import numpy as np
import matplotlib.pyplot as plt
import random

#Total number of points
N = 4

#xy is input, xy_o outputs
#Both are two-dimensional arrays and shapes,[[x1, y1], [x2, y2], [x3, y3], ...]
def circle_c(xy):
    #Since 3 points are used to find the center of the circle, the output is reduced by 2 points.
    xy_o_len = len(xy) - 2
    #Set the array for output.
    xy_o = np.zeros((xy_o_len, 2))
    #Find the center of the circle by 3 points in order from the front.
    for i in range(xy_o_len):
        #Auxiliary calculation
        x12 = xy[i+0, 0] + xy[i+1, 0]
        # x13 = xy[i+0, 0] + xy[i+2, 0]
        x23 = xy[i+1, 0] + xy[i+2, 0]
        x21 = xy[i+1, 0] - xy[i+0, 0]
        # x31 = xy[i+2, 0] - xy[i+0, 0]
        x32 = xy[i+2, 0] - xy[i+1, 0]
        y12 = xy[i+0, 1] + xy[i+1, 1]
        # y13 = xy[i+0, 1] + xy[i+2, 1]
        # y23 = xy[i+1, 1] + xy[i+2, 1]
        y21 = xy[i+1, 1] - xy[i+0, 1]
        y31 = xy[i+2, 1] - xy[i+0, 1]
        y32 = xy[i+2, 1] - xy[i+1, 1]
        #Calculate the center of the circle
        xy_o[i, 0] = (y31 - x21*x12/y21 + x32*x23/y32)*0.5 / (x32/y32 - x21/y21) #x component
        xy_o[i, 1] = -(xy_o[i, 0] - x12 * 0.5)*x21/y21 + y12*0.5 #y component
    return xy_o

x = np.arange(N)
y = np.random.rand(N)
xy = np.c_[x, y]

cxy = circle_c(xy)

f = plt.subplot()
f.plot(xy[:, 0], xy[:, 1], marker='.', markersize=20)
f.scatter(cxy[:, 0], cxy[:, 1], s=900, c="pink", alpha=0.5, linewidths="2", edgecolors="red")
f.set_aspect('equal')
plt.show()

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