Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON THE GEOMETRY OF RATIONAL BÉZIER CURVES

  • Received : 2020.09.30
  • Accepted : 2021.02.13
  • Published : 2021.03.25
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Abstract

The purpose of this paper is to assign a movable frame to an arbitrary point of a rational Bézier curve on the 2-sphere S2 in Euclidean 3-space R3 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.

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References

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