如何根据色标为voronoi上色?以及每个单元格的面积 [英] How to color voronoi according to a color scale ? And the area of each cell

问题描述

是否可以为 scipy.spatial.Voronoi 图? 我知道.

但是现在我的目标是根据色标为每个单元格着色，以代表物理量.

But now my goal is to color each cell according to a color scale to represent a physical quantity.

如下图(PRL 107，155704(2011)):

As in the image below (PRL 107, 155704 (2011)):

我还想知道是否有可能计算每个像元的面积，因为这是我要计算的数量

And I would also like to know if it is possible to calculate the area of each cell, because it is a quantity that I would like to calculate

推荐答案

色阶:

实际上，您提供的链接提供了着色Voronoi图所需的代码.为了给每个单元分配代表物理量的颜色，您需要使用将值映射到matplotlib .

Color scale:

Actually the 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速度"相对应的颜色:

For example, if I want to assign each cell a color corresponding to a quantity '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:

)

scipy.spatial.Voronoi允许您访问每个单元的顶点，您可以对其进行排序并应用鞋带公式.我还没有测试输出足以知道Voronoi算法给出的顶点是否已经排序.但是，如果没有，则可以使用点积来获取每个顶点的矢量和某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:

scipy.spatial.Voronoi allows you to access the vertices of each cell, which you can order and apply the shoelace formula. I haven't tested the outputs enough to know if the vertices given by the Voronoi algorithm come already ordered. But if not, you can use the dot product to get the angles between the vector to each vertex and some reference vector, and then order the vertices using these angles:

# 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)

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