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MathGroup Archive 2009

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Re: Extracting Graphics3D from Plots


It's not difficult as long as you pay attention to the InputForm of  
your Graphic3D object. Usually it will contain a GraphicsComplex  
primitive, which makes this particularly easy. Here is an example

Here is a Grpahics3D object from the Documentation obtained by using  
RevolutionPlot3D

gr = RevolutionPlot3D[t^4 - t^2, {t, 0, 1}]

Here is the rotation transform:

tt = RotationTransform[Pi/3, {0, 1, 0}];

Now rotate gr:

gr1 = gr /. v__GraphicsComplex :> GeometricTransformation[v, tt];

Now show it with the option PlotRange set to All:

Show[gr1, PlotRange -> All]

Andrzej Kozlowski



On 23 Jan 2009, at 11:07, Ernst H.K. Stelzer wrote:

> Dear Mathematicans,
>
> a problem I have been struggling for quite a while is how to extract  
> a manipulatable Graphics3D object from the result of e.g. a Plot3D  
> or RevolutionPlot3D call.  By manipulatable I mean an object I can  
> rotate or translate using "RotationTransform" and then combine with  
> other objects such as "Cylinder".  What I do not intend to do is use  
> "Epilog" in a Plot3D call.
>
> I am actually looking for the CORRECT Mathematica-way, i.e. the one  
> anticipated by the Wolfram people and not some workaround that might  
> fail in future versions of Mathematica.
>
> Somewhat related is another question.  Is it possible to put a  
> texture on a "Cylinder", "Tube" or "Cone"?  I do know how to place  
> an image onto the surface of a Plot3D output (in a seemingly correct  
> Mathematica way, see below).
>
> Greetings
>
> 	Ernst
>
>
>
> img = Import["ExampleData/rose.gif"]
>
> imgS = Rasterize[img, "Data", RasterSize -> {32, 32}]/255.0;
>
> Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}, =
>
> ColorFunction -> (RGBColor[
>     imgS[[1 + Round[10 #1], 1 + Round[10 #2]]]] &), =
>
> ColorFunctionScaling -> False, Mesh -> False, PlotPoints -> 32]
>
>



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