Computing

, Volume 48, Issue 3–4, pp 363–371 | Cite as

Positive, monotone, andS-convexC1-interpolation on rectangular grids

Positive, monotone undS-konvexeC1-Interpolation auf Rechteckgittern

  • J. W. Schmidt
Article

Abstract

This paper is concerned with shape preservingC1-interpolation of data sets given on rectangular grids. Using special rational biquadratic splines, criteria are derived which are sufficient for the positivity, monotonicity, andS-convexity and which, in addition, are satisfied for sufficiently large rationality parameters.

AMS (MOS) Subject Classifications

65 D 07 41 A 15 41 A 63 

Key words

Shape preservingC1-interpolation special rational biquadratic splines construction by a search procedure 

Zusammenfassung

Diese Arbeit befaßt sich mit formerhaltenderC1-Interpolation von Daten auf Rechteckgittern. Bei Verwendung von speziellen rational-biquadratischen Splines werden Bedingungen hergeleitet, welche hinreichend für die Positität, Monotonie undS-Konvexität sind und welche sich darüber hinaus erfüllen lassen, sofern die Rationalitätsparameter hinreichend groß sind.

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References

  1. [1]
    Costantini, P.: Algorithms for shape-preserving interpolation. Math. Research52, 31–46. Berlin: Akademie-Verlag 1989.Google Scholar
  2. [2]
    Schmidt, J. W.: Rational biquadraticC 1-splines inS-convex interpolation. Computing47, 87–96 (1991).Google Scholar
  3. [3]
    Späth, H.: Zweidimensionale Spline-Interpolations-Algorithmen. München, Wien: Oldenbourg 1991.Google Scholar
  4. [4]
    Utreras, F. I.: Constrained surface construction. Topics in Multivariate Approximation, pp. 233–254. New York, London: Acadamy Press 1987.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • J. W. Schmidt
    • 1
  1. 1.Insitute of Numerical AnalysisTechnical University of DresdenDresdenFederal Republic of Germany

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