A Condition Number Analysis of a Surface-Surface Intersection Algorithm

The problem of finding all intersections between two surfaces has many applications in computational geometry and computer-aided geometric design. We propose an algorithm based on Newton’s method and subdivision for this problem. Our algorithm uses a test based on the Kantorovich theorem to prevent the divergence or slow convergence problems normally associated with using unsuitable starting points for Newton’s method. The other main novelty of our algorithm is an analysis showing that its running time is bounded only in terms of the condition number of the problem instance.