如何使用 matplotlib 在立方体上绘制等高线 4D？

Question

我想在立方体 (x,y,z) vs. q 上绘制 4D 图，使用立方体 3 个表面上的颜色图，其中颜色和轮廓取决于 q 变量。基本上，我正在寻找类似这样的图片：

感谢任何帮助。

Answer 1

看我的例子3D ABC feild

import pyvista as pv
import numpy as np
from numpy import mgrid
import matplotlib.pyplot as plt

print('initializing domain')
xmin = -800.
xmax = 800.
Lx = xmax-xmin
B0 = 1
k = 1
alpha = 2.0*np.pi*k/Lx
x, y, z = Lx*mgrid[0:1:51j, 0:1:51j, 0:1:51j]


print('initializing 3D B field')
Bx = B0*(np.sin(alpha*z) + np.cos(alpha*y))
By = B0*(np.sin(alpha*x) + np.cos(alpha*z))
Bz = B0*(np.sin(alpha*y) + np.cos(alpha*x))
B = np.column_stack((Bx.ravel(), By.ravel(), Bz.ravel()))
grid = pv.StructuredGrid(x, y, z)
grid["ABC field magnitude"] = np.linalg.norm(B, axis=1)
grid["ABC field vectors"] = B
grid.set_active_vectors("ABC field vectors")
#contours = grid.contour(8, scalars="ABC field magnitude")
#arrows = contours.glyph(orient="ABC field vectors", factor=50.0)

print('plotting')
pv.set_plot_theme('document')
p = pv.Plotter(notebook=0, shape=(1,1))
#p.background_color='white'
#p.window_size
cmap = plt.cm.get_cmap("viridis", 4)
p.add_mesh(grid, cmap=cmap)
p.show_grid()
#p.add_mesh(arrows)
#p.subplot(0,1)
#slices = grid.slice_orthogonal(x=20, y=20, z=30)
#slices = grid.slice_orthogonal()
#p.add_mesh(slices, cmap=cmap)
##p.subplot(1,0)
#p.add_mesh(contours, opacity=1)
#p.subplot(1,1)
#p.add_mesh(arrows)
#single_slice = arrows.slice(normal=[1, 1, 0])
#slices = arrows.slice_orthogonal(x=20, y=20, z=30)
#slices = grid.slice_orthogonal()
#p.add_mesh(single_slice, cmap=cmap)
p.show_grid()

p.link_views()
p.view_isometric()
p.show(screenshot='abc3d_slicing.png')

Answer 2

一个简单的答案是

import numpy as np
import matplotlib.pyplot as plt

length = 10
data = length*np.mgrid[0:1:51j, 0:1:51j, 0:1:51j].reshape(3,-1).T
contour = np.random.rand(data.shape[0])

fig = plt.figure()
ax = fig.add_subplot(projection='3d')
data_plot = ax.scatter(data[:,0], data[:,1], data[:,2], c=contour)
fig.colorbar(data_plot)

只优化边界点

length = 10
vol_data = length*np.mgrid[0:1:51j, 0:1:51j, 0:1:51j].reshape(3,-1).T
bound_data = np.array([data_i for data_i in vol_data
              if any([coord in [0, length] for coord in data_i])])

contour = np.random.rand(bound_data.shape[0])

fig = plt.figure()
ax = fig.add_subplot(projection='3d')
data_plot = ax.scatter(bound_data[:,0], bound_data[:,1], bound_data[:,2], c=contour)
fig.colorbar(data_plot)

如何使用 matplotlib 在立方体上绘制等高线 4D？

How to 4D plot with contour over cube, using matplotlib?

python

3d

matplotlib

cube

contour