Impact crater records on planetary surfaces are often analyzed for their spatial randomness. Generalized approaches such as the mean second closest neighbor distance (M2CND) and standard deviation of adjacent area (SDAA) are available via a software tool but do not take the influence of the planetary curvature into account in the current implementation. As a result, the measurements are affected by map distortion effects and can lead to wrong interpretations. This is particularly critical for investigations of global data sets as the level of distortion typically increases with increasing distance from the map projection center. Therefore, we present geodesic solutions to the M2CND and SDAA statistics that can be implemented in future software tools. We apply the improved methods to conduct spatial randomness analyses on global crater data sets on Mercury, Venus, and the Moon and compare the results to known crater population variations and surface evolution scenarios. On Mercury, we find that the emplacement of smooth plain deposits strongly contributed to a global clustering of craters and that a random distribution of Mercury's basins is not rejected. On Venus, the randomness analyses show that craters are largely randomly distributed across all sizes but where local nonrandom distributions due to lower crater densities in regions of recent volcanic activity may appear. On the Moon, the global clustering of craters is more pronounced than on Mercury due to mare volcanism and the Orientale impact event. Furthermore, a random distribution of lunar basins is not rejected.
