Finding translation and scale on two sets of points to get least square error in their distance?

Question

I have two sets of 3D points (original and reconstructed) and correspondence information about pairs - which point from one set represents the second one. I need to find 3D

Answer 1

A good explanation Finding optimal rotation and translation between corresponding 3D points

The code is in matlab but it's trivial to convert to opengl using the cv::SVD function