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MathGroup Archive 2006

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Re: Sphere

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65548] Re: Sphere
  • From: dh <dh at metrohm.ch>
  • Date: Fri, 7 Apr 2006 06:14:24 -0400 (EDT)
  • References: <e12s6o$j7i$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com


Hi Matija,

If you are happy with longitude and lattitude, we may simply map the 

rectangular parameter space: phi=0..2Pi and theta=-P/2...Pi/2 onto the 

sphere. Here is an example.

Define some curve, here a loxodrome:



phi[x_]:=6 x;

theta[x_]:= Mod[x,Pi]-Pi/2;



here is the map:



mymap[phi_,theta_]:={Cos[theta] Cos[phi],Cos[theta] Sin[phi], Sin[theta]}



here is the drawing:



<< Graphics`Shapes`

Show[Graphics3D[{

       Sphere[1, 20, 20],

       Thickness[0.01],

       Line[

         Table[mymap[phi[x], theta[x]], {x, 0, 2Pi, 0.01}]

         ]

       }], AmbientLight -> GrayLevel[0.9], LightSources -> {}]



here is the same curve in parameterspace (phi axes extended):



ParametricPlot[{phi[x], theta[x]}, {x, 0, Pi}]



Daniel



Matija Herceg wrote:

> Hi,

> 

> My professor ask me if I could make program which would draw celestial 

> sphere with (celestial) measurements on it to show celestial coordinates 

> of some (celestial) body.

> 

> My idea was that I could draw sphere in mathematica, and with celestial 

> coordinates given by user input the program would draw celestial curves 

> (declination, ascension...).

> 

>   Can I draw curves on sphere in Mathematica?

> 

> Is this possible in new version of Mathematica (5.1 and higher)?

> Because GeometricalGeodesy (a new Mathematica application package) is 

> now available, and I don't know if some of this problems can be solved 

> without this new package.

> 

> Thanks,

> 

> Matija

> 



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