I don't know if it's the right forum, so please forgive me if it's not :)

I found Similiar topic: Transformation matrix from 3 points .
My question is: Is it possible to do that with one transformed and one untransformed point?

I have a vector 0;0;-1  and an another (transformed). both are normalized (length = 1.0). is it possible to get the tranfsormation matrix that thansforms my 0;0;-1 to this given vector?
Posted on 2005-06-15 18:34:14 by ti_mo_n
Do you have the original transformation matrix?  Then, it is a simple matter of matrix inversion, just like the thread you linked.

Otherwise... it might be or might not be possible depending on additonal assumptions.  For example, if you are trying to find out the matrix with only those two points, you may be able to find one possible representation, but that is not unique.
Posted on 2005-06-15 18:49:26 by Starless
ah, ok. I just thougth that there exists a miraculous way to do that :P
Posted on 2005-06-15 18:54:46 by ti_mo_n
With one point, you can only generate a linear transformation matrix.  With two points you can generate a transformation matrix for points on a plane.  With three points you can generate a transformation matrix in 3-space - rotating, scaling, and simple transforms.  With four points you can represent any transformation at all including perspective correction, convolution, and others.

You are very limited with what you can do with just your two-point dataset.

Posted on 2005-06-15 19:35:40 by Sparafusile
Um, how does perspective correction fit in a matrix? That doesn't make any sense at all. You can't eliminate the division.
You'll need 4 points to get all 12 coefficients anyhow. Almost any 3 vectors can be transformed into any other 3 vectors using a homogenous transform, assuming that no vector is proportional to another.
Posted on 2005-06-16 12:20:28 by Sephiroth3
It's been a while since I've worked on this so my memory might not be perfect.  I was simply trying to make the point that you can't represent every transformation with a 3x3 matrix. For example, mapping an image onto a sphere or a cylinder (which is what I was doing in the original post) requires a 4x4 matrix.  This is what I ment by "perspective correction".

Posted on 2005-06-16 14:34:42 by Sparafusile
That's true. In the rightmost column you have the offset, of course, but what do you have in your bottom row? I don't see how putting anything other than 0,0,0,1 could be useful in any way. That would mean you're rotating your offset into your rotation/scaling coefficients. And that helps you, how...?
Posted on 2005-06-16 16:56:07 by Sephiroth3