I have two identical boxes in the space, each box is defined by it''s center coordinate and the normals of the up, right and forward faces of the box. I want to find a third box that it''s orientation is an interpolation between the orientation of the first and the second box. I though to use SLERP and quaternions, but think for SLERP I need two matrices where each matrix defines a rotation. In my case I don''t have the matrices, I just have a center and normals. So Do you have any idea how can I convert my representation to quaternions ?

Ahh! But you do have matrices.. The normals of your faces will give you the columns (or rows, depending on the exact space orientations in your system). Now doing SLERPS with matrices I think is trickier then with quaternions, so you can look at the matrixfaq to convert your matrices to quaternions.

thanks JuNC
"depending on the exact space orientations in your system"
do you mean coordinate system ?
in my application Z axis is toward the viewer, (-Z) is toward the screen.
(openGL)

so is it raw or columns ?