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MathGroup Archive 2006

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Re: Sphere

  • To: mathgroup at
  • Subject: [mg65548] Re: Sphere
  • From: dh <dh at>
  • Date: Fri, 7 Apr 2006 06:14:24 -0400 (EDT)
  • References: <e12s6o$j7i$>
  • Sender: owner-wri-mathgroup at

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`


       Sphere[1, 20, 20],



         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}]


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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