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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Mon Aug 13, 2012 1:24 pm    Post subject: PovRay picture with sdl source Reply with quote

Barths modified Se.xtik surface rendered with PovRay 3.7RC6...

And for those who want to do there own experiments the Povray sdl source...
Code:
//*********************************************************
// Persistence of Vision Ray Tracer Scene Description File
// File:  surface_1311.pov
// Info:  algebraic surface: PG_DecicStar_1
//        http://cage.ugent.be/~hs/barth/barth.html
//        http://mathworld.wolfram.com/BarthDecic.html   
// Date:  14. August 2012
// Prog:  PovRay v3.7 RC6
// Auth:  Gerd Platl
// Time:  0:10:00  640*480  Intel Pentium 2.8 GHz dual core
//*********************************************************
#version 3.6;
#include "colors.inc"
#include "functions.inc"
#include "glass.inc"
global_settings
{ assumed_gamma 1.2
  max_trace_level 6
}
//-------------------------------------------
#declare camPos = < -16, 16, -36>;
camera
{
  location camPos
  look_at  <-2.5, 1, 0>   
  right    x*image_width/image_height
  angle    30
}
//-------------------------------------------
light_source {camPos color White*0.2}
light_source {<+100, 100, -100> color <0.8, 0.8, 0.5>}
light_source {<-100, 100,  -75> color Yellow*0.6}
//-------------------------------------------
plane { <0, 1, 0>, -3.0  texture {pigment {color rgb <0.85, 0.70, 0.50>} } }
//-------------------------------------------
// test containment sphere
//-------------------------------------------
#declare center = <0,1,0>;
//sphere { center 7.5 texture { pigment {rgbt <0.2, 0.2, 1.0, 0.7> } } }
//-------------------------------------------
// algebraic surface: "PG_Se.xtikStar_1"
//-------------------------------------------
#declare gr = (1+sqrt(5))*0.5;   // golden ratio = 1,618033988749895
#declare g2 = gr*gr;             //    g2 = gr^2 = 2,618033988749895

isosurface
{
  function
  { -0.3 -4 * (g2*x*x - y*y)
            * (g2*y*y - z*z)
            * (g2*z*z - x*x)
      + pow((x*x + y*y + z*z - 1),2) * 6
  }
  threshold 0.1
  max_gradient 333
  contained_by { sphere { <0,0,0> 1.5 } }
  pigment {color rgb <0.2, 0.7, 1> }
  texture {
    pigment { color rgb  <0.2, 0.7, 1.0> }   // opaque
    finish { F_Glass10 }
  }
  scale 5.0
  translate (center)
}


Last edited by inode on Thu Dec 27, 2012 2:33 pm; edited 5 times in total
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Furan



Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

PostPosted: Mon Aug 13, 2012 4:27 pm    Post subject: Reply with quote

I wonder if I can use PovRay to render the same object and environment as my engine and then compare the results. How long did this image take to render? Would you be so kind and help me with the settings? I'm heading for a colored glass on black and bright white (glowing) background. Thanks.
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Mon Aug 13, 2012 4:50 pm    Post subject: Reply with quote

It took about 10 minutes to render a picture with a size of 640*480 pixel (see source code at line 'time:').
Using a glass texture will need about 70 minutes.
A complete overview of predefined PovRay textures with picture and source code examples you can get from
http://www.3dplumbing.net/tutorials/textures_guide_POV/th_textures.html
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Furan



Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

PostPosted: Tue Aug 14, 2012 5:58 am    Post subject: Reply with quote

Excellent, thank you !
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sat Dec 08, 2012 10:46 pm    Post subject: About Gyroid Balls... Reply with quote

If you want to play with gyroidal balls you can start with this one...
Btw. this algebraic surface was rendered with PovRay 3.7RC6...

Code:
Name: PG_GyroidBall1
/* Isosurface: PG_GyroidBall1  8/2012 Gerd Platl */
F(): x*x+y*y+z*z -(x*x+y*y+z*z)^2*0.01
     -abs(cos(x)*sin(z) +cos(y)*sin(x) +cos(z)*sin(y))
     -24
[x]: -7.7 , 7.7
[y]: -7.7 , 7.7
[z]: -7.7 , 7.7
;

have fun Wink


Last edited by inode on Thu Dec 27, 2012 2:33 pm; edited 1 time in total
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Thu Dec 27, 2012 2:25 pm    Post subject: formula for a basic meshwork Reply with quote

I have created a formula to generate a basic meshwork.

