Estimating aspect ratio of a convex hull

Question

What would be the best way to approximate the aspect ratio of a convex hull in Python? I have already tried doing this by fitting the vertices of the convex hull with an ellipse and taking the ratio of the semi- and major-axis. The results are not satisfactory though, so I'm now looking into deriving the aspect ratio directly from the convex hull. Any ideas or solutions would be much appreciated.

Cheers

Answer 1

Typically, you'd find the eigenvectors of the covariance matrix of the point cloud. The aspect ratio is the ratio of the largest to smallest eigenvalues.

As an example for a bunch of random points (you'd just apply the same thing to your convex hull, only using the vertices):

import matplotlib.pyplot as plt
import numpy as np

# Random data
num = 100
xy = np.random.random((2,num)) + 0.01 * np.arange(num)

eigvals, eigvecs = np.linalg.eig(np.cov(xy))

fig, (ax1, ax2) = plt.subplots(nrows=2)
x,y = xy
center = xy.mean(axis=-1)
for ax in [ax1, ax2]:
    ax.plot(x,y, 'ro')
    ax.axis('equal')

for val, vec in zip(eigvals, eigvecs.T):
    val *= 2
    x,y = np.vstack((center + val * vec, center, center - val * vec)).T
    ax2.plot(x,y, 'b-', lw=3)

plt.show()