Nearest Neighbor Distance in Three-Dimensional Space

This paper deals with the nearest neighbor distance in three-dimensional space. The distribution of the nearest neighbor distance is derived for grid and random point patterns. The distance is measured as the Euclidean and rectilinear distances. An application of the nearest neighbor distance can be found in facility location problems. The nearest neighbor distance represents the service level of facility location. The distribution shows how the distance to the nearest facility is distributed in a study region, and is useful for facility location problems in threedimensional space. The distribution of the kth nearest neighbor distance is also derived for the random pattern.