Voronoi Polygons for 2-D Point Sets

Author: Serge Rey (http://github.com/sjsrey)

Basic Usage

[1]:
import sys
import os
sys.path.append(os.path.abspath('..'))
import libpysal
[2]:
from libpysal.cg.voronoi  import voronoi, voronoi_frames
[3]:
points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3)]
[4]:
regions, vertices = voronoi(points)
[5]:
regions
[5]:
[[1, 3, 2], [4, 5, 1, 0], [0, 1, 7, 6], [9, 0, 8]]
[6]:
vertices
[6]:
array([[  4.21783296,   4.08408578],
       [  7.51956025,   3.51807539],
       [  9.4642193 ,  19.3994576 ],
       [ 14.98210684, -10.63503022],
       [ -9.22691341,  -4.58994414],
       [ 14.98210684, -10.63503022],
       [  1.78491801,  19.89803294],
       [  9.4642193 ,  19.3994576 ],
       [  1.78491801,  19.89803294],
       [ -9.22691341,  -4.58994414]])
[7]:
region_df, point_df = voronoi_frames(points)
[8]:
%matplotlib inline
import matplotlib
import numpy as np
import matplotlib.pyplot as plt
[9]:
fig, ax = plt.subplots()
region_df.plot(ax=ax, color='blue',edgecolor='black', alpha=0.3)
point_df.plot(ax=ax, color='red')

[9]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f3304d59e48>
../_images/notebooks_voronoi_10_1.png

Larger Problem

[10]:
n_points = 200
np.random.seed(12345)
points = np.random.random((n_points,2))*10 + 10
results = voronoi(points)
mins = points.min(axis=0)
maxs = points.max(axis=0)
[11]:
regions, vertices = voronoi(points)
[12]:
regions_df, points_df = voronoi_frames(points)
[13]:
fig, ax = plt.subplots()
points_df.plot(ax=ax, color='red')
[13]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f32fd486b38>
../_images/notebooks_voronoi_15_1.png
[14]:
fig, ax = plt.subplots()
regions_df.plot(ax=ax, color='blue',edgecolor='black', alpha=0.3)
points_df.plot(ax=ax, color='red')
[14]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f32fd3c76a0>
../_images/notebooks_voronoi_16_1.png

Trimming

[15]:
points = np.array(points)
maxs = points.max(axis=0)
mins = points.min(axis=0)
xr = maxs[0] - mins[0]
yr = maxs[1] - mins[1]
buff = 0.05
r = max(yr, xr) * buff
minx = mins[0] - r
miny = mins[1] - r
maxx = maxs[0] + r
maxy = maxs[1] + r
[16]:
fig, ax = plt.subplots()
regions_df.plot(ax=ax, edgecolor='black', facecolor='blue', alpha=0.2 )
points_df.plot(ax=ax, color='red')
plt.xlim(minx, maxx)
plt.ylim(miny, maxy)
plt.title("buffer: %f, n: %d"%(r,n_points))
plt.show()

../_images/notebooks_voronoi_19_0.png

Voronoi Weights

[17]:
from libpysal.weights.contiguity import Voronoi as Vornoi_weights
[18]:
w = Vornoi_weights(points)
[19]:
w.n
[19]:
200
[20]:
w.pct_nonzero
[20]:
2.685
[21]:
w.histogram
[21]:
[(1, 1),
 (2, 6),
 (3, 17),
 (4, 34),
 (5, 41),
 (6, 63),
 (7, 24),
 (8, 7),
 (9, 5),
 (10, 1),
 (11, 0),
 (12, 1)]
[22]:
idx = [i for i in range(w.n) if w.cardinalities[i]==12]
[23]:
points[idx]
[23]:
array([[16.50851787, 13.12932895]])
[ ]: