An algorithm for circle fitting in $\mathbb{R}^3$

Ik Sung Kim

doi:10.4134/CKMS.c180328

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2019; 34(3): 1029-1047

Online first article July 8, 2019 Printed July 31, 2019

https://doi.org/10.4134/CKMS.c180328

An algorithm for circle fitting in $\mathbb{R}^3$

Ik Sung Kim

Korea Maritime and Ocean University

Abstract

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Abstract

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in $\mathbb{R}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function $Q(u)$ to a local minimum. Numerical examples are given.

Keywords: circle fitting, geometric distance, steepest descent

MSC numbers: Primary 65D18, 68U05