Spherical Indexing for Neighborhood Queries

Abstract

This is an algorithm for finding neighbors when the objects can freely move and have no predefined position. The query consists in finding neighbors for a center location and a given radius. Space is discretized in cubic cells. This algorithm introduces a direct spherical indexing that gives the list of all cells making up the query sphere, for any radius and any center location. It can additionally take in account both cyclic and non-cyclic regions of interest. Finding only the K nearest neighbors naturally benefits from the spherical indexing by minimally running through the sphere from center to edge, and reducing the maximum distance when K neighbors have been found.