A robust algorithm for finding the real intersections of three quadric surfaces (Q2573874)

The authors present an efficient method how to obtain all of the real points of intersection of three quadric surfaces, the isolated points and the connected components including. The suggested method is based on \textit{J. Levin}'s [Commun. ACM 19, 555--563 (1976; Zbl 0334.68050)] method of computing the intersection curve of two quadric surfaces. Using this method, the problem of computing the intersection points of three quadric surfaces can be simplified to the problem of finding the intersection points of parametric polynomial curves. In the article, the conditions under which the real intersections of three quadric surfaces exist and under which the number of these real intersections is finite or infinite are investigated. The procedure and examples of computation are also presented. Quadric surfaces, as the simplest curved surfaces, are widely used in CAD/CAM/CAE systems for shape representation. The suggested method of finding intersections of three quadric surfaces can be useful in many applications of computer geometry, for example in solid modelling systems of computer graphics, in robotics to detect collisions of moving parts, etc.