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

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Rigid transformations in eigen: use of dual quaternions*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Sat, 12 Sep 2009 16:10:19 -0400*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type; bh=ROzDg0g7ue52UXNnb90K7pq3EqaAH/AvSPhvAEfGi5w=; b=dN+nAiyJT2N1NmDPNmk6KnO2BeTbQTnC44jmusG4T/l08nKnBPFJrrKn7gmj4Vov34 q0ZGbJfX4oQZGfzn9khcp91HRwWzAjQvaWpO3AQUWGJ2rLkACgFbrljisdMEvqms+K3X wv83Jm2tZPYi8HkaVuu8eNu9BkxvkQ9juDWa8=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type; b=cldOtayFtIiVy3YJCs/Wx6akhvlfivSD4rQGqFG62nZZBire5o//iyDAJhbzgClvC+ rkP+SEAU+sBIb95rog6tHMi4JJ4zhdT8TelWiRc/ry5VPEs+k0edsHH1PY0TkU6fsfik SxXC9Dbbbu2sMMM26wA+eN+76kAvN/iqIfFhQ=

2009/9/12 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 Ah, one precision: here it's crucial that data is 128 bit aligned! We don't have any way to map a non-128bit-aligned buffer as a quaternion. Benoit

**Follow-Ups**:**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Gael Guennebaud

**References**:**[eigen] Rigid transformations in eigen: use of dual quaternions***From:*Rohit Garg

**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Benoit Jacob

**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Rohit Garg

**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Benoit Jacob

**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Rohit Garg

**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Benoit Jacob

**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Benoit Jacob

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