Geodesic
Notes on Infinitesimal Bending of a Toroid Formed by Revolution of a Polygonal Meridian
Journal for geometry and graphics, Tome 13 (2009) no. 2, pp. 177-186 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 53A05, 53C45, 68U05
Mots-clés : Infinitesimal bending, infinitesimal deformation, rigidity, toroid, polygon, OpenGL 
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     author = {L. S. Velimirovic and S. R. Rancic },
     title = {Notes on {Infinitesimal} {Bending} of a {Toroid} {Formed} by {Revolution} of a {Polygonal} {Meridian}},
     journal = {Journal for geometry and graphics},
     pages = {177--186},
     year = {2009},
     volume = {13},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2009_13_2_JGG_2009_13_2_a3/}
}
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L. S. Velimirovic; S. R. Rancic . Notes on Infinitesimal Bending of a Toroid Formed by Revolution of a Polygonal Meridian. Journal for geometry and graphics, Tome 13 (2009) no. 2, pp. 177-186. http://geodesic.mathdoc.fr/item/JGG_2009_13_2_JGG_2009_13_2_a3/