A five-dimensional geometric uniformity framework for spherical diamond grids

Discrete Global Grid Systems (DGGS), as a next-generation framework for the digital Earth, inevitably suffer from geometric non-uniformity, which impacts the accuracy of data representation and analysis. Existing quality assessments, predominantly based on Goodchild's criteria, are inadequate for diamond-based grids, particularly in evaluating angular and distance uniformity. This paper addresses this gap by proposing a comprehensive evaluation framework for spherical diamond grids. We extend the Goodchild criteria by incorporating metrics for angular and distance uniformity, creating an integrated five-dimensional system (shape, topology, size, distance, and angle). Using this framework, we systematically compare three typical diamond DGGS derived from the cube, octahedron, and icosahedron. Our results demonstrate that the icosahedron-based grid exhibits optimal uniformity across all five dimensions. Critically, we reveal that the octahedron-based grid, despite having more initial faces, suffers from severe angular distortion in the across-face boundary regions, rendering its uniformity inferior to that of the cube-based grid. We further validate our framework by constructing a Spherical Residual Network for Diamond Grids (SResNet-DG) for a classification task. Our experimental results demonstrate a strong positive correlation between grid uniformity and the SResNet-DG's performance, substantiating the effectiveness and practical relevance of our proposed geometric evaluation system.