🚀 go-pugleaf

Hi,

I am working on a surface registration problem and is trying to solve it
using singular value decomposition. The problem is set up as follows:

PR = Q

where P is [mx3], R is [3x3] and Q is [mx3]

Using the SVD on Q I get: 

P = UDV

where U is [mxm], D is [mx3] and V is [3x3]  m>>3

What I have understood I can now find the matrix R that gives the minimal
solution to PR = Q with:

R = (V*)(D+)(U*)Q 

Where (V*) means the adjoint matrix of V and (D+) means the pseudoinverse of
D.

My question 1 is: 
I want to have an orthogonal matrix R as this R should be a rigid rotation
matrix. My calculations does not seem to give an orthogonal R though, so
what should I do to add this restriction on R ?

My question 2 is:
As the U matrix gets dimensions [mxm] this can be very large for big
datasets and thus demands huge amounts of memory on my machine. Is there
anything to avoid this without reducing the dataset ? Is U sparse ?

/Daniel Bengtsson