[Insight-users] Composition of two versor transforms

[Luis Ibanez]

Hi Patrik,

Each Versor Transform does the equivalent of:

                     P'  = Transform(P) = M x P + T

Where M is a rotation matrix computed from the Versor parameters,
and T is the Translation vector.

to be more precise,
this Transform also has a Center of rotation "C",
so the actual computation is:

    P' = Transform(P) = M x ( P - C ) + T + C

Now, when you compose two Versor Transforms you should do:

   P" = Transform2( P' ) = Transform2( Transform1( P ) )

This leads to:

  P" = M2 x ( P' - C2 ) + T2 + C2
  P" = M2 x ( M1 x ( P - C1 ) + T1 + C1  - C2 ) + T2 + C2

which leads to

  P" =  M2 x M1 x ( P - C1 )  + M2x(T1+C1-C2)  + (T2+C2)

You can get the matrix M from each transform by calling the
method: GetMatrix(); the translation by calling GetTranslation();
and the center C by calling the method GetCenter().



    Regards,


         Luis


--------------------------------------------------------
On Thu, Nov 26, 2009 at 4:05 AM, Patrik Brynolfsson
<patrik.brynolfsson at gmail.com> wrote:
> Hello everyone,
> I have a question I hope someone can clarify for me. I want to combine the
> result from two versor transforms. From what I've gathered I shouldn't add
> the elements of the two, but how then? Can someone please explain?
> Thanks in advance!
> --
> Patrik Brynolfsson
>
>
> _____________________________________
> Powered by www.kitware.com
>
> Visit other Kitware open-source projects at
> http://www.kitware.com/opensource/opensource.html
>
> Kitware offers ITK Training Courses, for more information visit:
> http://www.kitware.com/products/protraining.html
>
> Please keep messages on-topic and check the ITK FAQ at:
> http://www.itk.org/Wiki/ITK_FAQ
>
> Follow this link to subscribe/unsubscribe:
> http://www.itk.org/mailman/listinfo/insight-users
>
>