Accurate and Robust Geometric Algorithms for Regridding on the Sphere

Abstract. Regridding is one of the most common operations in geoscientific modeling and data analysis. There are many types of regridding, each drawing from a common set of fundamental computational geometry algorithms. However, these algorithms are rarely documented together or systematically compared in a manner that elucidates their relative strengths and appropriate use. In particular, several recent studies have highlighted the importance of careful treatment of floating point operations in the implementation of these algorithms to ensure numerical robustness and stability. In this work, we organize non-conservative and conservative regridding operations end-to-end, from spatial indexing, great-circle and constant latitude geometry, and spherical predicates to spherical clipping, triangulation, and area calculation with constant latitude corrections, into a coherent set of geometric kernels on the sphere. When known, we present numerically stable floating-point formulas and characterize their error behavior. We also indicate where higher-precision techniques, such as Error Free Transformations, can be incorporated when additional accuracy is needed. The resulting framework establishes a practical and performance-portable baseline for accurate and robust regridding on the sphere.