Rational Quadratic Conics

While the projective treatment of conics reveals most of their fundamental properties in an elegant way, “real world” applications of conics happen in an affine environment. In this chapter, we will thus shift our emphasis from the projective treatment of conics to an affine viewpoint. 1

5.1 The Rational Quadratic Form

In the projective plane IP2, a conic may be described by a quadratic Bezier curve:

Figure 5.1. Weight signs: for zo > 0 and z i,z 2 < 0, the weight function has a zero in [0 , 1].