Surface modeling algorithm for pyramid architectures

A parallel version of the random midpoint displacement algorithm is developed to take advantage of the similarities between the structure of the algorithm and massively parallel machines with pyramid (quadtree) architectures. The proposed random fractal surface algorithm is designed to be used with massively parallel (greater than 1000 processing elements) pyramid architectures in a three-dimensional environment. The general algorithm is explained, followed by an explanation and comparison of the sequential and parallel algorithms. It is shown that to implement this algorithm on a machine with a single processor, much overhead is involved in the recursion (four calls to itself). In addition, the single-processor solution is inefficient for this type of algorithm since it has to perform each calculation for each area subdivision and displacement sequentially. It is also found that the depth of recursion must be greater than two and the number of levels must be at least as great as the depth of recursion