3D scatterplot, matrix operations and calculation of the inverse

Question

I have a scatter-plot with the code shown below.

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
x = np.random.rand(100)
y = np.random.rand(100)
z = np.random.rand(100)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
scatter = ax.scatter(x, y, z, c='r', marker='o')
plt.show()

We can say

A = np.column_stack((x, y, z)).

Additionally, I have a matrix B, which equals the matrix A times a rotation operation, a shift operation + noise.

B = A x rot(X) + shift(Y) + Noise

If only matrix A and B are given, how can I find the necessary rotation angle and shift vector to overlap matrix B with matrix A / revert the operations on matrix B? Is a center of mass approach best or what would be the recommended approach?

• Aaron: hard to say.. It probably depends heavily on your type of data. The keyword you're looking for is Point-set registration. There's a decent video from the YouTube channel Computerphile on the Iterative Closest Point (ICP) algorithm.
• cerv21: It is 3D electron diffraction data: en.wikipedia.org/wiki/Electron_diffraction