ON THE GEOMETRY OF RATIONAL BEZIER CURVES

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

HONAM MATHEMATICAL JOURNAL, cilt.43, sa.1, ss.88-99, 2021 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.5831/hmj.2021.43.1.88
  • Dergi Adı: HONAM MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.88-99
  • Anahtar Kelimeler: Darboux frame field, Geodesic curvature, Rational Bezier curve, 2-sphere
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.