Higher order Bezier circles

Abstract

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. Circles that are formed by higher order rational Bezier curves which are nonplanar in the homogeneous space are shown. The problem of whether it is possible to represent a complete circle with one Bezier curve is investigated. In addition, some other interesting properties of cubic Bezier arcs are discussed.