Representation of conics in the oriented projective plane

Guilherme Albuquerque PintoPedro J. de Rezende

We present a geometric definition of conic sections in the oriented projective plane and describe some of their nice properties. This definition leads to a very simple and unambiguous representation for affine conics and conic arcs. A conic (of any type) is represented by the homogeneous coordinates of its foci and one point on it, hence, the metric plays a major role in this case as opposed to the traditional algebraic characterization of conics as second degree polynomial curves. This representation is particularly suitable for the implementation of geometric solutions of problems that involve the concept of distance. Furthermore, we discuss point location with respect to conic curves which constitutes an important elementary operation for the solution of many such problems.

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