An algorithm using edge attribution and bilateral scanning to generate spherical raster Voronoi diagrams

Abstract

Abstract The spherical Voronoi diagram is an important research field in computational geometry, and the method that generates it is a key technology. Most spherical raster algorithms are extensions of planar algorithms. The attribution determination algorithm is one of the most accurate spherical raster Voronoi algorithms. However, it deals inefficiently with large amounts of data. To overcome this issue, a spherical Voronoi diagram generation algorithm that combines edge attribution with bidirectional scanning based on octahedral subdivision is proposed. A coordinate conversion method is built to perform coordinate transformation between latitude–longitude and Cartesian coordinates. The Voronoi attributions of edge grids are determined by computing and comparing the distances to all the sites. A 3×3 template is designed for forward scanning, where grids obtain attributions from their neighbors. Reverse error correction scanning is conducted based on the forward scanning result to guarantee that all grids are correctly assigned. Experiments were conducted to compare the proposed algorithm with the attribution determination algorithm, showing that it has the same accuracy while saving more than 40% of computations. The efficiency advantage of the proposed algorithm becomes more obvious at higher resolutions.