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Spatial shape‐preserving interpolation using ν‐splines

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Abstract

We present a global iterative algorithm for constructing spatial G 2‐continuous interpolating ν‐splines, which preserve the shape of the polygonal line that interpolates the given points. Furthermore, the algorithm can handle data exhibiting two kinds of degeneracy, namely, coplanar quadruples and collinear triplets of points. The convergence of the algorithm stems from the asymptotic properties of the curvature, torsion and Frénet frame of ν‐splines for large values of the tension parameters, which are thoroughly investigated and presented. The performance of our approach is tested on two data sets, one of synthetic nature and the other of industrial interest.

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References

  1. B.D. Bojanov, H.A. Hakopian and A.A. Sahakian, Spline Functions and Multivariate Interpolations(Kluwer, Boston, 1993).

    MATH  Google Scholar 

  2. W.K. Dziadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials(Nauka, Moscow, 1977) (in Russian).

    Google Scholar 

  3. B.Z. Kacewicz and M.A. Kowalski, Approximating linear functionals on unitary spaces in the presence of bounded data errors with applications to signal recovery, J. Adapt. Control Signal Processing 9 (1995) 19-31.

    MathSciNet  MATH  Google Scholar 

  4. B.Z. Kacewicz and M.A. Kowalski, Recovering linear operators from inaccurate data, J. Complexity 11 (1995) 227-239.

    Article  MathSciNet  MATH  Google Scholar 

  5. C.A. Micchelli and T.J. Rivlin, A survey of optimal recovery, in: Optimal Estimation in Approximation Theory, eds. C.A. Micchelli and T.J. Rivlin (1977).

  6. E. Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis, Lecture Notes in Mathematics, Vol. 1349 (Springer, Berlin/Heidelberg, 1988).

    MATH  Google Scholar 

  7. L. Plaskota, Noisy Information and Computational Complexity(Cambridge Univ. Press, Cambridge, 1996).

    MATH  Google Scholar 

  8. J.F. Traub and H. Wózniakowski, A General Theory of Optimal Algorithms(Academic Press, New York, 1980).

    MATH  Google Scholar 

  9. A.A. Žensykbaev, Approximation of differentiable periodic functions by splines on equidistant partition, Mat. Zametki 6 (1973) 807-816 (in Russian).

    Google Scholar 

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Authors
  1. M.I. Karavelas
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  2. P.D. Kaklis
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Karavelas, M., Kaklis, P. Spatial shape‐preserving interpolation using ν‐splines. Numerical Algorithms 23, 217–250 (2000). https://doi.org/10.1023/A:1019156202082

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  • DOI: https://doi.org/10.1023/A:1019156202082

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