Rational Polynomial Surface Intersections

Abstract This paper presents a new algorithm for the computation of the intersection of two rational B-spline surface patches. This algorithm is based on the computation of significant points of the intersection in the parameter space of one of the patches using direct numerical techniques; partitioning of the intersection domain at these points; tracing of the resulting intersection segments using subdivision and Newton or marching techniques; and verification of computation of all intersection branches using convexity properties of the two surfaces and their partial derivatives.