Voronoi diagram generation on the ellipsoidal earth

Voronoi diagram on the earth surface is a powerful tool to study spatial proximity at continental or global scale. However, its computation remains challenging because geospatial features have complex shapes. This paper presents a raster-based algorithm to generate Voronoi diagrams on earth׳s surface. The algorithm approximates the exact point-to-point geographical distances using the cell-to-cell geographical distances calculated by a geographical distance transform. The result is a distance image on which Voronoi diagram is delineated. Compared to existing methods, the proposed algorithm calculates geographical distances based on an earth ellipsoid and allows Voronoi generators to take complex shapes. Most importantly, its approximation error is bounded thus enabling users to control the accuracy of the Voronoi diagram through grid resolution.