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Least-squares fitting by circles

Die Methode der kleinsten Quadrate bei Kreisen

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Abstract

In reflectometry and in the aircraft industry the problem of fitting data points by a circle is relevant. In contrast with other authors we realize a very special iterative method to determine such a circle. Former approximations for the parameters are used as starting values and are improved. Numerical examples are given.

Zusammenfassung

Beim Messen von Neigungswinkeln von reflektierten Strahlen und in der Flugzeugindustrie tritt das Problem auf, gegebene Punkte mit einem Kreis anzupassen. Im Gegensatz zu anderen Autoren realisieren wir ein sehr spezielles Iterationsverfahren zur Bestimmung eines solchen Kreises. Frühere Näherungswerte für die Parameter werden als Startwerte benutzt und verbessert. Numerische Beispiele werden angegeben.

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References

  1. Delonge, P.: Computer optimization of Deschamps' method and error cancellation in reflectometry. Proc. IMEKO-Symp. Microwave Measurement, pp. 117–123. Budapest 1972.

  2. Gander, W., Golub, G. H., Strebel, R.: Least-squares fitting of circles and ellipses. BIT34, 558–578 (1994).

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  3. Kasa, I.: A circle fitting procedure and its error analysis. IEEE Trans. Instr. Measurement25, 8–14 (1976).

    Google Scholar 

  4. Liming, R. A.: Mathematics for computer graphics. Fallbrook: Aero Publishers 1979.

    Google Scholar 

  5. Späth, H.: Orthogonal squared distance fitting with parabolas. In: Proceedings of the IMACSGAMM International Symposium on Numerical Methods and Error-Bounds, University of Oldenburg, July 1995. (Alefeld, G., Herzberger, J., eds.). Berlin: Akademie-Verlag 1996.

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  6. Späth, H.: Least squares fitting of ellipses and hyperbolas. To be published in Computational Statistics, Physica-Verlag.

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Authors and Affiliations

  1. Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 25 03, 26111, Oldenburg, D-Federal Republic of Germany

    H. Späth

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  1. H. Späth
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Späth, H. Least-squares fitting by circles. Computing 57, 179–185 (1996). https://doi.org/10.1007/BF02276879

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  • DOI: https://doi.org/10.1007/BF02276879

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