如何根据色标对voronoi进行着色？和每个细胞的面积

Question

是否可以为scipy.spatial.Voronoi图表着色？我知道它是.

但现在我的目标是根据颜色标度为每个细胞着色以表示物理量.

如下图所示(PRL 107,155704(2011)):

而且我还想知道是否可以计算每个单元格的面积,因为它是我想要计算的数量

Answer 1

色标:

实际上,您提供的链接提供了使Voronoi图着色所需的代码.为了为每个单元格指定一个表示物理量的颜色,您需要使用在matplotlib中将值映射到颜色中显示的方法将此物理量的值映射到标准化的颜色图.

例如,如果我想为每个单元格分配与数量"速度"相对应的颜色:

import numpy as np
import matplotlib as mpl
import matplotlib.cm as cm
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi, voronoi_plot_2d

# generate data/speed values
points = np.random.uniform(size=[50, 2])
speed = np.random.uniform(low=0.0, high=5.0, size=50)

# generate Voronoi tessellation
vor = Voronoi(points)

# find min/max values for normalization
minima = min(speed)
maxima = max(speed)

# normalize chosen colormap
norm = mpl.colors.Normalize(vmin=minima, vmax=maxima, clip=True)
mapper = cm.ScalarMappable(norm=norm, cmap=cm.Blues_r)

# plot Voronoi diagram, and fill finite regions with color mapped from speed value
voronoi_plot_2d(vor, show_points=True, show_vertices=False, s=1)
for r in range(len(vor.point_region)):
    region = vor.regions[vor.point_region[r]]
    if not -1 in region:
        polygon = [vor.vertices[i] for i in region]
        plt.fill(*zip(*polygon), color=mapper.to_rgba(speed[r]))
plt.show()

样本输出:

)

细胞面积:

scipy.spatial.Voronoi允许您访问每个单元格的顶点,您可以订购并应用鞋带公式.我没有测试输出足以知道Voronoi算法给出的顶点是否已经订购.但如果没有,你可以使用点积来获得每个顶点的矢量和一些参考矢量之间的角度,然后使用这些角度对顶点进行排序:

# ordering vertices
x_plus = np.array([1, 0]) # unit vector in i direction to measure angles from
    theta = np.zeros(len(vertices))
    for v_i in range(len(vertices)):
        ri = vertices[v_i]
        if ri[1]-self.r[1] >= 0: # angle from 0 to pi
            cosine = np.dot(ri-self.r, x_plus)/np.linalg.norm(ri-self.r)
            theta[v_i] = np.arccos(cosine)
        else: # angle from pi to 2pi
            cosine = np.dot(ri-self.r, x_plus)/np.linalg.norm(ri-self.r)
            theta[v_i] = 2*np.pi - np.arccos(cosine)

    order = np.argsort(theta) # returns array of indices that give sorted order of theta
    vertices_ordered = np.zeros(vertices.shape)
    for o_i in range(len(order)):
        vertices_ordered[o_i] = vertices[order[o_i]]

# compute the area of cell using ordered vertices (shoelace formula)
partial_sum = 0
for i in range(len(vertices_ordered)-1):
    partial_sum += vertices_ordered[i,0]*vertices_ordered[i+1,1] - vertices_ordered[i+1,0]*vertices_ordered[i,1]
    partial_sum += vertices_ordered[-1,0]*vertices_ordered[0,1] - vertices_ordered[0,0]*vertices_ordered[-1,1]
area = 0.5 * abs(partial_sum)