Delimiting the service area of public facilities is an essential topic in spatial analysis studies. The adaptive crystal growth Voronoi diagrams based on weighted planes are one of the recently proposed methods to address service area delimitation, and consider the geographic distribution of the clients the facilities in question serve and the characteristic of the socioeconomic context, while at the same time mitigate the modifiable areal unit problem when dealing with the socioeconomic context, since the method is based on continuous weighted planes of socioeconomic characteristics rather than arbitrary areal units. However, in the method, the environmental and socioeconomic contexts are rasterized and represented by regular square grids (raster grid). Compared with a raster grid, the hexagon grid tiles the space with regularly sized hexagonal cells, which are closer in shape to circles than to rectangular cells; hexagonal cells also suffer less from orientation bias and sampling bias from edge effects since the distances to the centroids of all six neighbor cells are the same. The purpose of this study is to compare the raster grid and hexagon grid for implementing adaptive crystal growth Voronoi diagrams. With the case study of delimitating middle school service areas, the results are compared based on the raster grid and hexagon grid weighted planes. The findings indicate that the hexagon-based adaptive crystal growth Voronoi diagrams generate better delineation results compared with the raster-based method considering how commensurate the population in each service area is with the enrollment capacity of the middle school in the service area and how accessible the middle schools are within their service areas. The application of hexagon-based adaptive crystal growth Voronoi diagrams may help city managers to serve their citizens better and allocate public service resources more efficiently.
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