python之拟合圆心及半径

目录

1、公式推导

2、代码实现

1、公式推导

2、代码实现

import matplotlib.pyplot as plt
import numpy as np
def Show_Fig(X,Y,x, y, r):
    theta = np.arange(0, 2 * np.pi, 0.01)
    x = x + r * np.cos(theta)
    y = y + r * np.sin(theta)
    fig = plt.figure()
    axes = fig.add_subplot(111)
    axes.plot(x, y)
    axes.plot(X, Y,"r*")
    axes.axis('equal')
    plt.show()


def Fit_Circle(x=None, y=None):
    C = []
    A = []

    for i in range(len(x)):
        A.append([x[i], y[i], 1])
        C.append(np.square(x[i]) + np.square(y[i]))

    A = np.mat(A)
    B = np.dot(np.dot(np.linalg.inv(np.dot(A.T, A)), A.T), C)
    B = np.array(B, dtype='float32').flatten()
    return B[0]/2, B[1]/2, np.sqrt(B[2]+np.square(B[0])/4 + np.square(B[1])/4)


if __name__ == '__main__':
    # 定义圆的参数
    center_x = 1
    center_y = 2
    radius = 5

    # 生成圆上的点
    theta = np.linspace(0, 2 * np.pi, 100)  # 生成一个角度范围
    x = center_x + radius * np.cos(theta)  # x坐标
    y = center_y + radius * np.sin(theta)  # y坐标

    # 添加噪声
    noise = np.random.normal(0, 0.05, size=(100,))  # 生成一个标准正态分布的噪声
    X = x + noise
    Y = y + noise

    fitcenter_x, fitcenter_y, fitradius = Fit_Circle(x=X, y=Y)
    print(f"拟合得到的圆心是：({fitcenter_x}, {fitcenter_y}), 半径是：{fitradius}")
    Show_Fig(X,Y,fitcenter_x, fitcenter_y, fitradius)

​拟合得到的圆心是：(1.0052670240402222, 2.0036354064941406), 半径是：5.004283869935406