  In this paper we review the derivation of implicit equations for
non-degenerate quadric patches in rational Bezier triangular form. These are
the case of Steiner surfaces of degree two. We derive the bilinear forms for
such quadrics in a coordinate-free fashion in terms of their control net and
their list of weights in a suitable form. Our construction relies on projective
geometry and is grounded on the pencil of quadrics circumscribed to a
tetrahedron formed by vertices of the control net and an additional point which
is required for the Steiner surface to be a non-degenerate quadric.
