POV-Ray : Newsgroups : povray.object-collection : Has this interesting isosurface a common name? Server Time: 17 Jun 2019 12:45:40 GMT
  Has this interesting isosurface a common name? (Message 1 to 3 of 3)  
From: Lars R 
Subject: Has this interesting isosurface a common name?
Date: 18 Jan 2012 10:34:54
Message: <4f16a04e@news.povray.org>
I tried to render a 3D version of the quadrifolium
(http://mathworld.wolfram.com/Quadrifolium.html)
but my first try of a 3D variant of its formula does not work. So I
changed the formula arbitrarily and got a nice object, see attachment.

Do anyone know a common name of this nice thing? :-)

		Lars R.


-----<snip>-----
isosurface
{
// does not work:
//	function { pow(x*x + y*y + z*z  , 3) - 12 * x*x * y*y * z*z }

// works and looks interesting:
        function { pow(x*x + y*y + z*z  , 3) - 12 * x*y*z }
        contained_by { box{ -1,+1 } }
        accuracy 0.001
        max_gradient 100


        pigment { color rgb<0.3,0.6,0.9> }
        finish { phong 0.1 reflection 0.2 }

        rotate y*30
}


light_source { <-3,6,-9> color 1
        area_light <0.5,0,0>, <0, 0.5, 0>, 4,4 jitter
}

//light_source { <1,9,-2> color 0.4 }

box
{
        <-9.9,-9.9,-9.9> , <+9.9,+9.9, +9.9>
        pigment { checker color rgb 0.5 color rgb 0.77 }
}

camera
{
        location <0,5,-9>
        look_at <0,0,0>
        angle 20.3
}

-----<snap>-----


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Attachments:
Download 'ok.png' (60 KB)

Preview of image 'ok.png'
ok.png


 

From: Alain
Subject: Re: Has this interesting isosurface a common name?
Date: 18 Jan 2012 21:46:26
Message: <4f173db2@news.povray.org>
Le 2012/01/18 05:34, Lars R. a écrit :
> I tried to render a 3D version of the quadrifolium
> (http://mathworld.wolfram.com/Quadrifolium.html)
> but my first try of a 3D variant of its formula does not work. So I
> changed the formula arbitrarily and got a nice object, see attachment.
>
> Do anyone know a common name of this nice thing? :-)
>
> 		Lars R.
>
>
> -----<snip>-----
> isosurface
> {
> // does not work:
> //	function { pow(x*x + y*y + z*z  , 3) - 12 * x*x * y*y * z*z }
>
> // works and looks interesting:
>          function { pow(x*x + y*y + z*z  , 3) - 12 * x*y*z }
>          contained_by { box{ -1,+1 } }
>          accuracy 0.001
>          max_gradient 100
>
>
>          pigment { color rgb<0.3,0.6,0.9>  }
>          finish { phong 0.1 reflection 0.2 }
>
>          rotate y*30
> }
>
>
> light_source {<-3,6,-9>  color 1
>          area_light<0.5,0,0>,<0, 0.5, 0>, 4,4 jitter
> }
>
> //light_source {<1,9,-2>  color 0.4 }
>
> box
> {
>          <-9.9,-9.9,-9.9>  ,<+9.9,+9.9, +9.9>
>          pigment { checker color rgb 0.5 color rgb 0.77 }
> }
>
> camera
> {
>          location<0,5,-9>
>          look_at<0,0,0>
>          angle 20.3
> }
>
> -----<snap>-----
It looks like the SP hybrid electron orbitals.

Alain


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From: Le Forgeron
Subject: Re: Has this interesting isosurface a common name?
Date: 18 Jan 2012 21:47:46
Message: <4f173e02$1@news.povray.org>
Le 18/01/2012 11:34, Lars R. nous fit lire :
> Do anyone know a common name of this nice thing? :-)
> 
> 		Lars R.

As a 6th order polynomial, it might (unchecked!) be some aspect of Boy's
Surface.

You might enjoy Goursat's dodecaedric surfaces...

http://www.mathcurve.com/surfaces/goursat/goursat.shtml


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