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Python:从Scipy的Delaunay三角剖分中以3D计算Voronoi镶嵌

Python:从Scipy的Delaunay三角剖分中以3D计算Voronoi镶嵌

邻接信息可以neighborsdelaunay对象的属性中找到。不幸的是,该代码目前还没有向用户公开周围环境,因此您必须自己重新计算这些中心。

而且,不能以这种方式直接获得延伸到无穷大的Voronoi边缘。仍然可能,但还需要更多思考。

import numpy as np
from scipy.spatial import delaunay

points = np.random.rand(30, 2)
tri = delaunay(points)

p = tri.points[tri.vertices]

# Triangle vertices
A = p[:,0,:].T
B = p[:,1,:].T
C = p[:,2,:].T

# See http://en.wikipedia.org/wiki/Circumscribed_circle#Circumscribed_circles_of_triangles
# The following is just a direct transcription of the formula there
a = A - C
b = B - C

def dot2(u, v):
    return u[0]*v[0] + u[1]*v[1]

def cross2(u, v, w):
    """u x (v x w)"""
    return dot2(u, w)*v - dot2(u, v)*w

def ncross2(u, v):
    """|| u x v ||^2"""
    return sq2(u)*sq2(v) - dot2(u, v)**2

def sq2(u):
    return dot2(u, u)

cc = cross2(sq2(a) * b - sq2(b) * a, a, b) / (2*ncross2(a, b)) + C

# Grab the Voronoi edges
vc = cc[:,tri.neighbors]
vc[:,tri.neighbors == -1] = np.nan # edges at infinity, plotting those would need more work...

lines = []
lines.extend(zip(cc.T, vc[:,:,0].T))
lines.extend(zip(cc.T, vc[:,:,1].T))
lines.extend(zip(cc.T, vc[:,:,2].T))

# Plot it
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection

lines = LineCollection(lines, edgecolor='k')

plt.hold(1)
plt.plot(points[:,0], points[:,1], '.')
plt.plot(cc[0], cc[1], '*')
plt.gca().add_collection(lines)
plt.axis('equal')
plt.xlim(-0.1, 1.1)
plt.ylim(-0.1, 1.1)
plt.show()
python 2022/1/1 18:32:05 有516人围观

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