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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.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>




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