Rotation of a patch using eigenvectors

I've got an STL imported file, this file is randomly positioned in space. I want to regulate its position in order to get its symmetry axis overlapping with the coordinated axis. I used the Inertia tensor and eigen vectors and eigenvalues. However, I thought that would be enough to multiply the x,y,z coordinate matrix of my data by the eigenvector matrix to get it. I am wrong for sure because it's not what I am geting. What is missing? Help please

The code below

%First I have a Function to find geometric center of surface, then translation of surface in order to overlap geometric center and axis origin
%Function to calculate Inertia Tensor
function [ I ] = InertiaTensor( TrianglesGeometricCenter,AreaMatrix )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here
A=AreaMatrix
GCtri=TrianglesGeometricCenter

for i=1:length(GCtri)
    
    Ixx=sum(A(i)*(GCtri(i,2)^2+GCtri(i,3)^2))
    Iyy=sum(A(i)*(GCtri(i,1)^2+GCtri(i,3)^2))
    Izz=sum(A(i)*(GCtri(i,1)^2+GCtri(i,2)^2))
    
    Ixy=sum(A(i)*(GCtri(i,1)*GCtri(i,2)))
    Iyx=sum(A(i)*(GCtri(i,1)*GCtri(i,2)))
    Ixz=sum(A(i)*(GCtri(i,1)*GCtri(i,3)))
    Izx=sum(A(i)*(GCtri(i,1)*GCtri(i,3)))
    Iyz=sum(A(i)*(GCtri(i,2)*GCtri(i,3)))
    Izy=sum(A(i)*(GCtri(i,2)*GCtri(i,3)))
end

I=[Ixx Ixy Ixz;Iyx Iyy Iyz; Izx Izy Izz]
assignin('base','I',I)
    
end
%Get eigenvectores and eigenvalues

[Q,W]=eig(I)

%V is data matrix
R=V*Q
%Surface plot and I can see some rotation but not to the expected place

Answer 1

[darova]

If you have center of your body and you can manually get axis symmetry - use rotation matrix

Here vector is normal vector of plane created of three point (O c0 p0)

LINK Wikipedia

Then just simply multiple each point by R