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MathGroup Archive 2007

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From 3D to 2D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84128] From 3D to 2D
  • From: giovanni resta <g.restaCUT at CUTiit.cnr.it>
  • Date: Mon, 10 Dec 2007 22:20:15 -0500 (EST)

Probably this will seem a stupid question...

I wonder if there is a way to do the following:

create a simple 3D graphics  made of
lines and points, maybe rotate it to
choose a good point of view, then:

generate the 2D directives that will produce
a 2D graphic that mimic the given 3D graphic,
or even better, obtain, for each line or point
in 3D the corresponding "visual" coordinates
in 2D.

I don't know if I have been clear enough.
I explain what I'm doing.

For what I need currently,
I use Mathematica not to produce the final images, but to obtain
in a fast and nice way the set of coordinates for my figures.
For example, if I want to draw a Graph, say
GraphPlot[Table[k -> Mod[Prime[k], k], {k, 20}]]
I exploit the very nice GraphPlot, then the
capability of editing in a visual way the graph,
and then when I'm satisfied with the obtained layout,
by using some simple custom functions,
I convert the graph in simple primitives for
the very good pgf Latex package.
This machinery may seem complicated (since Mathematica
can indeed produce wonderful pictures) but I
like to be able to modify my simple b&w drawings later,
on a machine where Mathematica is not available,
for example to fine-tuning the line width depending on the
printer, or the apparence of the nodes of the graph and so on...

Now I wonder if I can do something similar
in 3D. For example:  issue to Mathematica some
Line[] or Cuboid[] commands to draw a cube in 3D and then
obtain back in some way the 2D lines that when
plotted in 2D will create the same scene. All I probably
need is wireframe, but some hidden edge removal will
be nice...

I apologize for the verbosity,
thanks
giovanni.


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