Re: To color surfaces using z values with ContourPlot3D

• To: mathgroup at smc.vnet.net
• Subject: [mg23912] Re: To color surfaces using z values with ContourPlot3D
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Fri, 16 Jun 2000 00:56:52 -0400 (EDT)
• References: <8i9ov0\$2dm@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Valeria,

We can add styling instructions to the polygons "from the outside":

eq = 81*(x^3 + y^3 + z^3) -
189*(x^2*y + x^2*z + y^2*x + y^2*z + z^2*x + z^2*y) + 54*x*y*z +
126*(x*y + x*z + y*z) - 9*(x^2 + y^2 + z^2) - 9*(x + y + z) + 1;

sup = ContourPlot3D[eq, {x, -1, 3/2}, {y, -1, 3/2}, {z, -1, 3/2},
PlotPoints -> {5, 7}, Axes -> True, ViewPoint ->
{0.056, -3.382, -0.076},
ContourStyle -> {EdgeForm[GrayLevel[0.6]]}, Lighting -> False]

Define acolor function.

cf[z_] := Hue[(z + 1)/3.5];

Use cf to give styles to the polygons.

sup2 = sup /.{p_Polygon :>
{cf[(Plus @@ (p[[1, All, 3]]))/Length[p[[1]]]], p}
}

Show the result

Show[sup2, AxesLabel -> {x, y, z}]

You might like to look at the furface in simulated lighting with RealTime3D,
it can then be grabbed by the pointer and rotated

<< RealTime3D`

ContourPlot3D[eq, {x, -1, 3/2}, {y, -1, 3/2}, {z, -1, 3/2},
PlotPoints -> {5, 7}, Axes -> True, ViewPoint -> {0.056, -3.382, -0.076},
ContourStyle -> {EdgeForm[]}]

<< Default3D`

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Valeria Olivati" <olivaleNNN at tin.it> wrote in message
news:8i9ov0\$2dm at smc.vnet.net...
> Hallo eveybody,
>
> I'm a student of Mathematics at University of Pavia, Italy.
>
> I start using Mathematica 4 two months ago, and I need to plot a cubic
> function and color it without using LightSources. I use ContourPlot3D to
> plot the function but I don't know how to color the surface using the z
> values, as you can do using Plot3D and ColorFunction->Hue.
> I cannot use Plot3D because the function is quite complicated:
>
> eq = 81*(x^3 + y^3 + z^3) - 189*(x^2*y + x^2*z + y^2*x + y^2*z + z^2*x +
> z^2*y) + 54*x*y*z + 126*(x*y + x*z + y*z) - 9*(x^2 + y^2 + z^2) -
9*(x+y+z)
> + 1
>
> Now I plot this funtion in this way:
>
> sup = ContourPlot3D[eq, {x, -1, 3/2}, {y, -1, 3/2}, {z, -1, 3/2},
> PlotPoints->{5,7}, Axes->True, ViewPoint->{0.056, -3.382, -0.076},
> ContourStyle->{Hue[1], EdgeForm[GrayLevel[0.6]]}, Lighitng->False]
>
> but with only one color It's not a clear shape.
> If I use the following LightSources instead of ConturStyle
>
> LightSources->{{{0,0,0.7}, RGBColor[0,1,0]}, {{1,0,1}, RGBColor[1,1,0]},
> {{-1,0,1}, RGBColor[0,0,1]}, {{-1,0,0}, GrayLevel[1]}}
>
> I don't like the colors I obtain, they are not linked to the surface but
> they are the best LightSources I found after a big number of changes. Of
> course my problem with LightSources is that I haven't understood how they
> work....
>
> I hope someone has suggestions for me
> Thanks a lot
>
> Best Regards
>
> Olivati Valeria
>
>
>

```

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