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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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