Code:
Name: PG_Grid_B5
/* Isosurface: PG_Grid_B5  12/2012  Gerd Platl */
F(): -(0.3 - (cos(x)+2*z)^2 - sin(0.5*y     )^2)   
    * (0.3 - (cos(x)-2*z)^2 - sin(0.5*y+pi/2)^2)
    * (0.3 - (cos(y)-2*z)^2 - sin(0.5*x     )^2)
    * (0.3 - (cos(y)+2*z)^2 - sin(0.5*x+pi/2)^2)   
[x]: -8 , 8
[y]: -8 , 8
[z]: -0.8 , 0.8
;

I think there is many room for creating more meshworks e.g. like this one...
http://www.bildburg.de/texturen/textilien/geflecht/index.html
http://www.bildburg.de/texturen/textilien/gewebe/index.html
Other creations are welcome Wink
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Mon Mar 11, 2013 9:29 am    Post subject: Alessandra Sartis Surface Reply with quote

"Sarti_D12"
An interesting and not really short formula created by Alessandra Sarti (D=12) with 600 nodes rendered by Jotero...
Code:
Name: Sarti_D12
/* Surface of Alessandra Sarti (D=12, 600 nodes)  2008
http://www.spektrum.de/artikel/966818&_z=798488
*/
F(): -22* (1+x^2+y^2+z^2)^6
+243*(48* (x^2*y^2+z^2) * (y^2+x^2*z^2) * (x^2+y^2*z^2)
-352*x^2*y^2*z^2*(x^2+y^2+z^2 +x^2*y^2 +x^2*z^2 +y^2*z^2)
+336*x^2*y^2*z^2* (1+x^4+y^4+z^4)
+2*(x^2+y^2+z^2 +x^2*y^2 +x^2*z^2 +y^2*z^2) * (1+x^4+y^4+z^4)^2
-14*(1+x^4+y^4+z^4) * ((z^2+x^2*y^2) * (y^2+x^2*z^2)
                     + (z^2+x^2*y^2) * (x^2+y^2*z^2)
                     + (x^2+y^2*z^2) * (y^2+x^2*z^2))
-6* (1+x^4+y^4+z^4) * ((z^2+x^2*y^2)^2
                     + (y^2+x^2*z^2)^2
                     + (x^2+y^2*z^2)^2)
+33*sqrt(5)
  * ((x^2*y^2+z^2)^2 * (y^2+x^2*z^2)
   - (y^2+x^2*z^2)^2 * (x^2*y^2+z^2) 
   - (x^2*y^2+z^2)^2 * (x^2+y^2*z^2)
   + (y^2+x^2*z^2)^2 * (x^2+y^2*z^2)
   + (x^2+y^2*z^2)^2 * (x^2*y^2+z^2)
   - (x^2+y^2*z^2)^2 * (y^2+x^2*z^2))
+19*((x^2*y^2+z^2)^2 * (y^2+x^2*z^2)
   + (y^2+x^2*z^2)^2 * (x^2*y^2+z^2)
   + (x^2*y^2+z^2)^2 * (x^2+y^2*z^2)
   + (y^2+x^2*z^2)^2 * (x^2+y^2*z^2)
   + (x^2+y^2*z^2)^2 * (x^2*y^2+z^2)
   + (x^2+y^2*z^2)^2 * (y^2+x^2*z^2))
+10* ((x^2*y^2+z^2)^3+ (y^2+x^2*z^2)^3+ (x^2+y^2*z^2)^3))
[x]: -7 , 7
[y]: -7 , 7
[z]: -7 , 7
;






Jotero, please can you publish the Formulas for Sarti's surface
- of degree 6 with 48 nodes and
- the 2nd surface of degree 8 with 144 node points?
They look also very interesting especially rendered as transparent 3d shapes.
Or may be you know a link to a readable surface definitions...
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jotero



Joined: 27 Jan 2007
Posts: 153
Location: Germany Hannover

PostPosted: Mon Mar 11, 2013 10:16 am    Post subject: Reply with quote

Hello all Smile

yes inode, i can Wink

Alessandra Sarti http://www-math.sp2mi.univ-poitiers.fr/~sarti/

Sarti's sextic 48 nodes Typ 1
Code:
(z-1+sqrt(2)*x)^6 + (z-1-sqrt(2)*x)^6 + (-(z+1+sqrt(2)*y))^6 + (-(z+1-sqrt(2)*y) )^6
+15.0*((z-1+sqrt(2)*x )^2*( z-1-sqrt(2)*x )^2*(-(z+1+sqrt(2)*y))^2
+(z-1+sqrt(2)*x )^2*(z-1-sqrt(2)*x)^2*(-(z+1-sqrt(2)*y))^2
+(z-1 + sqrt(2)*x)^2*(-(z + 1+sqrt(2)*y) )^2*(-(z + 1-sqrt(2)*y))^2
+(z-1-sqrt(2)*x)^2*(-(z+1+sqrt(2)*y))^2*(-(z+1-sqrt(2)*y))^2)
-7.0/12.0*(4*z^2+4 + 4*x^2 + 4*y^2)^3


