Re: 3D Solids

• To: mathgroup at smc.vnet.net
• Subject: [mg114314] Re: 3D Solids
• From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
• Date: Tue, 30 Nov 2010 06:23:39 -0500 (EST)

```Hi, Brien,

One rather simple way to do it is to use the graphic primitives. For
example, here is your case with the cylinders, one of the bored is
filled another is empty. Please have a look:

cyl1 = Graphics3D[{Opacity[0.7], Cylinder[{{0, 0, 0}, {0, 0, 3}}, 2]}];
cyl2 = Graphics3D[{EdgeForm[Directive[Thick, Blue]], Opacity[0.3],
White, Cylinder[{{-2., 0, 0.5}, {2., 0, 0.5}}, 0.2]}];
cyl3 = Graphics3D[{EdgeForm[Directive[Thick, Blue]], Yellow,
Cylinder[{{0, -2, 1.5}, {0, 2, 1.5}}, 0.1]}];
Show[{cyl1, cyl2, cyl3}]

Execute this in your notebook and play with options, such as Opacity,
characteristics of the EdgeForm and colors until you get what you may
have imagined.

Concerning your question on spiral axis, I do not clearly understand
what do you have in mind (since the term "spiral axis" may be used in
several meanings), but seems that GeometricTransformation should help.
Have a look into Help/GeometricTransformation. You can also combine the
GeometricTransformation with graphics primitives.

Have fun, Alexei

Hi all,

I'm exploring Mathematica as a tool to design 3D solids. The shape I'm
working on now is a cylindric solid with a few cylinders bored out of
the side (like screw holes into a cylinder). So far, I've figured out
that I can use RegionPlot3D to do this, since the shape specification
is a boolean expression. However, since RegionPlot3D is based on
sampling, sometimes artifacts show up in the model. Since I have
expressions for all the surfaces, I'm thinking that adding /
subtracting 3D solids "at the mesh level" would be better.  Are there
functions in Mathematica to specify 3D solids? For example, a
rectangle twisted around a spiral axis (for threading). I'm wondering
if anyone has experience doing this kind of thing in Mathematica. I'd
love to hear your approach and tools of choice.

TIA, Brien

--
Alexei Boulbitch, Dr. habil.
Senior Scientist
Material Development

IEE S.A.
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