Thought I'd share this with you all.
IMNSHO it's the best rendering of (part of) the Barth Decic that I've seen 
for a while.

For the record:
#declare a=1.0
#declare GM=(sqr(5)+1)/2
#declare GM4=pow(GM, 4)

function(x,y,z,a) {
 8*(pow(x, 2)-GM4*pow(y, 2))*(pow(y, 2)-GM4*pow(z, 2))*(pow(z, 2)-
 GM4*pow(x, 2))*(pow(x, 4)+pow(y, 4)+pow(z, 4)-2*pow(x, 2)*
 pow(y, 2)-2*pow(x, 2)*pow(z, 2)-2*pow(y, 2)*pow(z, 2))+(3+5*GM)
 *pow((pow(x, 2)+pow(y, 2)+pow(z, 2)-pow(a, 2)),2)*pow((pow(x, 2)
 +pow(y, 2)+pow(z, 2)-(2-GM)*pow(a, 2)),2)*pow(a, 2)
}

max_gradient 25060
contained_by{sphere {0, 1.9}}


...and the texture:
texture {
 pigment {
  aoi <3, 1, 3>
  color_map {
   [0 color rgb <1.0,0.4,0.25>]
   [0.8 color rgb <0.15,0.25,0.9>]
  }
 }
 finish {
  ambient 0
  diffuse 0.7
  specular 0.16
 }
}

Must be rendered using Megapov >=1.1

John
-- 
Run Fast
Run Free
Run Linux

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Attachments:
Download 'Decic.jpg' (82 KB)

Preview of image 'Decic.jpg'

Doctor John wrote:
> Thought I'd share this with you all.
> IMNSHO it's the best rendering of (part of) the Barth Decic that I've seen 
> for a while.
> 
> For the record:
> #declare a=1.0
> #declare GM=(sqr(5)+1)/2
> #declare GM4=pow(GM, 4)
> 
> function(x,y,z,a) {
>  8*(pow(x, 2)-GM4*pow(y, 2))*(pow(y, 2)-GM4*pow(z, 2))*(pow(z, 2)-
>  GM4*pow(x, 2))*(pow(x, 4)+pow(y, 4)+pow(z, 4)-2*pow(x, 2)*
>  pow(y, 2)-2*pow(x, 2)*pow(z, 2)-2*pow(y, 2)*pow(z, 2))+(3+5*GM)
>  *pow((pow(x, 2)+pow(y, 2)+pow(z, 2)-pow(a, 2)),2)*pow((pow(x, 2)
>  +pow(y, 2)+pow(z, 2)-(2-GM)*pow(a, 2)),2)*pow(a, 2)
> }
> 
> max_gradient 25060
> contained_by{sphere {0, 1.9}}
> 
> 
> ...and the texture:
> texture {
>  pigment {
>   aoi <3, 1, 3>
>   color_map {
>    [0 color rgb <1.0,0.4,0.25>]
>    [0.8 color rgb <0.15,0.25,0.9>]
>   }
>  }
>  finish {
>   ambient 0
>   diffuse 0.7
>   specular 0.16
>  }
> }
> 
> Must be rendered using Megapov >=1.1
> 
> John
> 

Spiny...

On another note... Anybody: Is there a way to duplicate the aoi pattern 
w/ the official POV-Ray?

-- 
~Mike

Things! Billions of them!

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"Mike Raiford" <mra### [at] hotmailcom> wrote in message 
news:433be6a8$1@news.povray.org...
>
> Spiny...
>
> On another note... Anybody: Is there a way to duplicate the aoi pattern w/ 
> the official POV-Ray?
>
Tough, Mike, you gotta get Megapov. It's not difficult to install.
hop over to http://megapov.inetart.net/ and away you go...
btw - make sure you get the latest version (1.2.1 at time of writing)

John
-- 
Run Fast
Run Free
Run Linux

Post a reply to this message

Doctor John wrote:
> "Mike Raiford" <mra### [at] hotmailcom> wrote in message 
> news:433be6a8$1@news.povray.org...
>> Spiny...
>>
>> On another note... Anybody: Is there a way to duplicate the aoi pattern w/ 
>> the official POV-Ray?
>>
> Tough, Mike, you gotta get Megapov. It's not difficult to install.
> hop over to http://megapov.inetart.net/ and away you go...
> btw - make sure you get the latest version (1.2.1 at time of writing)
> 
> John

I have MegaPOV, I'm just looking for an alternative.

-- 
~Mike

Things! Billions of them!

Post a reply to this message

> On another note... Anybody: Is there a way to duplicate the aoi pattern
> w/ the official POV-Ray?

You can fake it with the slope pattern if you're only going to see the
object from one direction (no reflections).

