Journal for Geometry and Graphics 13 (2009), No. 2, 177--186
Copyright Heldermann Verlag 2009
Notes on Infinitesimal Bending of a Toroid Formed by Revolution of a Polygonal Meridian
Ljubica S. Velimirovic
Faculty of Sciences and Mathematics, University of Nis, Visegradska 33, 18000 Nis, Serbia
vljubica@pmf.ni.ac.rs
Svetozar R. Rancic
Faculty of Sciences and Mathematics, University of Nis, Visegradska 33, 18000 Nis, Serbia
rancic@pmf.ni.ac.rs
Deformation theory focuses on the examination of rigidity conditions of surfaces. In this paper we present our tools for the examination of torus-like surfaces with a polygonal meridian in the Euclidean 3-space E3. Based on Cohn-Vossen's method we check infinitesimal bendings of the generated surfaces. Starting from given nodes of a meridian we perform the analysis and display the obtained toroids and their deformed shapes. We use C++ and OpenGL to carry out all underlaying calculations and the 3D model visualization.
Keywords: Infinitesimal bending, infinitesimal deformation, rigidity, toroid, polygon, OpenGL.
MSC: 53A05; 53C45, 68U05
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