Modifica di Asse Trasversale Cerniera (sezione)

===='''Script Python: Errore di fitting'''====
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import numpy as np
from scipy.optimize import least_squares
import matplotlib.pyplot as plt

# Original data provided
original_center = np.array([11.56, 61.21])
radius = 26.38
angles = np.linspace(0, 2 * np.pi, 10)
points = np.array([
    original_center + radius * np.array([np.cos(angle), np.sin(angle)])
    for angle in angles
])

# Function to add noise to the points
def add_noise_to_points(points, noise_level):
    noisy_points = points + np.random.normal(0, noise_level, points.shape)
    return noisy_points

# Add noise to the points
noise_level = 0.1  # Reduced noise level
noisy_points = add_noise_to_points(points, noise_level)

# Residual function for non-linear fitting
def residuals(c, points):
    xc, yc, r = c
    Ri = np.sqrt((points[:, 0] - xc)**2 + (points[:, 1] - yc)**2)
    return Ri - r

# Calculate the center and radius using noisy points
x_m = np.mean(noisy_points[:, 0])
y_m = np.mean(noisy_points[:, 1])
r_m = np.mean(np.sqrt((noisy_points[:, 0] - x_m)**2 + (noisy_points[:, 1] - y_m)**2))
initial_guess = [x_m, y_m, r_m]

# Fitting the circle using the Levenberg-Marquardt method
result = least_squares(residuals, initial_guess, args=(noisy_points,))
xc, yc, r = result.x

calculated_center = np.array([xc, yc])

# Calculate the error between the centers
error = np.linalg.norm(calculated_center - original_center)
error_mm = error * 10  # Convert to millimeters (assuming the points might be in centimeters)

# Verify the calculated center
print(f'Calculated Center: {calculated_center}')
print(f'Radius: {r:.4f}')
print(f'Error: {error_mm:.4f} mm')

# Visualization of the fitted circle
theta = np.linspace(0, 2 * np.pi, 100)
x_fit = calculated_center[0] + r * np.cos(theta)
y_fit = calculated_center[1] + r * np.sin(theta)

plt.figure(figsize=(8, 8))
plt.scatter(points[:, 0], points[:, 1], color='b', label='Original Points')
plt.scatter(noisy_points[:, 0], noisy_points[:, 1], color='r', label='Noisy Points')
plt.scatter(original_center[0], original_center[1], color='r', marker='x', s=100, label='Original Center')
plt.plot(x_fit, y_fit, 'g--', label='Fitted Circle')
plt.scatter(calculated_center[0], calculated_center[1], color='g', label='Calculated Center')
plt.xlabel('X')
plt.ylabel('Y')
plt.legend()
plt.title('Circle Fitting with Noisy Points')
plt.grid(True)
plt.show()

</syntaxhighlight>