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Re: 2D Plot for a face of a 3D plot box?

• To: mathgroup at smc.vnet.net
• Subject: [mg122870] Re: 2D Plot for a face of a 3D plot box?
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Sun, 13 Nov 2011 07:17:59 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111130943.EAA00017@smc.vnet.net>

You could use MeshFunctions to draw curves on a 3D surface. For example

f[x_, y_] := Sin[x y];
Plot3D[f[x, y], {x, 0, 2 Pi}, {y, 0, 2 Pi}, PlotPoints -> 40,
 MeshFunctions -> Function[{x, y, z}, (x - Pi)^2 + (y - Pi)^2],
 Mesh -> {{4}},
 MeshStyle -> {Thick, Blue}]

Alternatively, you could use ParametricPlot3D to draw the curve 
separately and use Show to combine the plots, e.g.

Show[{Plot3D[Sin[x y], {x, 0, 2 Pi}, {y, 0, 2 Pi}, Mesh -> None, 
PlotPoints -> 40],
  ParametricPlot3D[{Pi + 2 Cos[t], Pi + 2 Sin[t], f[Pi + 2 Cos[t], Pi + 
2 Sin[t]]},
   {t, 0, 2 Pi},
   PlotStyle -> {Thick, Blue}]}]

You can also use this method to plot graphs on the bounding box of a 3D 
plot. For example

With[{bb = {{0, 2 Pi}, {0, 2 Pi}, {-1.5, 1.5}}},
 Show[{
   Plot3D[Sin[x y], {x, 0, 2 Pi}, {y, 0, 2 Pi}, Mesh -> None, PlotPoints 
-> 40],
   ParametricPlot3D[{Pi + 2 Cos[t], Pi + 2 Sin[t], bb[[3, -1]]},
    {t, 0, 2 Pi},
    PlotStyle ->  {Thick, Red}]},
  PlotRange -> bb]]

Heike

On 13 Nov 2011, at 10:43, Brentt wrote:

> Hello,
>
> Is there a way to have a 2D plot on a face of the bounding box of a 3D
> surface plot? Only ordered pairs in the 2D function would have any opacity
> of course, so the view of the 3D surface won't be obstructed.

• References:
  • 2D Plot for a face of a 3D plot box?
    • From: Brentt <brenttnewman@gmail.com>