Plot the convex hull around a set of points as a shaded polygon.

hull_plot.py

# -*- coding: utf-8 -*-
"""
Plot the convex hull around a set of points as a
shaded polygon.

@author: Nicolas Guarin Zapata and Kaiwen
@date: February 6, 2023
"""
import numpy as np
from scipy.spatial import ConvexHull
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon

m = 30  # number of points
points = np.random.rand(m, 2)   # m random points in 2-D
plt.plot(points[:,0], points[:,1], 'o')
cent = np.mean(points, 0)

# ConvexHull won't work when m < dimension + 1
if m < 2 + 1:  # where 2 is dimension
    # augment the points by sampling around existing points
    # so that ConvexHull works again
    r_eps = 0.005  # in what radius to sample
    n = 50  # how many additional points to sample
    points = np.concatenate([p + r_eps * np.random.randn(n, 2) for p in points])
hull = ConvexHull(points)
pts = points[hull.vertices] # in 2-dimension context, guaranteed in counterclockwise

# Plot the polygon
k = 1.1  # how large is the polygon in terms of the size of the hull
color = 'green'
poly = Polygon(k*(pts - cent) + cent,
               facecolor=color, alpha=0.2, capstyle='round')
plt.gca().add_patch(poly)
plt.savefig('convex.png')
# Above codes (lines 34, 35) can also be written in object-oriented interface as:
#fig, ax = plt.subplots()
#ax.add_patch(poly)
#fig.savefig('convex.png')
#plt.close(fig)