       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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