Selfintersection of composite curves and surfaces Original Research Article

This paper provides computationally tractable conditions to determine whether a composite spline 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 exposition 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 R3, made up of properly-joined parametric patches, will retain its original topological form when its control points are perturbed.