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ON THE GEOMETRY OF RATIONAL BÉZIER CURVES
( Ayşe Yilmaz Ceylan ),( Tunahan Turhan ),( Gözde Özkan Tükel ) 호남수학회 2021 호남수학학술지 Vol.43 No.1
The purpose of this paper is to assign a movable frame to an arbitrary point of a rational Bézier curve on the 2-sphere S<sup>2</sup> in Euclidean 3-space R<sup>3</sup> to provide a better understanding of the geometry of the curve. Especially, we obtain the formula of geodesic curvature for a quadratic rational Bézier 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 Bézier curve are illustrated on a unit 2-sphere.