[Closed] Rotate TM to match another TM

A * (inverse A) = Identity Matrix

Given matrices A, B, find matrix C:

From linear algebra:
A*C=B
C=(inverse A)*B. …but then heirarchies complicate things– they need to be in the same coordinate space– you need to find the common ancestor. Transform A and B into that common space and then I think you can find your matrix C.

…look at the xformMat command to transform a matrix into the coordinate space of another.

There are no heirarchies in this case. Just 2 simple nodes in the scene. And all I want to do is rotate the one node to match the other.

If you have the transforms for nodes A and B then try:

A * C = B

C =( inverse (A.transform.rotationpart as matrix3) ) * ( B.transform.rotationpart as matrix3 )

Then when you multiply A * C to orient A to B it should leave node A in it’s current position since the translation rows are set to zero in the above.

I don’t have access to 3ds Max to verify right now, but… I believe you could leave the rotations as Quats and use the preRotate maxscript command as well…

preRotate <matrix3> <quat>
[left]Applies an incremental rotation transformation to the input matrix or matrices. This is equivalent to multiplying on the LEFT by the transform. If the matrix3 parameter is a single matrix, this function returns the transformed matrix. If the parameter is an array of matrices, this function returns the value OK. In both cases, the input matrix3 value(s) are replaced with the transformed matrix value(s).[/left]

tempTM = preRotate A.transform ( B.transform.rotationpart * ( inverse A.transform.rotationpart ) )

A.transform = tempTM

Or also, the Rotate command and switching the order of the quats should give the same results…

tempTM = Rotate A.transform ( ( inverse A.transform.rotationpart ) * B.transform.rotationpart )

A.transform = tempTM

I’m not sure I’ve been of any help… but as you probably know, internally rotations are stored differently than what you see in the scene. See the attached primer on 3dsMax Rotations written by Kees Rijnen.
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here is a function I wrote to match the pos /rot of obj to target.
perhaps you can adat it to your needs.
It is based on Bobo’s video the Matrix Explained
( which can be found inyou tube installments )

the challenge is that , while positon xyz is simply encoded in row 4 of a matrix ,
the scale rotation data is mingled and scattered between rows 1-3,
so to avoid matching the scale you have to replace the scale part of the target transform
with the scale part of the object transform.

	fn matchPosRot obj target = (
		t=target.transform
		--we don't want the scale copied, so remove target scale  info
		tScale=t.scalepart
		t.row1 /= tScale.x
		t.row2 /= tScale.y
		t.row3 /= tScale.z
		--replace with obj scale info
		oScale=obj.transform.scalepart
		t.row1 *= oScale.x
		t.row2 *= oScale.y
		t.row3 *= oScale.z
		--comment the line below to remove translation info , keeping only rotation
		t.row4 = target.transform.row4
		obj.transform = t
	)

Correct. I have two nodes in which I want to rotate,move,scale node A to match node B.

It can be linear.

It can be an instant thing as well. It does not have to happen over the course of time.

Are you doing anything to the nodes’ geometry object? i.e., offseting it from the pivot or manipulating the object with modifiers (e.g., bend, taper, FFDs, etc.)? Or do you only care to operate on the node transforms?

How do you want to affect the change to node A’s transform? You stated it wasn’t as simple as saying: nodeA.transform = nodeB.transform… (<– why isn’t it that simple? Because that captures position, rotation, and scale all at once) …you said that you needed to rotate node A to match node B. Can you explain in more detail?

Or is this a single match TM operation (like, something to be achieved by a custom attribute button press that would match node A to node B any time the button is pressed?) or do you want node A to follow along with node B for some amount of time?

Correct. I have two nodes in which I want to rotate,move,scale node A to match node B.

yeah, I’m confused what you are asking now, because the above sounds like

A.transform = B.transform

Is it possible you are speaking not of matching object transforms, but of matching one object’s pivot point to another, while leaving the geometry in place?