Re: [eigen] Rigid transformations in eigen: use of dual quaternions

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

2009/9/12 Rohit Garg <rpg.314@xxxxxxxxx>:
>>> For what-are-dual-quaternions, look at the paper here
>>>
>>> http://isg.cs.tcd.ie/projects/DualQuaternions/
>>
>> Hm that page wasn't very explicit, but I found this:
>>
>> http://en.wikipedia.org/wiki/Dual_quaternion
>
> Must have been taken down. Paper attached.

woops, please don't attach heavy files to mails on this list! I'll
edit the wiki to mention that.

the link wasn't down, i had seen the file, still i found it less
explicit than the wikipedia page as far as the definition of dual
quaternions was concerned.

>>> All in all, dual quaternions are to rigid transformations what
>>> quaternions are to 3D rotations. The biggest advantage is to treat
>>> rotation and translation in a unified framework.
>>
>> If it were just that, we have the Transform class. But I understand
>> that the dual quaternion representation allows for that interesting
>> slerp-like interpolation, i can believe it's useful, and dual
>> quaternions have a wikipedia page mentioning applications to 3D
>> graphics, so, no need to convince me any more than that. I'd say, go
>> for it!
>
> The advantages are cheaper to store, cheaper to compose, more stable
> and interpolation. In that sense, they correspond to the advantages of
> quaternions over matrices.

ok, understood.

>
> Question: can you map a piece of memory as a Quaternion<datatype>
> (with vectorization)? Like the question I raised earlier today where a
> vec4i wasn't vectorized.

Hm, no you currently can't. But Eigen can be modified so that you
could. If you want to give it a try, look at DiagonalMatrix.h, how
DiagonalMatrix is storing its own coeffs like Quaternion does while
DiagonalWrapper wraps an existing MatrixBase (which could be a
Map...).

Benoit