Re: WorldPlot, WorldRotation... with a twist?
- To: mathgroup at smc.vnet.net
- Subject: [mg90616] Re: WorldPlot, WorldRotation... with a twist?
- From: dh <dh at metrohm.ch>
- Date: Wed, 16 Jul 2008 06:29:08 -0400 (EDT)
- References: <g5htgm$j9d$1@smc.vnet.net>
Hi,
what your are asking is how to add Euler angles. This is not simple, but
you can do it by translating the Euler angles into a rotation matrix
(RotationMatrix3D), then you multiply the matrices. Finally you must
extract the result angles from the result. The result (angles:
psi,theta,phi) has the form:
{Cos[phi] Cos[psi] - Cos[theta] Sin[phi] Sin[psi], Cos[psi] Sin[phi] +
Cos[phi] Cos[theta] Sin[psi], Sin[psi] Sin[theta]}
, {-Cos[psi] Cos[theta] Sin[phi] - Cos[phi] Sin[psi], Cos[phi] Cos[psi]
Cos[theta] - Sin[phi] Sin[psi], Cos[psi] Sin[theta]}
, {Sin[phi] Sin[theta], -Cos[phi] Sin[theta], Cos[theta]}
}
starting at Cos[theta] you may then extract the angles.
Daniel
Mr Stuff wrote:
> At last I have a beautiful Orthographic projection of the world and a
> great circle on it (not the usual construction between two points, but
> between one point and a specified tangent latitude, but that's beside
> the point, so to speak)
>
> Question (Mathematica 5) I can place a specified point in the centre
> of the projection by doing a WorldRotation->{lat, 0, -long} - but how
> can I *also* rotate the image so that the g.c. runs top-bottom (i.e.
> move away from "North up")
>
> Given that WorldRotation does y,z, z' rotations I have no idea how to
> combine rotations...
>
> Any thoughts?
>
> TIA
>
--
Daniel Huber
Metrohm Ltd.
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CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
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