import numpy as np
from scipy import optimize

from matplotlib import pyplot as plt, cm, colors


def distance_from_center(c, x, y):
    '''
    Distance of each 2D points from the center (xc, yc)

    Parameters
    ----------
    c : array_like
        Coordinates of the center

    x,y : array_like
        Arrays with the x,y coordinates
    '''
    xc = c[0]
    yc = c[1]
    
    Ri = np.sqrt((x-xc)**2 + (y-yc)**2)
    
    return Ri - Ri.mean()


def least_square_circle(x, y):
    '''
    Least-square determination of the center of a circle

    Parameters
    ----------
    x,y : array_like
        Arrays with the x,y coordinates of the points on/inside the circle    
    '''
    
    # coordinates of the barycenter
    x_m = np.mean(x)
    y_m = np.mean(y)
    center_estimate = x_m, y_m
    
    center, ier = optimize.leastsq(distance_from_center, center_estimate, args=(x, y))

    # results
    xc, yc = center
    Ri     = np.sqrt((x-xc)**2 + (y-yc)**2)
    R      = Ri.mean()    
    residu = np.sum((Ri - R)**2)
    
    return xc, yc, R, residu


def plot_data_circle(x, y, xc, yc, R):
    f = plt.figure(0)
    plt.axis('equal')

    theta_fit = np.linspace(-np.pi, np.pi, 180)

    x_fit = xc + R*np.cos(theta_fit)
    y_fit = yc + R*np.sin(theta_fit)
    plt.plot(x_fit, y_fit, 'b-', label="fitted circle", lw=2)
    plt.plot([xc], [yc], 'bD', mec='y', mew=1)
    plt.xlabel('x')
    plt.ylabel('y')
    
    # plot data
    plt.plot(x, y, 'r-.', label='data', mew=1)

    plt.legend(loc='best', labelspacing=0.1)
    plt.grid()
    plt.title('Least Squares Circle')

import numpy as np
from scipy import optimize

from matplotlib import pyplot as plt, cm, colors


def distance_from_center(c, x, y):
    '''
    Distance of each 2D points from the center (xc, yc)

    Parameters
    ----------
    c : array_like
        Coordinates of the center

    x,y : array_like
        Arrays with the x,y coordinates
    '''
    xc = c[0]
    yc = c[1]
    
    Ri = np.sqrt((x-xc)**2 + (y-yc)**2)
    
    return Ri - Ri.mean()


def least_square_circle(x, y):
    '''
    Least-square determination of the center of a circle

    Parameters
    ----------
    x,y : array_like
        Arrays with the x,y coordinates of the points on/inside the circle    
    '''
    
    # coordinates of the barycenter
    x_m = np.mean(x)
    y_m = np.mean(y)
    center_estimate = x_m, y_m
    
    center, ier = optimize.leastsq(distance_from_center, center_estimate, args=(x, y))

    # results
    xc, yc = center
    Ri     = np.sqrt((x-xc)**2 + (y-yc)**2)
    R      = Ri.mean()    
    residu = np.sum((Ri - R)**2)
    
    return xc, yc, R, residu


def plot_data_circle(x, y, xc, yc, R):
    f = plt.figure(0)
    plt.axis('equal')

    theta_fit = np.linspace(-np.pi, np.pi, 180)

    x_fit = xc + R*np.cos(theta_fit)
    y_fit = yc + R*np.sin(theta_fit)
    plt.plot(x_fit, y_fit, 'b-', label="fitted circle", lw=2)
    plt.plot([xc], [yc], 'bD', mec='y', mew=1)
    plt.xlabel('x')
    plt.ylabel('y')
    
    # plot data
    plt.plot(x, y, 'r-.', label='data', mew=1)

    plt.legend(loc='best', labelspacing=0.1)
    plt.grid()
    plt.title('Least Squares Circle')

Distance of each 2D points from the center (xc, yc)      Parameters     ----------     c : array_like         Coordinates of the center      x,y : array_like         Arrays with the x,y coordinates Least-square determination of the center of a circle      Parameters     ----------     x,y : array_like         Arrays with the x,y coordinates of the points on/inside the circle # coordinates of the barycenter # results # plot data