[Insight-users] changing Center of Rotation for MatrixOffsetTransformBase

[Karthik Krishnan]

Michael:

Its simple. Derive it yourself :-)

For a centered transform (with parameters : C = Center, T= Translation. R=
Rotation matrix.), given a point 'p'

TransformedPoint = R (p - C)  + C  + T

Now if you want your own Center C', let's find the parameters R' and T'

R (p - C)  + C  + T  = R' (p - C')  + C'  + T'

The result is
  R' = R
  T' = T + (C-C') - R (C-C')

ie. You will contruct a new transform with the same rotation matrix, your
center and the new translation is given by the above equation.

Hope this helps.
--
karthik

On 11/16/07, Michael Schildt <michael.schildt at ifn-magdeburg.de> wrote:
>
> Hello!
>
> I got a rigid transform of an itk registration with a certain center of
> rotation. But for further processing i need to use an other center. Is
> it possible to recompute the matrix of a rigid/affine transform for a
> different center? Because, just setting a new center will result in a
> different transform.
>
> Here are some numbers:
>
> TransformMatrix = -0.0183916 0.938708 -0.344223 -0.0411616 -0.3447
> -0.93781 -0.998983 -0.00307907 0.0449783
> Offset = 5.64609 -44.9436 -0.107986
> CenterOfRotation = 1.09089 6.36365 -2.33333
>
> I need to have a new center at [127.5, 127.5, 127.5].
>
> Any hints are welcome :)
>
>
> Best reguards,
>     Michael Schildt
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