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)


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.


Smooth Manifold Interpolation Formula Natural Parametrization Hermite Interpolation Regular Curve 
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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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