       Re: RE: Avoid meshing

• To: mathgroup at smc.vnet.net
• Subject: [mg18143] Re: [mg18119] RE: [mg17352] Avoid meshing
• From: John Fultz <jfultz at wolfram.com>
• Date: Fri, 18 Jun 1999 00:51:44 -0400
• Organization: Wolfram Research, Inc.
• References: <199906171626.MAA20141@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```Actually, Mesh is quite versatile if you use the MeshStyle

Making a gray mesh with Plot3D:
Plot3D[Sin[x y],{x,0,3},{y,0,3},
MeshStyle->{GrayLevel[0.6]}];

Making a gray mesh with DensityPlot:
DensityPlot[f,{x,xmin,xmax},{y,ymin,ymax},
MeshStyle->{GrayLevel[0.6]}];

John Fultz
Front End Group
Wolfram Research, Inc.

Ersek, Ted R wrote:
>
:
:
> Notice EdgeForm is much more versatile than the Mesh option. Consider the
> next line where the shade of the polygon edges is a function of (r).
>
> In:=
>  ParametricPlot3D[{r*Cos[phi],r*Sin[phi],0,
>     {EdgeForm[GrayLevel[r]],RGBColor[1,0,0]}},
>     {phi,0,Pi/2},{r,0,1},Lighting->False
>    ];
>
> --------------
> In the next line two graphic directives are used inside EdgeForm.  In this
> case
>   EdgeForm[{d1,d2}] must be used.
>
>
> In:=
>  ParametricPlot3D[{r*Cos[phi],r*Sin[phi],0,
>
> {EdgeForm[{GrayLevel[r-2],AbsoluteThickness}],RGBColor[(4-r)/2,0,0]}},
>     {phi,0,Pi/8},{r,2,3},Lighting->False,PlotPoints->6
>    ];
>
> --------------------
>
> The usage message for EdgeForm suggests it can be used with Graphics3D
> expressions.  This can be demonstrated with one of the standard packages.
>
> In:=
> <<Graphics`Shapes`
>
> The next two lines respectively make a torus with no edges and then with
> gray edges.
>
> In:=
>   Show[Graphics3D[{EdgeForm[], Torus[ ] }]];
>
>
> In:=
>   Show[Graphics3D[{EdgeForm[GrayLevel[0.6]], Torus[ ] }]];
>
> --------------------
>
> I found it's a little difficult to get a gray mesh using Plot3D.
> I was able to do it with the code below.
>
> In:=
> Block[{\$DisplayFunction=Identity},
>  gr=Plot3D[Sin[x y],{x,0,3},{y,0,3}]];
> Show[Graphics3D[{EdgeForm[GrayLevel[0.6]],Part[Graphics3D[gr],1]}],
>  Axes->True,BoxRatios->{1,1,0.4}];
>
> --------------------
>
> Now how do you make a DensityPlot with a gray mesh?
> That's also tricky.  I haven't bothered to work it out, but you could use
>  Block[{\$DisplayFunction=Identity},
>  densty=DensityPlot[f,{x,xmin,xmax},{y,ymin,ymax},Mesh->False]]
>
> Then use the parts of (densty) to make a gray mesh made of 2D primitives and
> directives, and display the two using
>  Show[densty, GrayMesh]
>
> ---------------------
>
> Regards,
> Ted Ersek

```

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