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

By Bezout's theorem, three quadric surfaces have at most eight isolated intersections although they may have infinitely many intersections. In this paper, we present an efficient and robust algorithm, to obtain the isolated and the connected components of, or to determine the number of isolated real intersections of, three quadric surfaces by reducing the problem to computing the real intersections of two planar curves obtained by Levin's method.