将弧的3d点拟合为圆(Python中的回归)

import numpy as np
from scipy.optimize import minimize

def circle_fit(points):
    def cost_function(center, points):
        return np.sum((np.linalg.norm(points - center, axis=1))**2)

    def jacobian(center, points):
        return 2 * np.sum(points - center, axis=0)

    def hessian(center, points):
        return 2 * np.ones((3, 3))

    center_init = np.mean(points, axis=0)
    center_fit = minimize(cost_function, center_init, args=(points,), method='Newton-CG', jac=jacobian, hess=hessian, tol=1e-9)

    radius = np.mean(np.linalg.norm(points - center_fit.x, axis=1))

    return center_fit.x, radius

points = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0]])
center, radius = circle_fit(points)

print("Center:", center)
print("Radius:", radius)