Surface/Surface Intersection on Bezier surfaces was one of the main subjects in my mathematics studies. This topic is well known for its time eating algorithms. My aim was to build an algorithm that can be run on multi-prozessor computers. For solving this problem we used a Divide and Conquer Strategy for parallelization. We therfore recursivly split up the controlpoint nets through a subdivision routine. Before subdividing the new areas any further we calculate bounding boxes surrounding the surfaces patches. Examining the bounding boxes we can eliminate some patches with no curves on it. On all other patches we try to find startpoints on the domain borders. If this search is successful we use a local tracing algorithm for the calculation of this curve part.
Problems may arise on patches, where the intersection curve intersects itselfs or at least comes close to any other curve. The steplength in local tracing method will drop to 0.