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When primitive parametric surfaces are combined and modified inferactively to form complex intersecting surfaces, it becomes important to find the curves of intersection. One must distinguish between finding the shape of the intersection curve, which might only be useful for display, and finding an accurate mathematical representation of the curve. The latter is important for any meaningful geometric modeling, analysis, design, or manufacture involving the intersection. The intersection curve between parametric surfaces is important in such computer-aided design and manufacturing (CAD/CAM) functions as shape design, analysis of groins, design of fillets, and computation of numerically controlled tooling paths. The algorithm presented here provides an adequately accurate mathematical representation of the intersection curve. It also provides a database to simplify such operations as hidden-surface removal, surface rendering, profile identification, and interference or clearance computations. Further, the algorithm facilitates creating and changing a finite element mesh in the intersection region.