ON THE GEOMETRY OF RATIONAL BEZIER CURVES

The purpose of this paper is to assign a movable frame to an arbitrary point of a rational Bezier curve on the 2-sphere S-2 in Euclidean 3-space R-3 to provide a better understanding of the geometry of the curve. Especially, we obtain the formula of geodesic curvature for a quadratic rational Bezier curve that allows a curve to be characterized on the surface. Moreover, we give some important results and relations for the Darboux frame and geodesic curvature of a such curve. Then, in specific case, given characterizations for the quadratic rational Bezier curve are illustrated on a unit 2-sphere.