Optimality of the parameterization of quadrics and their intersections

Daniel Lazard (1, 2)

1 CALFOR - Calcul formel
2 SPACES - Solving problems through algebraic computation and efficient software

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.

Mots clés: paramétrisation; parameterization; quadric surfaces; surface quadrique; intersection

Domaines: Autre [cs.OH]

Daniel Lazard. Optimality of the parameterization of quadrics and their intersections. Journées de cloture Visi3D et CoSTIC, 2001, Paris, France. ⟨inria-00099402⟩