The invention relates to image decomposition strategies and computer-based methods for implementing them. In one method of the invention, the ordering of tetrahedral shapes that define or approximate an image is performed in such a way that neighboring tetrahedral shapes can be identified, located and efficiently used. In one aspect, binary location code array is used to represent an image and the method for identify the neighbor shape employs a bit manipulation step in code or psuedo-code for operating a computer. In this aspect, the invention allows one to move between adjacent tetrahedra, and any data corresponding to the tetrahedra, in constant time.