Finding neighbors of equal size in linear quadtrees and octrees in constant time

Abstract

Linear quadtrees and octrees are data structures which are of interest in image processing, computer graphics, and solid modeling. Their representation involves spatial addresses called location codes. For many of the operations on objects in linear quadtree and octree representation, finding neighbors is a basic operation. By considering the components of a location code, named dilated integers, a representation and associated addition and subtraction operations may be defined which are efficient in execution. The operations form the basis for the definition of location code addition and subtraction, with which finding neighbors of equal size is accomplished in constant time. The translation of pixels is a related operation. The results for linear quadtrees can be generalized without difficulty to linear octrees.