Query Sphere Indexing for Neighborhood Requests

Abstract

This is an algorithm for finding neighbors for point objects that can freely move and have no predefined position. The query sphere consists of a center location and a given radius within which nearby objects must be found. Space is discretized in cubic cells. This algorithm introduces an indexing scheme that gives the list of all the cells making up the query sphere, for any radius and any center location. It can additionally take into account both cyclic and noncyclic regions of interest. Finding only the k-nearest neighbors naturally benefits from the query sphere indexing by running through the list of cells from the center in increasing distance and prematurely stopping when the k neighbors have been found. Source code is available online.