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Cyclical Surfaces Created by Helix on Torus
American Journal of Applied Mathematics
Volume 2, Issue 6, December 2014, Pages: 204-208
Received: Nov. 25, 2014; Accepted: Dec. 6, 2014; Published: Dec. 17, 2014
Author
Tatiana Olejníková, Department of Applied Mathematics, Civil Engineering Faculty, Technical University of Košice, Košice, Slovakia
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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.
Keywords
Torus, Helix, Cyclical Surface, Frenet-Serret Moving Trihedron, Transformation Matrice
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
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