Volume 2, Issue 6, December 2014, Page: 204-208
Cyclical Surfaces Created by Helix on Torus
Tatiana Olejníková, Department of Applied Mathematics, Civil Engineering Faculty, Technical University of Košice, Košice, Slovakia
Received: Nov. 25, 2014;       Accepted: Dec. 6, 2014;       Published: Dec. 17, 2014
DOI: 10.11648/j.ajam.20140206.12      View  2501      Downloads  150
Abstract
This paper describes method of modelling of cyclical surfaces created by helix on the torus . The axis of the cyclical surface ´ is the helix s as a trajectory of movement of a point composed of two motions of rotation. The circle moves together with Frenet-Serret moving trihedron along the helix s and creates the cyclical surface ´. The paper describes modelling of cyclical surfaces created by moving circles about tangent, principal normal or binormal of the helix s. Paper describes also modelling of triangular grids on the torus. The grids are created by right-handed and left-handed cyclical helical surfaces and by cyclical surfaces with axis on meridians and circles on the torus.
Keywords
Torus, Helix, Cyclical Surface, Frenet-Serret Moving Trihedron, Transformation Matrice
To cite this article
Tatiana Olejníková, Cyclical Surfaces Created by Helix on Torus, American Journal of Applied Mathematics. Vol. 2, No. 6, 2014, pp. 204-208. doi: 10.11648/j.ajam.20140206.12
Reference
[1]
Budinský,B., Kepr,B.: Introduction to differential geometry with technical applications, SNTL-Publishers of technical literature, Praha, 1970
[2]
Granát, L., Sechovský, H.: Computer graphics. SNTL – Publishers of technical literature, Praha, 1980
[3]
Olejníková,T.: Two helical surfaces. In: Journal of civil engineering, Selected scientific papers, Slovakia, Košice, 2010, Vol. 5, Issue 1, ISSN 1336-9024, pp.7-16
[4]
Olejníková,T.: Composed Cyclical Surfaces. Transactions of the universities of Košice, 2007, Issue.3, ISSN 1335-2334, pp.54-60
[5]
Olejníková,T.: Rope of Cyclical Helical surfaces. In: Journal of civil engineering, Selected scientific papers, Košice, 2012, Vol. 7, Issue 2, ISSN 1336-9024, pp.23-32, DOI: 10.2478/v10299-012-0003-4
[6]
Olejníková,T.: Cyclical surfaces created by helix on general surface of revolution. In: Journal of civil engineering, Selected scientific papers, Košice, 2013, Vol. 8, Issue 2, ISSN 1336-9024, pp.33-40, DOI: 10.2478/sspjce-2013-0016
[7]
Olejníková,T.: Helical-one, two, three-revolutional cyclical surfaces. In: Global journal of science frontier research, Mathematics and decision sciences, India, 2013, Vol. 13. Issue 4, online ISSN 2249-4626, print ISSN 0975-5896, pp. 47-56
[8]
Študencová,Z., Zámožík,J., Szarková,D.: Skrut-Art. In: G-Slovak journal of geometry ang grafic, Bratislava 2012, Vol. 9, Issue 17, ISSN 1336-524X, pp. 41-52
[9]
Velichová D.: Klasifikácia dvojosových rotačných plôch. In: G - Slovak journal of geometry and grafic, Bratislava 2007, Vol. 4, Issue, ISSN 1336-524X,pp. 63-82
[10]
Velichová D.: Trajektórie zložených rotačných pohybov. In: G - Slovak journal of geometry and grafic, Bratislava 2006, Vol. 5, Issue 3, ISSN 1336-524X,pp. 47-64
[11]
Velichová D.: Two-axial Surfaces of Revolution. In: KoG, Scientific and Professional Information Journal of Croatian Society for Constructive Geometry and Computer Graphics, Zagreb 2005, N°9, Croatia, ISSN 1331-1611, pp. 11-20
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