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.
The research of Dechevsky and Georgiev was partially supported, respectively, by the 2010 and 2011 Annual Research Grant of the Priority R&D Group for Mathematical Modeling, Numerical Simulation and Computer Visualization at Narvik University College, and by the Bulgarian Ministry of Education, Youth and Science under EEA Grant No. D02-780/20.10.2010.
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References
Dechevsky, L.T., Lakså, A., Bang, B.: Expo-Rational B-splines. International Journal of Pure and Applied Mathematics 27(3), 319–369 (2006)
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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)
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Dechevsky, L.T., Georgiev, G.H. (2012). Interpolation of Curvature and Torsion Using Expo-Rational B-Splines. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_46
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DOI: https://doi.org/10.1007/978-3-642-29843-1_46
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