Optimality of the parameterization of quadrics and their intersections

Abstract : It is shown that any intersection of two quadrics may be pamareterized with at most two square roots by components (except when the intersection consists in 4 colinear lines), and we provide an algorithm for computing which is always optimal in the number of square roots which are involved. However, in some cases, this optimality needs a sub-algorithm for finding a ratiaonal point on a conic, if any.