We expose a few geometric techniques for determining intersections between lines and conic curves in a plane, and between planes and quadric surfaces in 3D projective space. We hope these techniques to be useful as elements for handling conies and quadrics in a Grassmann-Cayley algebra framework. In order to comply with this objective, we mostly derive our algorithms from ruler-only constructions, which possess an immediate translation in Grassmann-Cayley' s formalism. At the basis of these constructions we use reference points which determine the conic or quadric. Besides intersections, we also address the determination of poles and polars, and we mention a possible application to the parameterization of portions of quadrics.
['Frédéric Jourdan']
Quadric modeling in a Grassmann-Cayley algebra setting