Re: 3D graphs with constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg49785] Re: 3D graphs with constraints
• From: Daniel Herring <dherring at at.uiuc.dot.edu>
• Date: Sat, 31 Jul 2004 03:14:04 -0400 (EDT)
• References: <cdj1p9\$nap\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Mario Biondini wrote:
> In need to plot a function f[r,l] but only within the following domain
> for r, and l: a<r<b and l < v/(pi*r^2) where a, b, and v are constants.
> Any idea of how to do that.

Plot3D doesn't like that variable range on l...
Would something like the following work for you?

a = -1/2;
b = 1/2;
v = 2;
f[r_, l_] := Sin[r] Cos[l];
Plot3D[If[ l<v/(Pi*r^2), f[r, l], -10000],
{l, 0, 40}, {r, a, b},
PlotRange -> {{0, 40}, {-1/2, 1/2}, {-1, 1}},
Mesh -> False, PlotPoints -> 100]

Basically, the added If statement sets the function to an invalid low
level outside the region of interest.  The PlotRange option keeps this
extreme low from ruining the scaling of the plot.  The other options
allow for a visually pleasing edge.

Hope that helps,
Daniel

```

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