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MathGroup Archive 1998

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RE: Mesh on graphics3D objects

  • To: mathgroup at
  • Subject: [mg14359] RE: [mg14327] Mesh on graphics3D objects
  • From: "Ersek, Ted R" <ErsekTR at>
  • Date: Thu, 15 Oct 1998 00:29:00 -0400
  • Sender: owner-wri-mathgroup at

Scott Morrison (scott at wrote:
>I am trying to plot a complicated surface in Mathematica, using
>ParametricPlot3D or SurfaceListPlot3D (from Graphics`Graphics3D`).
>These both produce Graphics3D objects.
>I am trying to remove the mesh drawn over the surface (for Plot3D this
>is easily acheived with Mesh->False). Does anyone know how to do this?
>I can't work out anything!

Allan Hayes posted the following to the Mathgroup on 5/25/98 in 
[mg12588] Re: About plotting a surface.

ParametricPlot3D[{x,y,Sin[x+ Sin[y]], EdgeForm[]},{x,0,6},{y,0,6}]


Allan Hayes also posted the following to the Mathgroup on 5/30/98 in 
[mg12655] Re: About plotting a surface.

Graphics3D[{EdgeForm[],c/._EdgeForm :>Sequence[]},rest]

The code above is a more robust (and a bit more complicated) than a
version Roman-Meader gave in 
The Mathematica Journal 2(3), 32.  This version is more robust because
it will get rid of any EdgeForm directives that may be present.


P.J. Hinton posted the next solution to the Mathgroup on 5-25-98 in 
[mg12570]Re: About plotting a surface.

The graphics generated by Plot3D[] are represented by Mathematica as
SurfaceGraphics objects, for which Mesh is a valid option.  Surfaces
generated by ParametricPlot3D[] are represented internally with more
general Graphics3D objects, which do not support a Mesh option.  The
elimination of lines can be achieved through the EdgeForm[] directive,
which is used to modify the Polygon[] primitives in the Graphics3D

Here is an example using a ParametricPlot3D[]-generated sphere


gr = (ParametricPlot3D[
  {Cos[u] Cos[v], Sin[u] Cos[v], Sin[v]},
    {u, 0, 2Pi, Pi/20},
    {v, -Pi/2, Pi/2, Pi/10}, DisplayFunction -> Identity] /. 
      Polygon[x_] -> {EdgeForm[], Polygon[x]} )

Show[gr, DisplayFunction -> $DisplayFunction]

The operation above uses ReplaceAll[] (/.) to place all Polygon[]
primitives inside of lists which contain a null argument EdgeForm[]

See Section 2.9.9 of _the Mathematica Book_ for details.

You can also paste the following ButtonBox[] in a Mathematica notebook
to create a hyperlink that will point you to the relevant section.

    ButtonBox[\(Using\ the\ EdgeForm\ directive\),
      ButtonData:>{"2.9.9", "9.14"},

Ted Ersek

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