I use it for the following problem:
I need to draw arrows showing the magnetic field in the space. Using Java3D, I can draw a 3D arrow in z direction and the arrow center is the origin but I need to draw the arrow at point P and in direction given by the field at point P. Using the matrix, the object is first rotated to become parallel with the field direction, then by a translation, moves to the point. I think it is kind of similar to your problem.
