given two point clouds P,Q, and a permutation matrix X. We can say P = Q X. However X is unknown. Has Matlab a implementation for point clouds to find the right permutation matrix?
I think your issue is that you are getting too focused on point clouds and permutations. Lets rephrase:
"Given two matrices P, Q, and an unknown matrix X, can matlab solve QX=P?"
The answer is of course yes, this is just a normal linear system of equations, often described as Ax=b in the literature. Solving linear systems of equations is a subfield of mathematics itself, but it is so common to have this issue that MATLAB has a function that will try to choose the best algorithm for you. Simply:
x=A\b; % or x=Q\P;
Read the docs for mldivide