File:Regression circulaire coope points gruntz.svg
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Summary[edit]
| Description |
English: Circle fitting, using Kåsa and Coope linear method (method of the algebraic distance), with the data set proposed by D. Gruntz. Created with Scilab, modified by Inkscape.
Français : Régression circulaire par la méthode linéaire de Kåsa et Coope (méthode de la distance algébrique), en utilisant le jeu de données proposé par Gruntz. Créé avec Scilab, modifié avec Inkscape. |
| Date | |
| Source |
Own work Coope, Ian D., Circle fitting by Linear and Nonlinear Least Squares, in "Journal of Optimization Theory and Applications", vol. 76, No. 2, pp. 381-388, february 1993 Gruntz, D., Finding the Best Fit Circle, in "The MathWorks Newsletter", Vol. 1, p. 5, 1990 |
| Author | Cdang (Christophe Dang Ngoc Chan) |
Parameters of the circle:
- xc = 3.06;
- yc = 0.744;
- r = 4.11.
Scilab source
 |
This media was created with Scilab, a free open-source software. Here is a listing of the Scilab source used to create this file. |
// Initialisation
clear;
// données (D. Gruntz)
X0 = [0.7, 3.3, 5.6, 7.5, 6.4, 4.4, 0.3, -1.1];
Y0 = [4.0, 4.7, 4.0, 1.3, -1.1, -3.0, -2.5, 1.3];
// fonctions
// régression circulaire linéaire
function [C, r, R]=regression_circulaire(X, Y)
// X, Y : points expérimentaux (vecteurs ligne)
// C : coordonnées du centre du cercle (vecteur)
// r : rayon du cercle (scalaire)
A = [X ; Y];
d = X.^2 + Y.^2;
// xetoile = 2*xcentre
// yetoile = 2*ycentre
// zetoile = r^2 - (xcentre^2 + ycentre^2)
[xyetoile, zetoile, sigma] = reglin(A, d');
// A'\d' si l'on ne s'intéresse pas à l'écart
C = 0.5*xyetoile;
r = sqrt(zetoile + C(1)^2 + C(2)^2);
R = sigma;
endfunction
// **********
// programme principal
// **********
// lecture des données
// Xdef, Ydef : vecteurs ligne
Xdef = X0;
Ydef = Y0;
// regression
[centre, rayon, ecart] = regression_circulaire(Xdef, Ydef)
// tracé
clf;
// points
plot2d(Xdef, Ydef, style = -1) //, frameflag=4)
isoview(-2, 8, -4, 6);
xstring(-1.5, 5.5, 'C('+string(centre(1))+' ; '+string(centre(2))+') ; r = '+string(rayon))
// modèle
plot(centre(1), centre(2), 'r+')
diametre = 2*rayon;
xarc(centre(1) - rayon, centre(2) + rayon,...
diametre, diametre,...
0, 360*64)
a = get('hdl'); // ellipse
a.foreground = 5; // couleur
print(%io(2), centre)
print(%io(2), rayon)
print(%io(2), ecart)
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:07, 7 December 2012 | | 349 × 346 (21 KB) | Cdang (talk | contribs) | {{Information |Description ={{en|1=Circle fitting, using Coope linear method, with the data set proposed by D. Gruntz. Created with Scilab, modified by Inkscape.}} {{fr|1=Régression circulaire par la méthode linéaire de Coope, en utilisant le jeu... |
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