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>