单位球面上的热图

Question

I would like to plot a heat map on the unit sphere using the matplotlib library of python. There are several places where this question is discussed. Just like this: Heat Map half-sphere plot

I can do this partially. I can creat the sphere and the heatplot. I have coordinate matrices X,Y and Z, which have the same size. I have another variable of the same size as X, Y and Z, which contains scalars used to creat the heat map. However in case c contains scalars differ from zero in its first and last rows, just one polar cap will be colored but not the other. The code generates the above mentioned result is the next:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D

#Creating the theta and phi values.
theta = np.linspace(0,np.pi,100,endpoint=True)
phi   = np.linspace(0,np.pi*2,100,endpoint=True)

#Creating the coordinate grid for the unit sphere.
X = np.outer(np.sin(theta),np.cos(phi))
Y = np.outer(np.sin(theta),np.sin(phi))
Z = np.outer(np.cos(theta),np.ones(100))

#Creating a 2D matrix contains the values used to color the unit sphere.
c = np.zeros((100,100))
for i in range(100):
    c[0,i]  = 100
    c[99,i] = 100

#Creat the plot.
fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')
ax.set_axis_off()
ax.plot_surface(X,Y,Z, rstride=1, cstride=1, facecolors=cm.plasma(c/np.amax(c)), alpha=0.22, linewidth=1)
m = cm.ScalarMappable(cmap=cm.plasma)
m.set_array(c)
plt.colorbar(m)

#Show the plot.
plt.show()

The plot which was generated:

Could somebody help me what's going on here?

Thank you for your help in advance!

Answer 1

The values in the arrays define the edges of the grid. The color of the i th face is determined by the i th value in the color array. However, for n edges you only have n-1 faces, such that the last value is ignored.

Eg if you have 4 grid values and 4 colors, the plot will have only the first three colors in the grid.

Thus a solution for the above would be to use a color array with one color less than gridpoints in each dimension.

c = np.zeros((99,99))
c[[0,98],:] = 100

Answer 2

There are a number of small differences with your example but an important one, namely the shape of the values array c .

As mentioned in another answer the grid that defines the surface is larger (by one in both dimensions) than the grid that defines the value in each quadrangular patch, so that by using a smaller array for c it is possible to choose correctly the bands to color not only with respect to the beginnings of the c array but also with respect to its ends, as I tried to demonstrate in the following.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D

# Creating the theta and phi values.

intervals = 8
ntheta = intervals
nphi = 2*intervals

theta = np.linspace(0, np.pi*1, ntheta+1)
phi   = np.linspace(0, np.pi*2, nphi+1)

# Creating the coordinate grid for the unit sphere.
X = np.outer(np.sin(theta), np.cos(phi))
Y = np.outer(np.sin(theta), np.sin(phi))
Z = np.outer(np.cos(theta), np.ones(nphi+1))

# Creating a 2D array to be color-mapped on the unit sphere.
# {X, Y, Z}.shape → (ntheta+1, nphi+1) but c.shape → (ntheta, nphi)
c = np.zeros((ntheta, nphi)) + 0.4
# The poles are different
c[ :1, :] = 0.8
c[-1:, :] = 0.8
# as well as the zones across Greenwich
c[:,  :1] = 0.0
c[:, -1:] = 0.0

# Creating the colormap thingies.
cm = mpl.cm.inferno
sm = mpl.cm.ScalarMappable(cmap=cm)
sm.set_array([])

# Creating the plot.
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, facecolors=cm(c), alpha=0.3)
plt.colorbar(m)

# Showing the plot.
plt.show()