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

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

2009/9/12 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...).

Ah, I'm stupid. Since that's only for some internal code that you have
to write only once, what do you think of just doing a
reinterpret_cast? That gives the same result with much less hassle!

Like this

float data[4];

reinterpret_cast<Quaternionf*>(data)->slerp(....);

Benoit

>
> Benoit
>