The rational cubic Bézier representation of conics (Q1195752)

Rational cubic Bézier curves are a basic tool in computer aided geometric design. They have the advantage of incorporating both conic sections and parametric cubic curves. In this paper the authors discuss necessary and sufficient conditions for representing conic sections by a rational cubic Bézier curve in proper parametrization. These conditions are given in terms of the weights and of the Bézier vertices of the cubic curve. The paper concludes with a method to determine from the cubic curve whether the conic section is an ellipse, a parabola or a hyperbola.