ON THE GEOMETRY OF RATIONAL BEZIER CURVES


YILMAZ CEYLAN A., TURHAN T. , Tukel G. O.

HONAM MATHEMATICAL JOURNAL, vol.43, no.1, pp.88-99, 2021 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.5831/hmj.2021.43.1.88
  • Title of Journal : HONAM MATHEMATICAL JOURNAL
  • Page Numbers: pp.88-99

Abstract

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.