Implementation of a divide-and-conquer method for intersection of parametric surfaces (Q1819568)

The paper describes a subdivision-based intersection method of parametric surfaces which is independent of surface type. The algorithm handles all \(C^ 1\) continuous surfaces defined with a rectangular parametrization. The strategy comprises the steps of subdivision, intersection, sorting, and refinement. Subdivision looks for possible surface subpiece intersection. Intersection approximates each subpiece by two triangles and each subpiece pair intersection is approximated by intersecting the resultant four triangle pairs. Sorting connects intersection line segments to form curve. Refinements improve the accuracy of the computed intersection points. Two lists are output: one of disjoint curves, the other of isolated points. Examples are presented for surface combinations such as planes, trigonometrically parametrized quadrics, and rationally parametrized interpolation surfaces.