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From: JEMebius on 24 Jul 2010 19:49
Dave wrote:
> Hey all,
>
> Ken Shoemake wrote a great article about how to convert rotation
> matrices to Euler angles, and vice versa:
> http://etclab.mie.utoronto.ca/people/david_dir/GEMS/GEMS.html
>
> David Eberley has a similar article:
> http://www.geometrictools.com/Documentation/EulerAngles.pdf
>
> This all works great, though I find myself using a lot of quaternions,
> rather than matrices, so I end up having to convert quaternion ->
> matrix -> euler, which is slow and builds up roundoff.
>
> So, I was wondering if anyone has seen ways to convert directly
> between general euler angles and quaternions? Various sources
> (wikipedia, euclideanspace) have conversions for one type of euler
> angles, but not the general case.
>
> Thanks,
>
> Dave


Perhaps the best you can do is to study and use the EULERANG.PAS Turbo-Pascal unit
available at my web page http://www.xs4all.nl/~jemebius/Eulerang.htm .

I am afraid there does not exist a "general case of Euler angles".
EULERANG deals with just two conventions for Euler angles:
(A) the physics mode, where the rotation order is ZXZ;
(B) the aeronautics mode, with rotation order XYZ.
(Complete explanations in the software comments)

There exist at least 46 other conventions in defining Euler angles. Each single one of
them requires its own specific set of conversion formulas. So a "general case" is doomed
to boil down to 48 different cases without any continuous transitions among them.

Please feel free to use and adapt this software to your own needs: it is practically
public-domain stuff. You may always ask questions through mailto:jemebius-at-xs4all-dot-nl

Good luck: Johan E. Mebius
From: richard i pelletier on 24 Jul 2010 22:05
In article <4C4B7C18.1040107(a)xs4all.nl>, JEMebius <jemebius(a)xs4all.nl>
wrote:

>
> There exist at least 46 other conventions in defining Euler angles. Each
> single one of
> them requires its own specific set of conversion formulas. So a "general
> case" is doomed
> to boil down to 48 different cases without any continuous transitions among
> them.

I'm curious. I figure 12 cases assuming rotations about X,Y, or Z axes:
3 choices for the first, 2 for the second, 2 for the third. I assume you
have additional choices -- how do you get 48?

vale,
rip

--
email address is r i p 1 AT c o m c a s t DOT n e t
From: Tim Little on 24 Jul 2010 22:34
On 2010-07-25, richard i pelletier <bitbucket(a)comcast.net> wrote:
> I'm curious. I figure 12 cases assuming rotations about X,Y, or Z
> axes: 3 choices for the first, 2 for the second, 2 for the third. I
> assume you have additional choices -- how do you get 48?

I suppose there's a handedness choice for the coordinate system, and
sign conventions on angles.


- Tim
From: spudnik on 25 Jul 2010 20:35
3 choices, 2 choices, 1 choices (3?, or "three summorial" .-)
irection cosines are nice & homogenous, but
wh not stay with vectors (quaternions' inner and
outer products) ??

thus: IFF probably is "if & only if," that is to say,
Liebniz's neccesity & sufficiency, used in literate manner!
>   Iff ... then ...

--les ducs d'oil!
http://tarpley.net
From: Dave on 26 Jul 2010 20:52
On Jul 24, 7:05 pm, richard i pelletier <bitbuc...(a)comcast.net> wrote:
> In article <4C4B7C18.1040...(a)xs4all.nl>, JEMebius <jemeb...(a)xs4all.nl>
> wrote:
>
>
>
> > There exist at least 46 other conventions in defining Euler angles. Each
> > single one of
> > them requires its own specific set of conversion formulas. So a "general
> > case" is doomed
> > to boil down to 48 different cases without any continuous transitions among
> > them.
>
> I'm curious. I figure 12 cases assuming rotations about X,Y, or Z axes:
> 3 choices for the first, 2 for the second, 2 for the third. I assume you
> have additional choices -- how do you get 48?
>
> vale,
> rip
>
> --
> email address is r i p 1 AT c o m c a s t DOT n e t

Ya, I have heard about 24 cases (the 12 mentioned above times two for
either rotating coordinate frames or stationary ones -- see Shoemake's
paper). Not sure where the other factor of 2 is coming from.
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