Representing Conics using the Oriented Projective Plane

We present a geometric definition of conic sections in the oriented projective plane and describe some of their nice properties. The three main classes of affine conics are unified by a generalized distance notion on that space. This definition leads to a very simple representation of conic arcs suitable for implementations of geometric solutions to problems involving the concept of distance, in particular, the construction of various generalizations of Voronoi diagrams.

1998