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 14:22:27 -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=8G3ZYf/ASj/WT4ead6Y7xjVYmCbJdqd4XYOu8Mh/iTQ=; b=w1KKwhCxCtDCipVa2WzPF4ZJx4oea2N9t0dn0EjLP/FDX4ZUeFhKqeDjOyEOQx1pDK HY8GMXMrGwmF7reO61JSJq+k3+e6egc+MS1VRIHCDOd6Mubuhw+aews3IfASW+zt9omr zufAl6DX/DfnyQ0szJuAoFjwagzyYC2NrjgRY=*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=s0wuzNwV1CZi55fHtb7ozw96SHO08h73JgMvXeLh1JOBykvGE1VPDVOZ8XUlsqd/Lo tSLjoen0o/co1XSxlzCjHVvvz1YBXkD4WoE/W7kc0zMoL9CfiuM8jhcbAuvz2TS4325V hniKaK10Ojg0w/2CyaEMUv0BaK/2A7d1wzRis=

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 >

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

**Re: [eigen] Rigid transformations in eigen: use of dual quaternions***From:*Hauke Heibel

**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

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