Re: Plotting surface with thickness

• To: mathgroup at smc.vnet.net
• Subject: [mg100977] Re: [mg100915] Plotting surface with thickness
• From: "David Park" <djmpark at comcast.net>
• Date: Thu, 18 Jun 2009 20:50:39 -0400 (EDT)
• References: <322649.1245316788499.JavaMail.root@n11>

```top[x_, y_] := Sin[x y]
bottom[x_, y_] := Sin[x y] - 0.5

You could try something like the following:

RegionPlot3D[
bottom[x, y] < z < top[x, y] \[And] -1 < x < 1 \[And] -1 < y <
1, {x, -1, 1}, {y, -1, 1}, {z, -2, 1}]

But that looks more like a cushion than a thick surface. So with the
Presentations package I would get a nice crisp thick surface by drawing all
of the sides.

Needs["Presentations`Master`"]

Draw3DItems[
{(* Draw the top and bottom *)
Orange,
Draw3D[top[x, y], {x, -1, 1}, {y, -1, 1}, Mesh -> None],
Draw3D[bottom[x, y], {x, -1, 1}, {y, -1, 1}, Mesh -> None],
(* Draw the four sides *)
Brown,
ParametricDraw3D[{x, -1, z}, {x, -1, 1}, {z, bottom[x, -1],
top[x, -1]}, Mesh -> None],
ParametricDraw3D[{x, 1, z}, {x, -1, 1}, {z, bottom[x, 1],
top[x, 1]}, Mesh -> None],
ParametricDraw3D[{-1, y, z}, {y, -1, 1}, {z, bottom[-1, y],
top[-1, y]}, Mesh -> None],
ParametricDraw3D[{1, y, z}, {y, -1, 1}, {z, bottom[1, y],
top[1, y]}, Mesh -> None]},
NeutralLighting[0, .5, .1],
NiceRotation,
Boxed -> False,
ImageSize -> 350]

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

From: Bill [mailto:WDWNORWALK at aol.com]

Plotting surface with thickness

Hi:

Using the following code with Mathematica 5.2 works without any problem.
Using it with Mathematica 6.0.1 doesn't work.

top = Plot3D[Sin[x y], {x, -1, 1}, {y, -1, 1}]

bottom = Plot3D[Sin[x y] - 0.5, {x, -1, 1}, {y, -1, 1}]

g = Plot[{Sin[x y], Sin[x y] - 0.5} /. y -> -1 // Evaluate, {x, -1, 1}]

(* Mathematica 5.2 works with the following line, Mathematica 6.0.1 does
not. *)

front = Graphics3D[
Polygon[Insert[#, -1, 2] & /@
Join[g[[1, 1, 1, 1, 1]], Reverse[g[[1, 2, 1, 1, 1]]]]]]

Question: How can the code (front) be modified to run in Mathematica 6.0.1?

Thanks,

Bill

Ref:  http://forums.wolfram.com/student-support/topics/7384

```

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