如何根据色标给 voronoi 上色？以及每个单元格的面积

Question

是否可以给 scipy.spatial.Voronoi diagram? I know it is.

上色

但现在我的目标是根据色标为每个单元格着色以表示物理量。

如下图 (PRL 107, 155704 (2011)):

而且我也想知道是否可以计算每个单元格的面积，因为这是一个我想计算的数量

Answer 1

色阶：

其实 link you provide gives the code needed to colorize the Voronoi diagram. In order to assign each cell a color representing a physical quantity, you need to map the values of this physical quantity to a normalized colormap using the method shown in Map values to colors in matplotlib.

例如，如果我想为每个单元格分配一种与数量相对应的颜色 'speed'：

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()

示例输出：

)

单元格面积：

scipy.spatial.Voronoi 允许您访问每个单元格的顶点，您可以对其进行排序并应用 shoelace formula。我还没有对输出进行足够的测试以了解 Voronoi 算法给出的顶点是否已经排序。但如果没有，您可以使用点积来获取每个顶点的向量与某个参考向量之间的角度，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)

如何根据色标给 voronoi 上色？以及每个单元格的面积

How to color voronoi according to a color scale ? And the area of each cell

python

physics

voronoi

numpy

色阶：

示例输出：

单元格面积：