File:Regression circulaire coope arc de cercle.svg

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Description
English: Circle fitting, the points describing only an arc. Kåsa and Coope linear algorithm (method of the algebraic distance). The real values are:
  • C(1 ; 1);
  • r = 4.
Created with Scilab, modified with Inkscape.
Français : Régression circulaire sur des points ne décrivant qu'un arc. Algorithme linéaire de Kåsa et Coope (méthode de la distance algébrique). Les valeurs réelles sont :
  • C(1 ; 1) ;
  • r = 4.
Créé avec Scilab, modifié avec Inkscape.
Date
Source Own work
Author Cdang (Christophe Dang Ngoc Chan)

Scilab source

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Crée les données et les enregistre dans le fichier arc_cercle_bruite.txt. 

// ********** // Initialisation // **********  clear; chdir('monchemin/');  // ********** // Constantes // **********  // paramètres de l'arc de cercle centre=[1;1]; rayon = 4; angle = %pi/3:0.1:2*%pi/3;  // paramètres du bruit var = 0.05;  // ********** // Programme principal // **********  // génération des données ligne_rayon_bruite = rayon + var*rand(angle,'norm'); foo = [cos(angle);sin(angle)].* ...     [ligne_rayon_bruite;ligne_rayon_bruite]; arc_cercle_bruite(1,:) = centre(1) + foo(1,:); arc_cercle_bruite(2,:) = centre(2) + foo(2,:);  clf plot(arc_cercle_bruite(1,:), arc_cercle_bruite(2,:), '+') write('arc_cercle_bruite.txt', arc_cercle_bruite')

Lit les données de arc_cercle_bruite.txt et effectue la régression circulaire. 

// ********** // Initialisation // **********   clear; chdir('monchemin/')   // ********** // 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);     C = 0.5*xyetoile;     r = sqrt(zetoile + C(1)^2 + C(2)^2);     // A'\d' si l'on ne s'intéresse pas à l'écart     R = sigma; endfunction   // ********** // programme principal // **********   // lecture des données   // Xdef, Ydef : vecteurs ligne donnees = read('arc_cercle_bruite.txt', -1, 2)'; Xdef = donnees(1,:); Ydef = donnees(2,:);   // regression [centre, rayon, ecart] = regression_circulaire(Xdef, Ydef)   // tracé   clf; // points plot2d(Xdef, Ydef, style = -1) //, frameflag=4) isoview(-2, 4, 1, 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)

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7 December 2012

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current15:51, 7 December 2012Thumbnail for version as of 15:51, 7 December 2012442 × 363 (20 KB)Cdang{{Information |Description ={{en|1=Circle fitting, the points describing only a bow. Coope linear algorithm. The real values are: * C(1 ; 1); * ''r'' = 4. Created with Scilab, modified with Inkscape.}} {{fr|1=Régression circulaire sur des points d ...

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