On the classification of rational second-order Bézier curves (Q946068)

The authors study the projective (fractional rational) second-order Bézier curves. An equation of such a curve in barycentric coordinates, which depends on a parameter, is derived. A complete classification of projective second-order Bézier curves has been given by \textit{G. Farin} [Curves and surfaces for CAGD, 5th ed., Academic, San Diego, 220--223 (2002)]. More precisely it is proved that a fractional rational second-order Bézier curve is an arc of a parabola for \(\mu =1 \), an arc of a hyperbola for \(\mu >1 \) and an arc of an ellipse for \(\mu <1 \), where \(\mu \in (0,1)\).