The use of triangulation based methods for intersection is based on the assumption that it is possible to triangulate the surfaces dense enough to ensure that all intersection curves are found. In the case of transversal intersections, when the normals of the surfaces intersected are not near parallel along the intersection curve, such methods work well. However, when the intersection is singular or near singular along the intersection triangulation based intersection methods will easily loose some intersections and produce false intersections. The main advantage of triangulation based intersection methods is speed, and in most cases corrects results when transversal intersections are sought.