Robust intersection of quadrics

the intersection of two arbitrary implicit quadrics with rational coefficients.
Our method is similar in spirit to the pencil method introduced by J. Levin
(1976) for explicitly describing the intersection of two quadrics, but extends
it in several directions. Combining results from the theory of quadratic forms,
a projective formalism and new theorems relating the geometry of the
intersection to properties of the discriminant of the pencil, we show how to
obtain parametric representations that are both ``simple'' (the size of the
coefficients is small) and ``as rational as possible'' (the size of the field
extension in which the coefficients live is optimal in the worst case). Since
computing the intersection of two surfaces is an important step in
CSG-to-Brep conversion, the output of our algorithm is well suited for the robust
boundary evaluation of second-order CSG models.