       RE: remicing the mesh in ParamtericPlot3D

• To: mathgroup at smc.vnet.net
• Subject: [mg32111] RE: [mg32102] remicing the mesh in ParamtericPlot3D
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 27 Dec 2001 03:34:13 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Eric,

Yes, you can remove the mesh. But the regular Mathematica method is, to my
mind, a little ackward.

Here is a parametrization of a sphere and a plot using ParametricPlot3D.

sphere[p_, t_] := {Cos[t]Cos[p], Sin[t]Cos[p], Sin[p]}
ParametricPlot3D[Evaluate[sphere[p, t]], {p, -Pi/2, Pi/2}, {t, 0, 2Pi}];

To get with of the so-called "mesh" you really have to use EdgeForm[] and
put it in the fourth argument of the parametrization. In other words, you
have to reparametrize.

sphere2[p_, t_] := {Cos[t]Cos[p], Sin[t]Cos[p], Sin[p], EdgeForm[]}
ParametricPlot3D[Evaluate[sphere2[p, t]], {p, -Pi/2, Pi/2}, {t, 0, 2Pi}];

It is much easier using my DrawGraphics package (at my web site). You just
put any graphics directives before the ParametricDraw3D command.

Needs["DrawGraphics`DrawingMaster`"]

Draw3DItems[
{EdgeForm[],
ParametricDraw3D[
Evaluate[sphere[p, t]], {p, -Pi/2, Pi/2}, {t, 0, 2Pi}]},
Axes -> True];

DrawGraphics also has routines that allow you to smoothly fit together a
number of surfaces at curved edges.

If you need many plot points to obtain a smooth surface but want a courser
"mesh" then there is a very nice package called Smooth3D done by Allan Hayes
and Hartmut Wolf. The package can be obtained from the MathGroup archives:

http://library.wolfram.com/mathgroup/archive/2001/May/msg00292.html

David Park

> From: Erich Neuwirth [mailto:erich.neuwirth at univie.ac.at]
To: mathgroup at smc.vnet.net
>
> can the mesh in a ParametricPlot3D be removed?
> The returned value is not a Surface object, bt a Graphics3D object.
>
> --
> Erich Neuwirth, Computer Supported Didactics Working Group