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Visualization of Infinitesimal Bending of Curves

In: Approximation and Computation

Author

Listed:
  • Ljubica S. Velimirović

    (University of Niš)

  • Svetozar R. Rančić

    (University of Niš)

  • Milan Lj. Zlatanović

    (University of Niš)

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.

Suggested Citation

  • Ljubica S. Velimirović & Svetozar R. Rančić & Milan Lj. Zlatanović, 2010. "Visualization of Infinitesimal Bending of Curves," Springer Optimization and Its Applications, in: Walter Gautschi & Giuseppe Mastroianni & Themistocles M. Rassias (ed.), Approximation and Computation, pages 469-480, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-6594-3_32
    DOI: 10.1007/978-1-4419-6594-3_32
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