Polytope manipulation example: Inner sphere approximation

This example shows how to manipulate polytopes using the pycapacity package. In particular, it shows how to calculate the inner sphere approximation of a polytope, using the Chebyshev ball algorithm.

from pycapacity.objects import Polytope # import polytope object
import numpy as np

# this seed is used to generate the same image
# as in the examples in the docs
np.random.seed(12345)

N = 10 # ten vertices
m = 3   # space dimension

points = np.array(np.random.rand(m,N))*2-1 # points

# create a polytope object
p = Polytope()
p.find_from_point_cloud(points)

# calculate the inner sphere approximation
s = p.chebyshev_ball()

# plotting the polytope
import matplotlib.pyplot as plt
from pycapacity.visual import * # pycapacity visualisation tools

fig = plt.figure(4)
# draw polytopes
plot_polytope(plot=fig,
    polytope=p,
    label='polytope',
    face_color="blue",
    edge_color='black',
    alpha=0.2)
plot_ellipsoid(plot=fig, ellipsoid=s, label='sphere')
plt.legend()
plt.show()

The output of the code is a visualisation of the the polytope and the inner sphere approximation.