Getting the circumcentres from a delaunay triangulation generated using matplotlib

Question

If I use matplotlib to generate a delaunay triangulation for a group of points, what is the most appropraite way of getting the circumcentres of the triangles that have been geenrated? I haven't yet managed to find an obvious method in the Triangulation library to do this.

Answer 1

You should be able to calculate it using matplotlib.delaunay.triangulate.Triangulation:

Triangulation(x, y) x, y -- the coordinates of the points as 1-D arrays of floats

. . .

Attributes: (all should be treated as read-only to maintain consistency) x, y -- the coordinates of the points as 1-D arrays of floats.

  circumcenters -- (ntriangles, 2) array of floats giving the (x,y)
    coordinates of the circumcenters of each triangle (indexed by a triangle_id).

Adapted from one of the matplotlib examples (there is probably a cleaner way to do this, but it should work):

import matplotlib.pyplot as plt
import matplotlib.delaunay
import matplotlib.tri as tri
import numpy as np
import math

# Creating a Triangulation without specifying the triangles results in the
# Delaunay triangulation of the points.

# First create the x and y coordinates of the points.
n_angles = 36
n_radii = 8
min_radius = 0.25
radii = np.linspace(min_radius, 0.95, n_radii)

angles = np.linspace(0, 2*math.pi, n_angles, endpoint=False)
angles = np.repeat(angles[...,np.newaxis], n_radii, axis=1)
angles[:,1::2] += math.pi/n_angles

x = (radii*np.cos(angles)).flatten()
y = (radii*np.sin(angles)).flatten()

tt = matplotlib.delaunay.triangulate.Triangulation(x,y)
triang = tri.Triangulation(x, y)

# Plot the triangulation.
plt.figure()
plt.gca().set_aspect('equal')
plt.triplot(triang, 'bo-')

plt.plot(tt.circumcenters[:,0],tt.circumcenters[:,1],'r.')
plt.show()