[Sidefx-houdini-list] rotating a rotation
Drew Whitehouse
Drew.Whitehouse at anu.edu.au
Tue Oct 17 16:59:37 EDT 2006
doh, s/(from 4)/(from 2)/ in the previous mail.
On 10/18/06, Drew Whitehouse <Drew.Whitehouse at anu.edu.au> wrote:
> A bit of math,
>
> If you have a rotation matrix R and a point p_old, then you rotate
> p_old by multiplying by R i.e.
>
> p_new = R p_old (1)
>
> Now assume we have a transform matrix T, that describes a change of
> space such that our points p_old and p_new now become q_old and q_new
> in the new space. (eg T could be a simple -90 rotation matrix about
> the X axis to flip from Z up to Y up).
>
> q_old = T p_old (2)
> q_new = T p_new (3)
>
> then we want to find the new matrix M where
>
> q_new = M q_old (4)
>
> M will be our transformed rotation matrix.
>
> Now,
>
> q_new = T p_new
> = T R p_old (from 1)
> = T R inverse(T) q_old (from 4)
>
> Hence our new matrix
>
> M = T R inverse(T)
>
> Note that for a pure rotation the inverse of the matrix is the same as
> it's transpose so we can say
>
> M = T R transpose(T).
>
> -Drew
>
>
>
>
>
> On 10/17/06, Peter Robbinson <probbins at corefa.com> wrote:
> > I vaguely remember many moons ago you could switch what axis is up in
> > one of the startup scripts.
> > I could be imagining things though.
> >
> > PeterR
> >
> > Ben Schrijvers wrote:
> >
> > >Hi Dan,
> > >
> > >Uhm.. yes obviously it was the most obvious. Indeed same swapping and
> > >inverting as the translate channels. I didn't swap the rotation order though
> > >which made me think the solution would be a lot more complex and maybe need
> > >a matrix.
> > >
> > >Uhm.. I couldn't find it so I gave up hope already but anyone able to
> > >confirm that you can't switch Houdini to a Z-up system?
> > >
> > >Having fun over here? Well as my question is about DOP's and converting
> > >coordinate systems you can geuss I do feel at home :-)
> > >
> > >Cheers,
> > >benS
> > >
> > >-----Original Message-----
> > >From: sidefx-houdini-list-bounces at sidefx.com
> > >[mailto:sidefx-houdini-list-bounces at sidefx.com] On Behalf Of Dan Seddon
> > >Sent: Monday, October 16, 2006 7:33 PM
> > >To: sidefx-houdini-list at sidefx.com
> > >Subject: Re: [Sidefx-houdini-list] rotating a rotation
> > >
> > >Hi Ben
> > >
> > >Hope you're having fun back in the Nether Netherlands.
> > >
> > >If you can do a channel swapping trick for the translation you should be
> > >able to do if for rotation too - though you'll need to swap the rotation
> > >order around too. Without checking I would imagine you should
> > >interchange your rotation orders in the same order you interchange each
> > >of your transforms (given that you ts rs and ss should match too),
> > >though you'll need to make sure you get your signs correct for the
> > >rotations (which is determined by the handedness or your coordinate system).
> > >
> > >Hop that gives you enough to play with, if you're not already there.
> > >
> > >Dan
> > >
> > >
> > >
> > >>Hi there,
> > >>
> > >>
> > >>
> > >>I've got to rotate some channels that where generated in DOP's.
> > >>
> > >>As it's quite a simple rotation I can rotate the translation channels by
> > >>swapping them.
> > >>
> > >>But that doesn't work for the rotation channels.
> > >>
> > >>I've tried the Transform Chop which does give me new rotation values but I
> > >>can't find the right ones.
> > >>
> > >>
> > >>
> > >>Anyone?
> > >>
> > >>benS
> > >>
> > >>_______________________________________________
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> > >>Sidefx-houdini-list at sidefx.com
> > >>https://lists.sidefx.com:443/mailman/listinfo/sidefx-houdini-list
> > >>
> > >>
> > >>
> > >
> > >_______________________________________________
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> > >
> > >
> > >
> > >
> >
> > --
> > Peter Robbinson
> > Trainer
> > robbinson at coredp.com
> > probbins at corefa.com
> >
> > Core Digital Pictures
> > http://www.coredp.com/
> >
> >
> >
> >
> > "gravity is not a force, it is a boundary layer"
> > "everything is coincident"
> > "Love: a state of suspended anticipation"
> >
> > _______________________________________________
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> >
> >
>
>
> --
> Drew Whitehouse
> ANU Supercomputer Facility Vizlab
>
--
Drew Whitehouse
ANU Supercomputer Facility Vizlab
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