logm on 4x4 affine matrices.

[Andrew Janke]

Hi all,

Here's hoping someone can point me in the right direction...

I need to average a few affine transformation matrices so have been doing this:

   > AVG = expm((logm(A000) + logm(A001)) / 2)

However the "translation component" doesn't seem to behave as I would expect.

ie:

octave:3> A000 = [1 0 0 0; 0 1 0 0; 0 0  1 0; 0 0 0 1];
octave:4> A001 = [1 0 0 1; 0 1 0 2; 0 0  1 3; 0 0 0 1];
octave:5> AVG = expm((logm(A000) + logm(A001)) / 2)
warning: inverse: matrix singular to machine precision, rcond = 1.42141e-17
AVG =

   1   0   0   0
   0   1   0   0
   0   0   1   0
   0   0   0   1


?

On affine matrices with translations that are non-identity things seem
to be as I would expect.

Thanks


-- 
Andrew Janke - address@hidden
Department of Geriatric Medicine, ANU
Canberra->Australia    +61 (402) 700 883