python - 如何从 3D numpy meshgrid 中提取 2D 平面

Question

[TLDR]:

基本上我的问题归结为如何从 3D numpy meshgrid 中提取平面的 2d 数据

[详细说明]:

我正在计算两个(或更多)点电荷的电场。我在 2D 中做了这个，可以使用 quiver 或 streamplot 通过 matplotlib 绘制结果

import numpy as np
from matplotlib import pyplot as plt

eps_0 = 8e-12
fac = (1./(4*np.pi*eps_0))

charges  = [1.0,-1.0]
qx       = [-2.0,2.0]
qy       = [0.0,0.0]

# GRID
gridsize = 4.0
N = 11
X,Y = np.meshgrid( np.linspace(-gridsize,gridsize,N),
                   np.linspace(-gridsize,gridsize,N))
# CALC E-FIELD   
sumEx = np.zeros_like(X)
sumEy = np.zeros_like(Y)

for q, qxi, qyi in zip(charges,qx,qy):
    dist_vec_x = X - qxi
    dist_vec_y = Y - qyi 
    dist = np.sqrt(dist_vec_x**2 + dist_vec_y**2)

    Ex = fac * q * (dist_vec_x/dist**3)
    Ey = fac * q * (dist_vec_y/dist**3)

    sumEx += Ex
    sumEy += Ey

# PLOT
fig = plt.figure()
ax = fig.add_subplot(111)
ax.streamplot(X,Y,sumEx,sumEy)
plt.show()

这会产生正确的结果

我可以轻松地将其扩展到 3D

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

eps_0 = 8e-12
fac = (1./(4*np.pi*eps_0))

charges = [1.0,-1.0]
qx      = [-2.0,2.0]
qy      = [0.0,0.0]
qz      = [0.0,0.0]

# GRID
gridsize = 4.0
N = 11
X,Y,Z = np.meshgrid( np.linspace(-gridsize,gridsize,N),
                     np.linspace(-gridsize,gridsize,N),
                     np.linspace(-gridsize,gridsize,N))

# CALC E-FIELD   
sumEx = np.zeros_like(X)
sumEy = np.zeros_like(Y)
sumEz = np.zeros_like(Z)
for q, qxi, qyi, qzi in zip(charges,qx,qy,qz):
    dist_vec_x = X - qxi
    dist_vec_y = Y - qyi
    dist_vec_z = Z - qzi

    dist = np.sqrt(dist_vec_x**2 + dist_vec_y**2 + dist_vec_z**2)

    Ex = fac * q * (dist_vec_x/dist**3)
    Ey = fac * q * (dist_vec_y/dist**3)
    Ez = fac * q * (dist_vec_z/dist**3)

    sumEx += Ex
    sumEy += Ey
    sumEz += Ez  

# PLOT
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.quiver(X,Y,Z,sumEx,sumEy,sumEz, pivot='middle', normalize=True)
plt.show()

在 3D 中绘制时，这也会产生正确的结果(据我所知)

但出于某种原因，我不知道如何从生成的 3D numpy 网格中提取一个 x-y 平面的数据。我以为我可以做类似的事情

zplane = round(N/2)
ax.quiver(X,Y,sumEx[:,:,zplane],sumEy[:,:,zplane])

但这并不能解决问题。有谁知道这里的正确方法吗？

Answer 1

删除 projection='3d' 和索引 X 和 Y:

fig = plt.figure()
ax = fig.gca()
zplane = round(N / 2)
ax.quiver(X[:, :, zplane], Y[:, :, zplane], sumEx[:, :, zplane], sumEy[:, :, zplane])
plt.show()

如果您选择特定的 zplane，您的绘图将不再是 3D 绘图。