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Regle Yüzeylere Farklı Yaklaşımlar

Different Approaches To Ruled Surfaces

Journal Name:

  • Süleyman Demirel Üniversitesi Fen Dergisi

Publication Year:

  • 2012

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this study, surfaces are defined by using dual vectors and line transformations. A new approach is given for the transformation of parametrically surfaces. Dual curve and dual surface representational model for 3-dimensional geometric entities based on dual unit vectors are proposed. Some well-known new approaches like Blaschke approach of ruled surfaces are used. Moreover, geometric explanations of Bishop and Frenet are presented. Finally, an analytical comparison and the relation between Blaschke and Darboux approaches are represented showing the merits of our method.
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Abstract (Original Language): 
Bu çalışmada, yüzeyler dual vektörler ve doğru transformasyonları kullanılarak tanımlanmaktadır. Sonrasında parametrik yüzey transformasyonları için yeni bir yaklaşım verilmektedir. Üç boyutlu geometric öğeler için temeli dual birim vektörlere dayanan temsili dual eğri ve dual yüzey modeli ileri sürülmektedir. Burada bazı bilinen yeni yaklaşımlar kullanılmaktadır. Ayrıca, Bishop ve Frenet geometrik tanımları sunulmaktadır. Sonuç olarak, Blaschke ve Darboux yaklaşımları arasındaki analitik mukayese ve ilişki, metodumuzun doğruluğu gösterilerek belirtilmektedir
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  • 1
56-68
  • Turkish

REFERENCES

References: 

[I] Bottema O., Roth B., 1979. Theoretical kinematics, North-Holland Publishing Company, New York, p. 558.
[2] Gugenheimer H.W., 1956. Differential Geometry, McGraw-Hill, New York, pp. 162-169. [3] Hacısalihoglu H.H., 1983. Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen-
EdebiyatFakültesi Yayınları, p.
338
. [4] Hacısalihoglu H.H., 1972. On the pitch of a closed ruled surface, Mech. Mach. Theory 7: 291-305 [5] Hacısalihoglu H.H., 1972. On the pitch of a closed ruled surface, Mech. Mach. Theory 7: 291-305 [6] Liu H., Wang F., 2008. Mannheim partner curves in 3-space, Journal of Geometry, 88: 120-126. [7] Papageorgiou S.G., Aspragathos N., 2006. Transformation and Normal Vector Calculation of Parametrically Defined Surfaces Based on Dual Vectors and Screw Theory: Application to Phong's Shading Model, Computer Graphics Forum, 25: 183-195. [8] Phillip A., Nikos A., 2001. Computer graphics representation and transformation of geometric entities
using dual unit vectors and line transformations, Computers & Graphics, 25: 195-209. [9] Monterde J., Salkowski curves revisited: A family of curves with constant curvature and non-constant
torsion, preprint submitted to Elsevier Science. [10] Özkaldı S., İlarslan K., Yaylı Y., 2009. On Mannheim Partner Curve in Dual Space, Analele Stiintifice ale Universitatii Ovidius Constanta, 17 (2): 131-142.
[II] Rashad A.A.B., 2005. One-Parameter Closed Dual Spherical Motions and Holditch's Theorem Sitzungsber, Abt. II, 214: 27-41.
[12] Rashad A.A.B., 2003. On the Blaschke Approach of Ruled Surface, Tamkang Journal of Math, 34
(2): 107-116.
[13] Shifrin T., 2010. Differential Geometry: A first Course in Curves and Surfaces, University of Georgia, p.125.
[14] Yaylı Y., 2000. On the Motion of the Frenet Vectors and Spacelike Ruled Surfaces in the Minkowski
3-Space, Mathematical and Computational Applications, 5 (1): 49-55. [15] Yaylı Y., Saracoglu S., 2012. Ruled Surfaces and Dual Spherical Curves, Acta Universitatis
Apulensis,No. 30 (accepted) [16] Yaylı Y., Saracoglu S., 2010. Different Approaches to to Ruled Surfaces, XVI. Geometrical
Seminar, 20-25 September, Serbia. (presented) [17] Clifford W.K., 1873. On the Hypotheses which Underlie the Foundations of Geometery, Proc.
London Math. Soc., 4: 381.
Yusuf Yaylı e-mail: yayli@science.ankara.edu.tr

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