Quadric-surface intersection curves: shape and structure

Abstract When cad models composed of quadric surfaces are processed, it is necessary to compute their mutual curve of intersection. A method for the analysis of such intersection curves is presented. Shape description is carried out by a modification of Levin's ruled-surface parameterization scheme, guided by invariant-factors classification. The decomposition of the intersection curve is performed by factorization of the parameterization polynomials. Further analysis of these polynomials yields the graph structure of the curve. The projection of the curve for boundary visualization and evaluation is also described. A full implementation for all nonplanar intersections is included.