[Insight-users] Derivatives of VersorRigidTransform and VersorRigid3DTransform unstable

Luis Ibanez luis.ibanez at kitware.com
Mon Sep 22 11:31:08 EDT 2008

Hi Sohan,

Thanks for pointing this out.

You are right, the divisions by "VW" in the computation of
the GetJacobian() method will result in divisions by zero
when the rotation angle of the Versor is 180 degrees.

Could you please enter a bug report on this issue ?


This seems to be a deficiency of the particular method
we used for computing the derivative, and not an inherent
limitation on the use of Versors for representing rotations.

Which is a way to say that: we should be able to find a
way to fix the Jacobian computation to make it stable.

We probably should explore the use of the successive
differentials described in Hamilton's book instead of
using the partial derivatives of the Versor components.



Ranjan, Sohan (GE, Research) wrote:
> Folks.
> The implementation of the computation of derivative for 
> VersorRigidTransform and VersorRigid3DTransform are
> unstable for rotations of 180 degrees, and after looking into the code, 
> I see that the divide-by-zero may
> happen for a range of versor values.
> Can someone check this out, and suggest corrections that may be needed? 
> Sohan 
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