Linear octtrees for fast processing of three-dimensional objects

A new, effective way of storing octtrees for three-dimensional representation of objects is given. The 10 fields normally required to identify a node of an octtree are reduced to only one. Algorithms are presented for (i) mapping cubic pixels from and to space array (with subscripts I, J, K), (ii) finding the stereographic projections on the IJ, IK, and JK planes, (iii) performing union (intersection) of two objects centered on the same array, and (iv) finding the pixel adjacent to a given one in a specified direction. The newly proposed data structure is a (dynamically built) array of sorted octal codes which reflects the successive octant subdivisions; it represents a dramatic improvement with respect to octtrees when space complexity is considered. Also, the formulation of the procedures mentioned above takes advantage of this “natural” structure and results in very simple algorithms, easy to code and optimize. Some of the proposed procedures could also be implemented in parallel mode.