Cyclical Surfaces Created by Helix on Torus

Tatiana Olejníková

doi:doi:10.11648/j.ajam.20140206.12

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Cyclical Surfaces Created by Helix on Torus

Tatiana Olejníková

Published in American Journal of Applied Mathematics (Volume 2, Issue 6)

Received: 25 November 2014 Accepted: 6 December 2014 Published: 17 December 2014

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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.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 6)
DOI	10.11648/j.ajam.20140206.12
Page(s)	204-208
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Torus, Helix, Cyclical Surface, Frenet-Serret Moving Trihedron, Transformation Matrice

References

[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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Tatiana Olejníková. (2014). Cyclical Surfaces Created by Helix on Torus. American Journal of Applied Mathematics, 2(6), 204-208. https://doi.org/10.11648/j.ajam.20140206.12

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ACS Style

Tatiana Olejníková. Cyclical Surfaces Created by Helix on Torus. Am. J. Appl. Math. 2014, 2(6), 204-208. doi: 10.11648/j.ajam.20140206.12

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AMA Style

Tatiana Olejníková. Cyclical Surfaces Created by Helix on Torus. Am J Appl Math. 2014;2(6):204-208. doi: 10.11648/j.ajam.20140206.12

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@article{10.11648/j.ajam.20140206.12,
  author = {Tatiana Olejníková},
  title = {Cyclical Surfaces Created by Helix on Torus},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {204-208},
  doi = {10.11648/j.ajam.20140206.12},
  url = {https://doi.org/10.11648/j.ajam.20140206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.12},
  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.},
 year = {2014}
}

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TY  - JOUR
T1  - Cyclical Surfaces Created by Helix on Torus
AU  - Tatiana Olejníková
Y1  - 2014/12/17
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140206.12
DO  - 10.11648/j.ajam.20140206.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 204
EP  - 208
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.12
AB  - 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.
VL  - 2
IS  - 6
ER  -

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Author Information

Tatiana Olejníková

Department of Applied Mathematics, Civil Engineering Faculty, Technical University of Ko?ice, Ko?ice, Slovakia

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APA Style

Tatiana Olejníková. (2014). Cyclical Surfaces Created by Helix on Torus. American Journal of Applied Mathematics, 2(6), 204-208. https://doi.org/10.11648/j.ajam.20140206.12

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ACS Style

Tatiana Olejníková. Cyclical Surfaces Created by Helix on Torus. Am. J. Appl. Math. 2014, 2(6), 204-208. doi: 10.11648/j.ajam.20140206.12

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AMA Style

Tatiana Olejníková. Cyclical Surfaces Created by Helix on Torus. Am J Appl Math. 2014;2(6):204-208. doi: 10.11648/j.ajam.20140206.12

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@article{10.11648/j.ajam.20140206.12,
  author = {Tatiana Olejníková},
  title = {Cyclical Surfaces Created by Helix on Torus},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {204-208},
  doi = {10.11648/j.ajam.20140206.12},
  url = {https://doi.org/10.11648/j.ajam.20140206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140206.12},
  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.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Cyclical Surfaces Created by Helix on Torus
AU  - Tatiana Olejníková
Y1  - 2014/12/17
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140206.12
DO  - 10.11648/j.ajam.20140206.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 204
EP  - 208
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140206.12
AB  - 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.
VL  - 2
IS  - 6
ER  -

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