Original scientific paper

Rectilinearity Determination of a Planar Point Set

Miljenko Lapaine orcid.org/0000-0002-9463-2329 ; Faculty of Geodesy, University of Zagreb, Zagreb, Croatia
Martina Triplat Horvat orcid.org/0000-0002-8304-7474 ; Faculty of Geodesy, University of Zagreb, Zagreb, Croatia

Abstract

This paper analyses the problem of determining parameters of a straight line by the method of Euclidean distances that best fit the given set of points in a plane. It is shown that the problem is not linear. However, the method of linearization, which is frequently applied in geodesy, is not applied. Instead, extreme values of the functions of one variable are found and finally quadratic equation is solved exactly. Furthermore, sufficient conditions for the extreme of the function are explored and it is shown that the problem generally has two solutions, one minimum and one maximum. To illustrate the described method, derived formulas were applied to determine the equation of the straight line which, by the Euclidean distance method, best fits the point set which represents a meridian drawn in an unknown map projection of J. R. Bošković’s and Ch. Maire’s map Nuova carta geografica dello Stato Ecclesiastico published in 1755.

Keywords

alignment; straight line fitting; Euclidean distance

Hrčak ID:

123585

URI

https://hrcak.srce.hr/123585

Publication date:

25.6.2014.

Article data in other languages: croatian

Visits: 2.142 *