ON THE GEOMETRY OF RATIONAL BEZIER CURVES
HONAM MATHEMATICAL JOURNAL, vol.43, no.1, pp.88-99, 2021 (ESCI)
- Publication Type: Article / Article
- Volume: 43 Issue: 1
- Publication Date: 2021
- Doi Number: 10.5831/hmj.2021.43.1.88
- Journal Name: HONAM MATHEMATICAL JOURNAL
- Journal Indexes: Emerging Sources Citation Index (ESCI)
- Page Numbers: pp.88-99
- Keywords: Darboux frame field, Geodesic curvature, Rational Bezier curve, 2-sphere
- Akdeniz University Affiliated: Yes
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.