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 14:17:14 -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=N4FO/nxqgIS9JctRMyy9CDLJJpZEH64WRAVPlueGvZg=; b=qcbZ+nPNMazj3AYn/FIssXOXhaf954ComJuO6lSUueyN3LUXcIcr0NtvShAVM7dRCx cCpMplpw7s9vv+grr3kznM9vmwGz1cWP1cB7brIevC3Ru2qD7V+ombERf1ujs4csNjCJ KuFpXONCPnPMT819TVQ9fn99dK0o/H3lK6h58=*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=Ocv5Nh72ZTOYECvybs36lmYQqa5PWGtQLIRYgr5Z9myMdJaZd2L7uxXbbs8+/99gTb CEpkAbhecfXSE6vW6zvfCwvsPu6IrwQAIvlPMOX+eVESmWvzvFbZ1dRsnmSHOPOjG9MP oscK2RLstniLk0dhAPrZo66vSfZgtnun4agbU=

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

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

**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

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