 - Slime
 [ http://www.slimeland.com/ ]

Post a reply to this message

Slime wrote:
>> On another note... Anybody: Is there a way to duplicate the aoi
>> pattern w/ the official POV-Ray?
>
> You can fake it with the slope pattern if you're only going to see the
> object from one direction (no reflections).

This works best with small camera angles though. Technically it only works 
perfectly with an orthographic camera.

Rune
-- 
3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com
POV-Ray Ring: http://webring.povray.co.uk

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Doctor John schreef:
> Thought I'd share this with you all.
> IMNSHO it's the best rendering of (part of) the Barth Decic that I've seen 
> for a while.
> 
> For the record:
> #declare a=1.0
> #declare GM=(sqr(5)+1)/2
> #declare GM4=pow(GM, 4)
> 
> function(x,y,z,a) {
>  8*(pow(x, 2)-GM4*pow(y, 2))*(pow(y, 2)-GM4*pow(z, 2))*(pow(z, 2)-
>  GM4*pow(x, 2))*(pow(x, 4)+pow(y, 4)+pow(z, 4)-2*pow(x, 2)*
>  pow(y, 2)-2*pow(x, 2)*pow(z, 2)-2*pow(y, 2)*pow(z, 2))+(3+5*GM)
>  *pow((pow(x, 2)+pow(y, 2)+pow(z, 2)-pow(a, 2)),2)*pow((pow(x, 2)
>  +pow(y, 2)+pow(z, 2)-(2-GM)*pow(a, 2)),2)*pow(a, 2)
> }
> 
> max_gradient 25060
> contained_by{sphere {0, 1.9}}
> 
> 
> ...and the texture:
> texture {
>  pigment {
>   aoi <3, 1, 3>
>   color_map {
>    [0 color rgb <1.0,0.4,0.25>]
>    [0.8 color rgb <0.15,0.25,0.9>]
>   }
>  }
>  finish {
>   ambient 0
>   diffuse 0.7
>   specular 0.16
>  }
> }
> 
> Must be rendered using Megapov >=1.1
> 
> John
Barth's SEXTIC is a surface with 65 double points. It's interesting to 
know that 20 of these double points are the vertices of a regular 
dodecahedron and 30 other double points are the midpoints of the edges 
of another regular dodecahedron. Both dodecahedra have the same center 
and the edges are parallel. I have illustrated this property in a small 
animated gif.
I used the "poly" representation of the surface and not "function".
More images can be seen here:
http://cage.ugent.be/~hs

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Attachments:
Download 'animbarth04d.gif' (443 KB)

Preview of image 'animbarth04d.gif'

hermans wrote:
> Barth's SEXTIC is a surface with 65 double points. It's interesting to 
> know that 20 of these double points are the vertices of a regular 
> dodecahedron and 30 other double points are the midpoints of the edges 
> of another regular dodecahedron. 

And the other five?

-- 
Anton Sherwood, http://www.ogre.nu/
"How'd ya like to climb this high *without* no mountain?" --Porky Pine

Post a reply to this message

Anton Sherwood schreef:
> hermans wrote:
> 
>> Barth's SEXTIC is a surface with 65 double points. It's interesting to 
>> know that 20 of these double points are the vertices of a regular 
>> dodecahedron and 30 other double points are the midpoints of the edges 
>> of another regular dodecahedron. 
> 
> 
> And the other five?
> 
That's an interesting question, but I can't give the answer. Perhaps 
somebody else can help.
As mentioned in a link on my page concerning this surface, Barth's 
sextic is a 6th degree surface that has the maximum number of double 
points (65) a 6th degree surface can have.

http://cage.ugent.be/~hs

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Wasn't it hermans who wrote:
>Anton Sherwood schreef:
>> hermans wrote:
>> 
>>> Barth's SEXTIC is a surface with 65 double points. It's interesting to 
>>> know that 20 of these double points are the vertices of a regular 
>>> dodecahedron and 30 other double points are the midpoints of the edges 
>>> of another regular dodecahedron. 
>> 
>> 
>> And the other five?
>> 
>That's an interesting question, but I can't give the answer. Perhaps 
>somebody else can help.
>As mentioned in a link on my page concerning this surface, Barth's 
>sextic is a 6th degree surface that has the maximum number of double 
>points (65) a 6th degree surface can have.

I spent a while trying to imagine how such a symmetric object could have
an extra 5 points that formed any sort of symmetrical pattern, and
became pretty well convinced that it can't happen.

Then I noticed that 65 - 30 - 20 = 15.

However, I still can't find them, and can't think of any symmetrical
patterns of 15 points that don't have a point at the centre.

-- 
Mike Williams
Gentleman of Leisure

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