Re: [eigen] Eigen and rigid body simulation |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Eigen and rigid body simulation*From*: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>*Date*: Fri, 27 Nov 2009 08:58:26 -0500*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=+9aUvNZr3L47FwFkParO+rOO4lcg6DgqDQM3ZGBewvk=; b=PHuelQZS+nxZLEATT8SJj5WS3LjCh/YDv/j/w5CAkJ3v9H9VlIT4HGKrLLYx/C0EGe /vUIXppgtVkwhS21rqFASFMHnUG/nbEZfUzXwN2saWg6p/6kcUc1gICMwx93mzj80oD7 wDDXuMUQ8ZGCPOqde2GY5mTDlqmG7Igr6i7Xc=*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=APZcBQppgsldAduDistp5Zvpc5CUKfSKnhQVgc6liR7QjV21AgPGsRFUr9dYuSu1nb XTHoiDMU1sI0A3mlU2JvM+5+zyYlwkYvjhhk8MJm4jhfDi8DSCpukBchbfBXzT7/9z1D EX+lzf47sCoolSoK7oRqXH9lw3cCLYoto4N9A=

2009/11/27 Mathieu Gautier <mathieu.gautier@xxxxxx>: >>> * a rotation 3d is an element of the special orthogonal group SO(3) which >>> is >>> a Lie group. We choose to represent it with a quaternion. >> >> That I understood. Do you think that there is a fundamental reason why >> you specialize on quaternions? Just a question, I guess it depends on >> technical details. Because otherwise you could leverage our >> RotationBase infrastructure, which is quite nice, it exactly means "3D >> rotation" but allows different kinds of storage, at no cost (in pure >> Eigen style, everything is done at compile time). > > We use only quaternion for their efficiency, but in order to generalized, it > would be better to use RotationBase with appropriate specialization. OK. Lie_so3 could be a template so it would have one specialization for Quaternion, one for AngleAxis, etc... in line with your colleague's idea, one could call it LieAlgebra<...>. > >>> * a Wrench is a member to the dual Lie aglebra se*(3) of se(3). >>> >>> * a Torque is a member of so*(3) dual of so(3). > >> Is there a canonical duality? Or does e.g. the natural dot product on >> R^3 give you at least a "usual" duality? >> >> If there is a reasonable "usual" duality then there's no need to >> implement a separate class for the dual, just implementing the >> bilinear form is enough. (Think of how we don't have a class for >> linear forms on R^n, the dual of R^n; instead we have the dot product >> function; so a linear form can just be represented by the vector that >> is dual to it in the usual dot product, and the dot product gives you >> the pairing between the vector space and its dual). > > I may not clearly understand what you mean by canonical or "usual". But, I'd > say that's a "usual" duality. Generalized forces "wrench" are build from > Twist and the notion of power : > > transpose(W)*T = p > > so this is a symmetric bilinear form, like the dot product in R^n. But it's > interesting to have the distinction between Twist and Wrench from a > mechanical point of view. > >> But if there is a reason to add specify methods or operators there, >> then I understand that you want to keep them as separate classes > > Actually, there's no specific methods for one or the other class, just the > distinction is important. OK, then OK for separate classes. Benoit

**References**:**[eigen] Eigen and rigid body simulation***From:*Mathieu Gautier

**Re: [eigen] Eigen and rigid body simulation***From:*Thomas Capricelli

**Re: [eigen] Eigen and rigid body simulation***From:*Mathieu Gautier

**Re: [eigen] Eigen and rigid body simulation***From:*Benoit Jacob

**Re: [eigen] Eigen and rigid body simulation***From:*Benoit Jacob

**Re: [eigen] Eigen and rigid body simulation***From:*Mathieu Gautier

**Re: [eigen] Eigen and rigid body simulation***From:*Benoit Jacob

**Re: [eigen] Eigen and rigid body simulation***From:*Mathieu Gautier

**Re: [eigen] Eigen and rigid body simulation***From:*Benoit Jacob

**Re: [eigen] Eigen and rigid body simulation***From:*Mathieu Gautier

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