Shape distortion analysis of hexagonal discrete global grid systems based on standard deviation of neighbor distance

Abstract

Hexagonal Discrete Global Grid Systems (HDGGS) are spatial reference frameworks based on the spatial discretization of the Earth’s surface, dividing it into a network of uniform hexagonal cells. They have been widely applied in geospatial analysis and environmental science fields. However, the hexagonal cells are not perfectly uniform, exhibiting inevitable shape distortion and area deformation. This study proposes a neighbor distance standard deviation method to characterize the shape deformation of individual hexagonal cells, and introduces a global deformation index to assess overall distortion magnitude, thereby addressing the limitations of deformation analysis based solely on cell area and perimeter differences. Finally, we experimentally analyzed deformation characteristics across three hexagonal discrete global grid systems projection types: Fuller3H, Fuller4H, ISEA3H, ISEA4H, and Uber H3. The experimental results show that, compared with ISEA-projection-based HDGGS grids, the Fuller-projection-based HDGGS grids’ cell neighbor distance standard deviation, grid neighboring distance standard deviation, and global deformation index are 72.09 % to 76.12 %, 74.25 % to 81.92 %, and 72.25 % to 76.29 % of the former’s values, respectively. In comparison, the Gnomonic-projection-based HDGGS’s global deformation index is 55.28 % and 40.35 % of the previous two’s values, respectively. Therefore, Gnomonic-projection-based HDGGS demonstrates the least cell shape deformation and optimal equidistant characteristics. This study pioneers quantifying local distance consistency as standardized neighbor distance standard deviation, transcending conventional evaluation paradigms that solely rely on cell perimeter mean squared error or compactness. Experimental results confirm the method’s effectiveness in quantitatively evaluating HDGGS shape deformation, providing a decision-support tool for HDGGS projection type selection.