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Visualization of Infinitesimal Bending of Curves

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Approximation and Computation

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 42))

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Abstract

Infinitesimal bending of curves in E 3 is considered and an infinitesimal bending field is determined and discussed. A special case of deformation of a plane curve staying plane under infinitesimal bending is analyzed. Also, the variations of the curvature and the torsion are obtained. Infinitesimal bending of an ellipse and Cassini curve are discussed and presented graphically. We present our tool InfBend aimed at infinitesimal deformation and visualization of curves and surfaces. It is written in C++ and uses OpenGL for modelling three-dimensional curves and surfaces.

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Authors and Affiliations

  1. Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Ljubica S. Velimirović, Svetozar R. Rančić & Milan Lj. Zlatanović

Authors
  1. Ljubica S. Velimirović
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  2. Svetozar R. Rančić
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  3. Milan Lj. Zlatanović
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Corresponding author

Correspondence to Ljubica S. Velimirović .

Editor information

Editors and Affiliations

  1. Dept. Computer Science, Purdue University, N. University Street 305, West Lafayette, 47907-2107, Indiana, USA

    Walter Gautschi

  2. Dipto. Matematica, Università Basilicata, Contrada Macchia Romana, Potenza, 85100, Italy

    Giuseppe Mastroianni

  3. Zagoras Street 4, Athens, 151 25, Greece

    Themistocles M. Rassias

Additional information

Dedicated to Professor Gradimir V. Milovanović on the occasion of his 60th birthday

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Velimirović, L.S., Rančić, S.R., Zlatanović, M.L. (2010). Visualization of Infinitesimal Bending of Curves. In: Gautschi, W., Mastroianni, G., Rassias, T. (eds) Approximation and Computation. Springer Optimization and Its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6594-3_32

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