A Study on Generalized Tubes

Abstract

In this paper, we consider generalized tubes, which we refer to in the paper as hereafter GTs, according to q-frame in Euclidean space $E^{3}$. First, we give a parametric representation of directional generalized tubes (DGTs). Since GT class is divided by two important subclasses, we investigate geometric properties of these two classes with respect to the q-frame.

Keywords

• Adapted frame,Frenet frame,Generalized tubes.

Kaynakça

1. [1] L. R. Bishop, There ’s more than one way to frame a curve, Amer Math Monthly, 82(3)(1975), 246-251.
2. [2] P. A. Blaga, On tubular surfaces in computer graphics, Studia univ Babes-Bolyaı, Informatica, 2 (2005), 2005.
3. [3] J. Bloomenthal, Calculation of reference frames along a space curve, Graphics gems, Academic Press Professional, Inc., San Diego, CA, 1990.
4. [4] M. Dede, C. Ekici, H. Tozak, Directional tubular surfaces, Int J Algebra, 9 (2005), 527 - 535.
5. [5] M. Dede, C. Ekici and A. Görgülü, Directional q-frame along a space curve, IJARCSSE, 5(12) (2015), 775-780.
6. [6] M. P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, New Jersey, 1976.
7. [7] C. Ekici, M. Dede and H. Tozak, Timelike directional tubular surfaces, Int. J. Mathematical Anal., 8(5): 1-11, 2017.
8. [8] A.D. Gross, Analyzing generalized tubes, Proc. SPIE 2354, Intelligent Robots and Computer Vision XIII: 3D Vision, Product Inspection, and Active Vision, 1994.

9. [9] A. D. Gross and T. E. Boult, Recovery of straight homogeneous generalizedcylinders using contour and intensity information, in Proc. of the 1989 SPIE Proc. On Visual Communications and Image Processing IV, 1661-1669, 1989.
10. [10] R. Horaud and J.M. Brady, On the geometric interpretation of image contours, in Proc. First Int’l Conference on Computer Vision, London, U.K., 1987.
11. [11] J. M. LaVest, R. Glachet, M. Dhome and J. T. LaPreste, Modeling solids of revolution by monocular vision, in Proceedings of the 1991 Computer Vision and Pattern Recognition Conference, pages 690-691, Lahaina, Maui, 1991.
12. [12] T. Maekawa, N.M. Patrikalakis, T. Sakkalis, and Yu, G., Analysis and applications of pipe surfaces, Comput Aided Geom Des, 15(1998), 437-458.
13. [13] M. Richetin, M. Dhome and J.T. LaPreste, Inverse perspective transform from zero-curvature curve points application to the localization of some generalized cylinders, in Proceedings of the 1989 Computer Vision and Pattern Recognition Conference, 1989.
14. [14] F. Ulupinar and R. Nevatia, Using symmetries for analysis of shape from contour, in Proceedings of the Second International Computer Vision Conference, 414-426, 1988.
15. [15] F. Ulupinar and R. Nevatia, , Shape from Contour: Straight Homogeneous Generalized Cylinders, in Proceedings of the Third International Computer Vision Conference, 582-586, 1990
16. [16] W. Wang and B. Joe, Robust computation of the rotation minimizing frame for sweep surface modelling, Comput Aided Des, 29 (1997), 379-391.
17. [17] Z. Xu, R. Feng and J. Sun, Analytic and Algebraic Properties of Canal Surfaces, J Comput Appl Math, 195(2006), 220-228.