Higher order Bézier circles

Rational Bezier and B-spline representations of circles have been heavily publicized. However, all the literature assumes the rational Bezier segments in the homogeneous space are both planar and (equivalent to) quadratic. This creates the illusion that circles can only be achieved by planar and quadratic curves. In this paper we show circles that are formed by higher order rational Bezier curves which are non planar in the homogeneous space. We also investigate the problem of whether it is possible to represent a complete circle with one Bezier curve. In addition, some other interesting properties of cubic Bezier arcs are discussed. *This work was performed in part under NASA Contract NAS 2-12961