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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2011 / Cilt: 60 - Sayı: 1

ON THE CURVATURES OF TUBULAR SURFACE WITH BISHOP FRAME

Fatih DOGAN
Yusuf YAYLI
Pages
59–69
Publication Date
2011-02-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this work, we investigate tubular surface with Bishop frame in place of Frenet frame and afterwards give some characterizations about special curves lying on this surface

📌 3 Key Takeaways

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Objective & Hypothesis:A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t) and it is parametrized through Frenet frame of the spine curve C(t).
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Key Findings & Data:If the radius function r(t) = r is a constant, then the canal surface is called a tube or tubular surface.
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Conclusion & Impact:In this work, we investigate tubular surface with Bishop frame in place of Frenet frame and afterwards give some characterizations about special curves lying on this surface
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bishop frame · Canal surface · tubular surface

Abstract

A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t) and it is parametrized through Frenet frame of the spine curve C(t). If the radius function r(t) = r is a constant, then the canal surface is called a tube or tubular surface. In this work, we investigate tubular surface with Bishop frame in place of Frenet frame and afterwards give some characterizations about special curves lying on this surface

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Cite This Article

DOGAN, F., YAYLI, Y. (2011). ON THE CURVATURES OF TUBULAR SURFACE WITH BISHOP FRAME. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 60 - Sayı: 1, 59–69. https://ajindex.com/articles/747439

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References (7)

  1. Bishop, R.L., There is more than one way to frame a curve, Amer. Math. Monthly, Volume 82, Issue 3 (1975), 246-251.
  2. Gray, A., Modern Diğerential Geometry of Curves and Surfaces with Mathematica, second ed., CrcPress, USA, 1999.
  3. Gross, A., Analyzing generalized tubes, Spie, 422-433, 1994.
  4. Kim, K.-J., Lee, I.-K., The perspective silhouette of a canal surface. Computer Graphics Forum, number 1, 15-22, 2003.
  5. Kühnel, W., Diğerential Geometry Curves-Surfaces-Manifolds, second ed., Friedr. Vieweg & Sohn Verlag, Wiesbaden, 2003.
  6. Maekawa, T., Patrikalakis, M.N., Sakkalis, T., Yu, G., Analysis and applications of pipe surfaces, Computer Aided Geometric Design 15 (1998), 437-458. O’neill, B., Elementary Diğerential Geometry, revised second ed. Academic Press, New York, 2006.
  7. Xu, Z., Feng, R. and Sun G.J., Analytic and algebraic properties of canal surfaces, Journal of Computational and Applied Mathematics 195 (2006), 220-228. Current address: Fatih DO ¼GAN, Yusuf YAYLI, Ankara University, Faculty of Sciences, Dept. of Mathematics, Ankara, TURKEY E-mail address: [email protected], [email protected] URL: http://communications.science.ankara.edu.tr