What has me confused about what you are trying to do is why the strict restriction to translation when this is a far easier problem to solve through a combination of translation and rotation.
Lets have two surfaces A and B and they start out intersecting each other and are in the orientation we want. If you select three points (a1,a2,a3) on surface A that are coincident with three points (b1,b2,b3) on surface B.
Then you randomly rotate and translate the two surfaces.
You could realign them in three steps (for this process I am assuming that we are only interested in realigning surface A to surface B and not the two surfaces to the world coordinates.)
(Step 1 - TRANSLATION) There must exist a translation A(tx,ty,tz) such that a1 and b1 are coincident. In other words move surface A until its a1 end point is point constrained to surface B's b1 end point.
(Step 2 - ROTATION) With points a1,b1 point constrained there must exist a rotation of surface A about point a1 => A(rx,ry,rz) will bring the middle point of surface A (a2) together with b2 of surface B. In other words rotate surface A about point a1 such that a2 and b2 are coincident.
(Step 3 - ROTATION) now with a1 point constrained to b1 through translation and a2 point constrained to b2 through rotation of surface A about point a1 it should be obvious that we now only need rotate surface A about an axis running through the straight line between points a1,b1 and a2,b2. So we have a vector V<a1b1,a2b2> and there must exist a rotation about that vector V(rv) that will bring the points a3 and b3 together.
How you accomplish it in Maya I don't really know but to me the most intuitive solution involves 1 translation, 1 multi-axis rotation about a point, 1 single-axis rotation about a Vector between the first two point to realign the surfaces.
"If I have seen further it is by standing on the shoulders of giants." Sir Isaac Newton, 1675
Last edited by ctbram; 03-05-2013 at 04:46 PM.