximity and dynamic stability, which has emerged as one of the most promising solutions for global spatial dynamic management and analysis. However, traditional algorithms for generating spherical raster Voronoi diagrams find it challenging to dynamically adjust the Voronoi diagram while maintaining precision and efficiency. The efficient and accurate construction of the spherical Voronoi diagram has become one of the bottleneck issues limiting its further large-scale application. To this end, this paper proposes a dynamic construction scheme for the spherical Voronoi diagram based on the QTM (Quaternary Triangular Mesh) system, with the aim of enabling efficient generation, local updates, and multi-scale visualization of the spherical Voronoi diagrams. In this paper, canonical ordering is introduced. Tailored for the properties of the spherical triangular grid, it constructs a unified and standardized sorting strategy for the dilation of the spherical grids. The construction and updating of the spherical Voronoi diagram are achieved through the ordered dilation of sites. Furthermore, the multi-scale visualization of the spherical Voronoi diagram is realized through the hierarchical structure of the QTM. The paper presents our algorithm intuitively through pseudocode, conducts comparative experiments on the feasibility and efficiency, and designs an experiment for the dynamic navigation and management of ocean-going vessels based on the global multi-resolution Voronoi diagram. The experimental results demonstrate that our algorithm effectively controls the error of the generation of the raster Voronoi diagram and has a significant efficiency advantage when processing dynamic environments.

Keywords

• spherical Voronoi diagram
• digital geographical grid systems
• dynamic modeling
• ordered dilation