Re: Countur/Density plot on sphere

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• Subject: [mg127473] Re: Countur/Density plot on sphere
• From: "djmpark" <djmpark at comcast.net>
• Date: Fri, 27 Jul 2012 04:59:16 -0400 (EDT)
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• References: <20120725063355.F39326866@smc.vnet.net> <10885246.50611.1343288228719.JavaMail.root@m06>

```For those who have Presentations here is a solution.

f[t_?NumericQ, p_?NumericQ] =
Integrate[(t + x)/(1 + p + x), {x, 0, 1}, Assumptions -> p > -1]

<< Presentations`

Draw2D[
{g1 = ContourDraw[
f[\[Theta], \[Phi]], {\[Theta], 0, 2 \[Pi]}, {\[Phi], 0, \[Pi]},
ColorFunction -> (ColorData["BrownCyanTones"][1 - #] &),
MaxRecursion -> 3]},
Frame -> True, FrameLabel -> {\[Theta], \[Phi]},
ImageSize -> 300]

f1 = n1 =
Function[{\[Theta], \[Phi]}, {Sin[\[Phi]] Cos[\[Theta]],
Sin[\[Phi]] Sin[\[Theta]], Cos[\[Phi]]}];
Draw3DItems[
{Opacity[1], g1 // RaiseTo3D[f1, n1]},
NeutralLighting[0, .5, .4, 120 Degree, -40 Degree],
NiceRotation,
Boxed -> False,
PlotRegion -> {{-0.3, 1.3}, {-0.3, 1.3}},
ViewPoint -> {1, -1, 1} 3,
ImageSize -> 250]

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/index.html

From: Bla=BE Kranjc [mailto:blaz.kranjc91 at gmail.com]

Suprisingly this work now (I tried it 10+ times before and it didn't), I
just have another question, SphericalPlot3D[1, {t, 0, 2 Pi}, {p, 0, Pi},
ColorFunction ->
Function[{x, y, z, t, p, r}, Hue[f[Abs@z]]] and   SphericalPlot3D[1, {t,
0, 2 Pi}, {p, 0, Pi},
ColorFunction ->
Function[{x, y, z, t, p, r}, Hue[f[z]]] returned the same plots,
therefore this isn't really plotting my values??
I don't really trust this now.

I also tried calculating a lot of points on a sphere and finding a value in
given point, than Show them all with Graphics3D giving them color based on
value, BUT sphere loses it's depth and is full of holes now. so it doesn't
look ok.

2012/7/25 Bob Hanlon <hanlonr357 at gmail.com>

> This is quite slow but if I understand what you want
>
> f[t_?NumericQ, p_?NumericQ] :=
>  NIntegrate[(t + x)/(1 + p + x), {x, 0, 1}]
>
>
> SphericalPlot3D[1, {t, 0, 2 Pi}, {p, 0, Pi},  ColorFunction ->
>   Function[{x, y, z, t, p, r}, Hue[f[t, p]]],  Mesh -> 10,
> MeshFunctions ->
>   {Function[{x, y, z, t, p, r}, f[t, p]]}]
>
>
> Bob Hanlon
>
>
> On Wed, Jul 25, 2012 at 2:33 AM, Bla=BE Kranjc
> <blaz.kranjc91 at gmail.com>
> wrote:
> > Hello,
> > I have a problem in which I need to evaluate a function on the the
> surface of the sphere. I've used ColorFunction and MeshFunctions
> before, but they seem to work only on analicial functions, my function
> is numerical integration in given point and returns a number. Is there
> any way to plot that kind of graph (colored sphere depending on a
> value) or can anybody suggest other ways to represent this.
> >
> > Thank you,
> >
> > Bla=C5=BE Kranjc
> >
>

```

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