       Re: ListSphericalDensityPlot[] ??

• To: mathgroup at smc.vnet.net
• Subject: [mg64546] Re: ListSphericalDensityPlot[] ??
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Wed, 22 Feb 2006 05:58:29 -0500 (EST)
• Organization: Uni Leipzig
• References: <dte2gk\$rjm\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

make a Graphics[] object out of your density plot
and
than transform the polygons, i.e,
gr = DensityPlot[
Re[SphericalHarmonicY[4, 2, th, phi]], {th,
0, Pi}, {phi, 0, 2Pi},
PlotPoints -> {64, 128}] // Graphics;

gg = gr /. Raster[bm_, {{x1_, y1_}, {x2_, y2_}},
{z1_, z2_}, ___] :>
Block[{n, m, dx, dy, poly},
{n, m} = Dimensions[bm];
dx = (x2 - x1)/m; dy = (y2 - y1)/n;
poly[{j_, i_}] := Block[{p}, p =
{x1, y1} + {dx, dy}*{i - 1, j - 1};
Polygon[{p, p + {dx, 0}, p + {dx,
dy}, p + {0, dy}}]];
MapIndexed[{GrayLevel[(#1 -
z1)/(z2 - z1)], poly[#2]} &, bm, {2}]
];

Show[Graphics3D[{EdgeForm[],
gg[]} /. {(h : (Polygon | Line))[pnts_] :>
Polygon[{Cos[#[]]*Sin[#[]],
Sin[#[]]*Sin[#[]],
Cos[#[]]} & /@ pnts],
GrayLevel[g_] :> SurfaceColor[Hue[g]]}
]
];

Regards

Jens

"Bob Buchanan" <Bob.Buchanan at millersville.edu>
schrieb im Newsbeitrag
news:dte2gk\$rjm\$1 at smc.vnet.net...
| Hello,
|
| I have numerically approximated the omega-limit
set of a model of a spherical, magnetic pendulum.
For a grid of theta and phi coordinates on the
unit sphere I have numerically solved the
Hamiltonian system of ODEs governing the pendulum
until it comes to rest (or pretty close to rest).
The data is in the form of a rectangular array
which I can easily display as a rectangular list
density plot.
|
| Is there a way to wrap this density plot back
around the surface of the unit sphere ---
something like a ListSphericalDensityPlot[]
function?
|
| I don't think there is an already defined
function to perform this type of operation. Is
there an easy way to do it myself?
|
| Thanks for any suggestions.
|
| Bob Buchanan
| Bob.Buchanan at millersville.edu
|

```

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