如何用平面方程对齐两个超平面

Question

I am trying to Euclidean transform one plane to other plane. I have two equation of planes and they have different sizes. How can I align two plane in one coordinate system?

My two planes in form of ax+by+cz+d=0.

first plane => a = -5.297742252442251, b = 21.751836101364013, c = -2.470896764133499, d = -0.5601826186620921

Second plane => a = 45.42557999642176, b = -16.9433283673388, c = 2.5117971500097287, d = -8.528560240570203]

For plotting on the matplotlib, I used following code using matplotlib

x = np.linspace(-1,1,100)
y = np.linspace(-1,1,100)

X,Y = np.meshgrid(x,y)
Z = (-d - a*X - b*Y) / c

fig = plt.figure(figsize=(10, 10))
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, alpha=0.45)
plt.show()

How can I align two planes and create 3d plot of two align planes in one graph?

At the end, I want to transform the datapoints on each sides of hyperplanes

Each datapoints with hyperplane should looks like following enter image description here

data points:

data1 = [[0.190133571624755, 0.146549582481384, 0.391435742378234, 'near'], [0.0154470205307006, 0.0959569215774536, 0.484999418258667, 'near'], [-0.119875073432922, 0.0414541959762573, 0.542818903923034, 'near'],[0.104917883872985, 0.058539867401123, 0.171926498413085, 'far'],[0.177520513534545, 0.130982756614685, 0.0330302715301513, 'far'],[0.246979117393493, 0.173633933067321, 0.373323440551757, 'far']]

data2 = [[0.334545135498046, -0.0318257808685302, 0.282101511955261, 'near'], [0.411889553070068, 0.0223467350006103, 0.183727979660034, 'near'], [0.330880641937255, -0.00959080457687378, 0.178299665451049, 'near'],[-0.00756144523620605, -0.07442307472229, -0.227764248847961, 'far'],[-0.268512785434722, -0.309048891067504, 0.456292867660522, 'far'],[-0.305409669876098, -0.304299354553222, 0.281461238861084, 'far']]
  
# Create the pandas DataFrame
df1 = pd.DataFrame(data1, columns=['A', 'B', 'C', 'NearOrFar'])
df2 = pd.DataFrame(data2, columns=['A', 'B', 'C', 'NearOrFar'])

Answer 1

If you simply want to plot the two planes on the same 3d axes, then you just need to compute two different values for Z and plot the two Z s relative to the same X s and Y s, like so:

import numpy as np
from mpl_toolkits.mplot3d import Axes3D

# first plane:

a1 = -5.297742252442251
b1 = 21.751836101364013
c1 = -2.470896764133499
d1 = -0.5601826186620921

# second plane:

a2 = 45.42557999642176
b2 = -16.9433283673388
c2 = 2.5117971500097287
d2 = -8.528560240570203

x = np.linspace(-1, 1, 100)
y = np.linspace(-1, 1, 100)

X, Y = np.meshgrid(x, y)
Z1 = (-d1 - a1 * X - b1 * Y) / c1
Z2 = (-d2 - a2 * X - b2 * Y) / c2

fig = plt.figure(figsize=(10, 10))
ax = plt.axes(projection="3d")
ax.plot_surface(X, Y, Z1, alpha=0.45)
ax.plot_surface(X, Y, Z2, alpha=0.45)
plt.show()

This produces the following figure:

As to "aligning" the two planes, it's not clear to me what you're asking...? Two planes will be coplanar if they have the same values of a, b, c and d in the equation you gave above - if they have different values of a, b, c and d, they won't be coplanar. They may intersect, they may not - and to ensure you graph them where they intersect (should they do so), you'd need to determine the values of x and y where they have equal values of z and set your xrange and yrange accordingly. If you can explain the meaning of "align" for your particular purposes, perhaps I could expand on this answer to accommodate.