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Interpolation of Curvature and Torsion Using Expo-Rational B-Splines

  • Lubomir T. Dechevsky
  • Georgi H. Georgiev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

Abstract

Expo-rational B-splines (ERBS) are well adapted for Hermite interpolation of any prescribed order [1]. This property of ERBS can be used to interpolate and approximate a variety of differential geometric structures of smooth manifolds, such as length, curvature, torsion, area, volume, etc. In this paper we solve the simplest of these problems: finding the explicit formulae for ERBS-based interpolation of curvature and torsion of unit-speed 3D-space curves and the order of the rate of approximation it provides.

Keywords

Smooth Manifold Interpolation Formula Natural Parametrization Hermite Interpolation Regular Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Dechevsky, L.T., Lakså, A., Bang, B.: Expo-Rational B-splines. International Journal of Pure and Applied Mathematics 27(3), 319–369 (2006)MathSciNetzbMATHGoogle Scholar
  2. 2.
    do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice-Hall (1976)Google Scholar
  3. 3.
    Gray, A.: Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd edn. CRC Press (1998)Google Scholar
  4. 4.
    Lakså, A., Bang, B., Dechevsky, L.T.: Exploring expo-rational B-splines for curves and surfaces. In: Dæhlen, M., Mørken, K., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces: Tromsø 2004, pp. 253–262. Nashboro Press, Brentwood TN (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lubomir T. Dechevsky
    • 1
  • Georgi H. Georgiev
    • 2
  1. 1.R&D Group for Mathematical Modelling, Numerical Simulation & Computer Visualization, Faculty of TechnologyNarvik University CollegeNarvikNorway
  2. 2.Faculty of Mathematics and InformaticsKonstantin Preslavsky UniversityShumenBulgaria

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