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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.11 No.1

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An Algorithm for Fitting of Spheres

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2004, v.11 no.1, pp.37-49
Kim, Ik-Sung
Kim,, I. (2004). An Algorithm for Fitting of Spheres. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 11(1), 37-49.

Abstract

We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

keywords
Orthogonal distance, fitting of spheres, least squares

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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