Get min and max distance withing a point cloud

Here we will learn how to find the maximal or minimal distance between two points in a cloud of points. To do so, we will use the pdist function available in the scipy.spatial.distance package.

This function computes the pairwise distances between observations in n-dimensional space; in order to find the longest or shortest distance, juste take the max or min.

import numpy as np
from scipy.spatial.distance import pdist

points = np.random.random((10,3)) #generate 100 points 

pairwise = pdist(points) # compute the pairwise distance between those points

#compute the maximal and minimal distance
print(f"maximal distance : {np.max(pairwise)}")
print(f"minimal distance : {np.min(pairwise)}")

maximal distance : 1.1393617436726384
minimal distance : 0.2382615513731064

The pdist function can that different metric for the distance computation. The default metrics are : * braycurtis * canberra * chebyshev * cityblock * correlation * cosine * dice * euclidean * hamming * jaccard * jensenshannon * kulsinski * mahalanobis * matching * minkowski * rogerstanimoto * russellrao * seuclidean * sokalmichener * sokalsneath * sqeuclidean * yule

You can also define your own distances with a lambda function

np.max(pdist(points, lambda u, v: np.sqrt(((u-v)**2).sum())))

1.1393617436726384

or with a classical function

def dfun(u, v):
    return np.sqrt(((u-v)**2).sum())


np.max(pdist(points,  dfun))

1.1393617436726384