Selfintersection of composite curves and surfaces

This paper provides computationally tractable conditions to determine whether a composi te splme curve or patch selfintersects, according to a definition that includes the important limiting cases of cusps, singularities, and tangential intersections of adjacent components . These results follow upon our exposit ion of necessary and sufficient conditions to preclude such selfintersections. The paper includes a numerical example illustrating the results, and discusses an important application, namely, guaranteeing that a finite curvilinear simplicial complex in R ~. made up of properly-joined parantetric patches, will retain its original topological form when its control points are perturbed. ~:; 1998 Elsevier Science B.V.