1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

from __future__ import division, print_function, absolute_import 

 

import numpy as np 

from scipy._lib.decorator import decorator as _decorator 

 

__all__ = ['delaunay_plot_2d', 'convex_hull_plot_2d', 'voronoi_plot_2d'] 

 

 

@_decorator 

def _held_figure(func, obj, ax=None, **kw): 

import matplotlib.pyplot as plt 

 

if ax is None: 

fig = plt.figure() 

ax = fig.gca() 

return func(obj, ax=ax, **kw) 

 

# As of matplotlib 2.0, the "hold" mechanism is deprecated. 

# When matplotlib 1.x is no longer supported, this check can be removed. 

was_held = ax.ishold() 

if was_held: 

return func(obj, ax=ax, **kw) 

try: 

ax.hold(True) 

return func(obj, ax=ax, **kw) 

finally: 

ax.hold(was_held) 

 

 

def _adjust_bounds(ax, points): 

margin = 0.1 * points.ptp(axis=0) 

xy_min = points.min(axis=0) - margin 

xy_max = points.max(axis=0) + margin 

ax.set_xlim(xy_min[0], xy_max[0]) 

ax.set_ylim(xy_min[1], xy_max[1]) 

 

 

@_held_figure 

def delaunay_plot_2d(tri, ax=None): 

""" 

Plot the given Delaunay triangulation in 2-D 

 

Parameters 

---------- 

tri : scipy.spatial.Delaunay instance 

Triangulation to plot 

ax : matplotlib.axes.Axes instance, optional 

Axes to plot on 

 

Returns 

------- 

fig : matplotlib.figure.Figure instance 

Figure for the plot 

 

See Also 

-------- 

Delaunay 

matplotlib.pyplot.triplot 

 

Notes 

----- 

Requires Matplotlib. 

 

""" 

if tri.points.shape[1] != 2: 

raise ValueError("Delaunay triangulation is not 2-D") 

 

x, y = tri.points.T 

ax.plot(x, y, 'o') 

ax.triplot(x, y, tri.simplices.copy()) 

 

_adjust_bounds(ax, tri.points) 

 

return ax.figure 

 

 

@_held_figure 

def convex_hull_plot_2d(hull, ax=None): 

""" 

Plot the given convex hull diagram in 2-D 

 

Parameters 

---------- 

hull : scipy.spatial.ConvexHull instance 

Convex hull to plot 

ax : matplotlib.axes.Axes instance, optional 

Axes to plot on 

 

Returns 

------- 

fig : matplotlib.figure.Figure instance 

Figure for the plot 

 

See Also 

-------- 

ConvexHull 

 

Notes 

----- 

Requires Matplotlib. 

 

""" 

from matplotlib.collections import LineCollection 

 

if hull.points.shape[1] != 2: 

raise ValueError("Convex hull is not 2-D") 

 

ax.plot(hull.points[:,0], hull.points[:,1], 'o') 

line_segments = [hull.points[simplex] for simplex in hull.simplices] 

ax.add_collection(LineCollection(line_segments, 

colors='k', 

linestyle='solid')) 

_adjust_bounds(ax, hull.points) 

 

return ax.figure 

 

 

@_held_figure 

def voronoi_plot_2d(vor, ax=None, **kw): 

""" 

Plot the given Voronoi diagram in 2-D 

 

Parameters 

---------- 

vor : scipy.spatial.Voronoi instance 

Diagram to plot 

ax : matplotlib.axes.Axes instance, optional 

Axes to plot on 

show_points: bool, optional 

Add the Voronoi points to the plot. 

show_vertices : bool, optional 

Add the Voronoi vertices to the plot. 

line_colors : string, optional 

Specifies the line color for polygon boundaries 

line_width : float, optional 

Specifies the line width for polygon boundaries 

line_alpha: float, optional 

Specifies the line alpha for polygon boundaries 

point_size: float, optional 

Specifies the size of points 

 

 

Returns 

------- 

fig : matplotlib.figure.Figure instance 

Figure for the plot 

 

See Also 

-------- 

Voronoi 

 

Notes 

----- 

Requires Matplotlib. 

 

Examples 

-------- 

Set of point: 

 

>>> import matplotlib.pyplot as plt 

>>> points = np.random.rand(10,2) #random 

 

Voronoi diagram of the points: 

 

>>> from scipy.spatial import Voronoi, voronoi_plot_2d 

>>> vor = Voronoi(points) 

 

using `voronoi_plot_2d` for visualisation: 

 

>>> fig = voronoi_plot_2d(vor) 

 

using `voronoi_plot_2d` for visualisation with enhancements: 

 

>>> fig = voronoi_plot_2d(vor, show_vertices=False, line_colors='orange', 

... line_width=2, line_alpha=0.6, point_size=2) 

>>> plt.show() 

 

""" 

from matplotlib.collections import LineCollection 

 

if vor.points.shape[1] != 2: 

raise ValueError("Voronoi diagram is not 2-D") 

 

if kw.get('show_points', True): 

point_size = kw.get('point_size', None) 

ax.plot(vor.points[:,0], vor.points[:,1], '.', markersize=point_size) 

if kw.get('show_vertices', True): 

ax.plot(vor.vertices[:,0], vor.vertices[:,1], 'o') 

 

line_colors = kw.get('line_colors', 'k') 

line_width = kw.get('line_width', 1.0) 

line_alpha = kw.get('line_alpha', 1.0) 

 

center = vor.points.mean(axis=0) 

ptp_bound = vor.points.ptp(axis=0) 

 

finite_segments = [] 

infinite_segments = [] 

for pointidx, simplex in zip(vor.ridge_points, vor.ridge_vertices): 

simplex = np.asarray(simplex) 

if np.all(simplex >= 0): 

finite_segments.append(vor.vertices[simplex]) 

else: 

i = simplex[simplex >= 0][0] # finite end Voronoi vertex 

 

t = vor.points[pointidx[1]] - vor.points[pointidx[0]] # tangent 

t /= np.linalg.norm(t) 

n = np.array([-t[1], t[0]]) # normal 

 

midpoint = vor.points[pointidx].mean(axis=0) 

direction = np.sign(np.dot(midpoint - center, n)) * n 

far_point = vor.vertices[i] + direction * ptp_bound.max() 

 

infinite_segments.append([vor.vertices[i], far_point]) 

 

ax.add_collection(LineCollection(finite_segments, 

colors=line_colors, 

lw=line_width, 

alpha=line_alpha, 

linestyle='solid')) 

ax.add_collection(LineCollection(infinite_segments, 

colors=line_colors, 

lw=line_width, 

alpha=line_alpha, 

linestyle='dashed')) 

 

_adjust_bounds(ax, vor.points) 

 

return ax.figure