How to find all neighbors of a given point in a delaunay triangulation using scipy.spatial.Delaunay?

Question

I have been searching for an answer to this question but cannot find anything useful.

I am working with the python scientific computing stack (scipy,numpy,matplotlib

Answer 1

The methods described above cycle through all the simplices, which could take very long, in case there's a large number of points. A better way might be to use Delaunay.vertex_neighbor_vertices, which already contains all the information about the neighbors. Unfortunately, extracting the information

def find_neighbors(pindex, triang):

    return triang.vertex_neighbor_vertices[1][triang.vertex_neighbor_vertices[0][pindex]:triang.vertex_neighbor_vertices[0][pindex+1]]

The following code demonstrates how to get the indices of some vertex (number 17, in this example):

import scipy.spatial
import numpy
import pylab

x_list = numpy.random.random(200)
y_list = numpy.random.random(200)

tri = scipy.spatial.Delaunay(numpy.array([[x,y] for x,y in zip(x_list, y_list)]))

pindex = 17

neighbor_indices = find_neighbors(pindex,tri)

pylab.plot(x_list, y_list, 'b.')
pylab.plot(x_list[pindex], y_list[pindex], 'dg')
pylab.plot([x_list[i] for i in neighbor_indices],
           [y_list[i] for i in neighbor_indices], 'ro')    

pylab.show()