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MathGroup Archive 2000

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Re: Not drawing lines at polygon edges, in ParametricPlot3D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21957] Re: [mg21947] Not drawing lines at polygon edges, in ParametricPlot3D
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sat, 5 Feb 2000 22:22:24 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

>As the subject header says ... how can I render a ParametricPlot3D, but not
>have the lines drawn at the polygon edges? I've tried every obvious (to me)
>option, but no dice.
>
>Also, can I make my 3D object transparent, in ParametricPlot3D?
>
>Thanks in advance,
>
>Aram
>


Aram,

If you look at the third form of ParametricPlot3D in Help you will see that there is
a provision for adding a color specification s to a parametric surface. But actually
you can put any kind of 3D graphics directive, or list of directives there. So you
can put EdgeForm[] which specifies that edges not be rendered. Thus:

ParametricPlot3D[{fx, fy, fz, EdgeForm[]}, ...]

As for making a surface transparent, the only method within Mathematica that I know
is to use a WireFrame which is in the Shapes package. However, it is somewhat
convoluted to use.

I have a package, DrawingCube (and also DrawingPaper for 2D graphics) which makes
it a lot easier. There you could make a first surface a wireframe and have a second
surface which is not a wireframe by the following statement:

Show[Graphics3D[{
    UseWireFrame[ParametricDraw3D[{fx, fy, fz}, ...]],
    EdgeForm[],ParametricDraw3D[{gx, gy, gz}, ...],
]}, options...]

This way you can paste together any number of parametric surfaces, with different
parametric ranges and different directives.

Another feature which is useful in this respect is a routine IteratorSubstitution
which allows you to transform a parametrization with variable ranges to one with
fixed ranges (which is required for plotting.) This is useful when you have one
surface which is to extend to its line of intersection with a second surface. The
illustration on my home page gives an example of using these techniques and the
tutorial shows how the plot was produced.

You can down load the packages from my web site below.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/













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