I have a sample of points that trace a very clear geometrical shape. I am trying to recover the shape. I can do it with simple shapes, but I cannot do it for more complex ones.

Here is my attempt:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import ConvexHull

# Define the size of the squares and the number of points
square_size = 3
num_points = 200

# Generate random points inside the first and second squares
square1_points = np.random.uniform(0, square_size, (num_points, 2))
square2_points = np.random.uniform(square_size - 1, 2 * square_size - 1, (num_points, 2))

# Combine the points from both squares
combined_points = np.vstack((square1_points, square2_points))

# Create a DataFrame
df_points = pd.DataFrame(combined_points, columns=['x', 'y'])


fig, ax = plt.subplots(figsize=(7, 7))
ax.grid(False)

ax.scatter(df_points['x'], df_points['y'], color='red')

# Compute and plot the convex hull
hull = ConvexHull(combined_points)
for simplex in hull.simplices:
    ax.plot(combined_points[simplex, 0], combined_points[simplex, 1], 'b-', linewidth=4)

plt.show()

The output looks like this:

Clearly the blue contour does not follow the contour generated by the red dots. How can I fix it?

As you can see, I obtain the expected output for simple geometrical figures (square and circle):