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MathGroup Archive 2002

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RE: How to suppress the mesh in ParametricPlot3D ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35278] RE: [mg35266] How to suppress the mesh in ParametricPlot3D ?
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sat, 6 Jul 2002 05:44:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Jos,

This is a frequent question on MathGroup. And rightly so because in this
case the standard graphics paradigm is awkward and confusing. First, Mesh
has nothing to do with it. Mesh is an option for SurfaceGraphics (Plot3D and
DensityPlot) and has nothing to do Graphics3D. That is the confusing part.
The proper method is to set EdgeForm[] for the surface. EdgeForm is a
directive that tells how the polygon edges in the surface are to be
rendered. EdgeForm[] directs that the edges are not to be drawn.

But, how do you sneak EdgeForm in? That is the awkward part. The most direct
way is to use the second form of ParametricPlot3D. You add the graphics
directives for the surface as a 4'th "coordinate" in the parametrization.
(You could have a list of directives.)

sphere2 = {Sin[v]Cos[u], Sin[v]Sin[u], Cos[v], EdgeForm[]};

Then use normal ParametricPlot3D.

ParametricPlot3D[sphere2 // Evaluate, {u, 0, 2 Pi}, {v, 0, Pi},
    PlotPoints -> 50];

If you want to work with the regular parametrization of the sphere...

sphere = {Sin[v]Cos[u], Sin[v]Sin[u], Cos[v]};
plot1 = ParametricPlot3D[sphere // Evaluate, {u, 0, 2 Pi}, {v, 0, Pi},
      PlotPoints -> 50];

Extract the First part of plot 1, which contains the primitive graphics for
the sphere and combine it with EdgeForm[].

Show[Graphics3D[{EdgeForm[], First[plot1]}],
    Axes -> True];

The DrawGraphics package at my web site handles it in a slightly more
natural matter. You just give the directives you want and then draw the
surface you want. You could combine a number of different surfaces with
different directives in that manner, adding one after the other.

Needs["DrawGraphics`DrawingMaster`"]

Draw3DItems[
    {EdgeForm[],
      ParametricDraw3D[sphere // Evaluate, {u, 0, 2 Pi}, {v, 0, Pi},
        PlotPoints -> 50]},
    Axes -> True];

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


> -----Original Message-----
> From: Jos R Bergervoet [mailto:antispam at nospam.com]
To: mathgroup at smc.vnet.net
> Sent: Friday, July 05, 2002 2:21 AM
> Subject: [mg35278] [mg35266] How to suppress the mesh in ParametricPlot3D ?
>
>
> How can I get a partametric 3D plot without gridlines on it? I tried
> "Mesh -> False" (also SurfaceMesh) but to no avail!
>
>
>   sphere = {Sin[v]Cos[u], Sin[v]Sin[u], Cos[v]}
>
>   ParametricPlot3D[sphere, {u,0,2Pi}, {v, 0,Pi}, PlotPoints -> 50]
>                                                    (* OK, but meshed *)
>
>   ParametricPlot3D[sphere, {u,0,2Pi}, {v, 0,Pi},
>        PlotPoints -> 50, Mesh -> False]            (* not accepted *)
>
>
> Thanks for any clues,
>
> Jos
>



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