[Insight-users] Re: Versor components

[Luis Ibanez]

Hi Andrew,

Yes, the Versor is intended to represent a rotation in 3D space.

Currently only some of the rigid transform provide a GetVersor()
method. Those are the transforms that actually use a Versor internally
in order to represent the rotation.

An example on how to get the rotational component out of a rotaion
matrix is presented in file

        Insight/
          Examples/
              Registration/
                  ImageRegistration9.cxx


in lines 117-125.


Note that if you know the rotations around specific axes, you
could use Versor composition in order to get the Versor equivalent
to the sequence of rotations.

You just need to be careful with the order in which the rotations
are applied, since Versor composition is not commutative.


    Regards,


        Luis



===============
Andrew Li wrote:
> Hi, Luis:
> 
> I assume that any strictly-rotational transform (in 3D space) can be
> uniquely specified by a versor component set {Rx, Ry, Rz}. Is it
> correct?
> 
> If it is the case, does ITK lib support this decomposition? Like:
> 	Transform->GetVersorComponents()
> Provided that the transform is orthonormal and its determinant= 1;
> 
> If it has not been implemented yet, do you know the formula?
> In fact, what I am interested is a special case:
> 	
> 	we know M = RzRyRx, 
> 	what is inv(M) = ?
> 	
> Thank you very much for your help!
> 
> 
> -Andrew
>