Sarti's sextic 48 nodes Typ 2
Code:
(z-1+sqrt(2)*x)^6 + (z-1-sqrt(2)*x )^6 + (-(z+1+sqrt(2)*y))^6 + (-(z+1-sqrt(2)*y) )^6
+15.0*((z-1+sqrt(2)*x )^2*( z-1-sqrt(2)*x )^2*(-(z+1+sqrt(2)*y))^2
+(z-1+sqrt(2)*x )^2*(z-1-sqrt(2)*x)^2*(-(z+1-sqrt(2)*y))^2
+ (z-1 + sqrt(2)*x)^2*(-(z + 1+sqrt(2)*y) )^2*(-(z + 1-sqrt(2)*y))^2
+ (z-1-sqrt(2)*x)^2*(-(z+1+sqrt(2)*y))^2*(-(z+1-sqrt(2)*y))^2)
-2.0/3.0*(4*z^2+4 + 4*x^2 + 4*y^2)^3


Sarti's Octic: 72 nodes
Code:
3584.0*z^4+256.0*z^8+1792.0*z^4*x^4+10752.0*z^2*x^4
+1792.0*x^4+256.0*x^8+256.0+1792.0*z^4*y^4+10752.0*z^2*y^4
+1792.0*y^4+256.0*y^8+10752.0*z^4*x^2*y^2-21504.0*z^2*x^2*y^2
+10752.0*x^2*y^2+3584.0*x^4*y^4-192-192*12*x^4*y^2*z^2
-192*24*x^2*y^2*z^2-192*12*x^2*y^2-192*12*x^2*z^2
-192*12*y^2*z^2-192*12*x^4*y^2-192*12*x^4*z^2-192*12*x^2*y^4
-192*12*x^2*z^4-192*12*y^4*z^2-192*12*y^2*z^4-192*4*x^6*y^2
-192*4*x^6*z^2-192*6*x^4*y^4-192*6*x^4*z^4-192*4*x^2*y^6
-192*4*x^2*z^6-192*4*y^6*z^2-192*6*y^4*z^4-192*4*y^2*z^6
-192*12*x^2*y^4*z^2-192*12*x^2*y^2*z^4-192*4*x^2-192*4*y^2
-192*4*z^2-192*6*x^4-192*6*y^4-192*6*z^4-192*4*x^6-192*4*y^6
-192*4*z^6-192*x^8-192*y^8-192*z^8


Sarti's Octic: 144 nodes
Code:
3584.0*z^4+256.0*z^8+1792.0*z^4*x^4+10752.0*z^2*x^4
+1792.0*x^4+256.0*x^8+256.0+1792.0*z^4*y^4+10752.0*z^2*y^4
+1792.0*y^4+256.0*y^8+10752.0*z^4*x^2*y^2-21504.0*z^2*x^2*y^2
+10752.0*x^2*y^2+3584.0*x^4*y^4
-9/16*256*(1+12*x^4*y^2*z^2+24*x^2*y^2*z^2+12*x^2*y^2+12*x^2*z^2
+12*y^2*z^2+12*x^4*y^2+12*x^4*z^2+12*x^2*y^4+12*x^2*z^4
+12*y^4*z^2+12*y^2*z^4+4*x^6*y^2+4*x^6*z^2+6*x^4*y^4
+6*x^4*z^4+4*x^2*y^6+4*x^2*z^6+4*y^6*z^2+6*y^4*z^4
+4*y^2*z^6+12*x^2*y^4*z^2+12*x^2*y^2*z^4+4*x^2+4*y^2
+4*z^2+6*x^4+6*y^4+6*z^4+4*x^6+4*y^6+4*z^6+x^8+y^8+z^8)

ciao
torolf
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Mon Mar 11, 2013 8:28 pm    Post subject: Alessandra Sarti's surfaces Reply with quote

Hi Jotero
Thanx a lot for that immediate answer.
In the meantime I found also some formulas at
http://www-sop.inria.fr/galaad/surface/.

To get it more readable I rearranged some formulas a little bit...

Code:
Name: AS_SartisSe.xtik48T1
/* Isosurface of Alessandra Sarti (degree=6, type 1, 48 nodes) */
F(): (z-1+sqrt(2)*x)^6
   + (z-1-sqrt(2)*x)^6
   + (z+1+sqrt(2)*y)^6
   + (z+1-sqrt(2)*y)^6
+15*((z-1+sqrt(2)*x)^2 *(z-1-sqrt(2)*x)^2 *(z+1+sqrt(2)*y)^2
   + (z-1+sqrt(2)*x)^2 *(z-1-sqrt(2)*x)^2 *(z+1-sqrt(2)*y)^2
   + (z-1+sqrt(2)*x)^2 *(z+1+sqrt(2)*y)^2 *(z+1-sqrt(2)*y)^2
   + (z-1-sqrt(2)*x)^2 *(z+1+sqrt(2)*y)^2 *(z+1-sqrt(2)*y)^2)
-7/12*(4 +4*x^2 +4*y^2 +4*z^2)^3
[x]: -2.4 , 2.4
[y]: -2.4 , 2.4
[z]: -2.4 , 2.4
;


Code:
Name: AS_SartisSe.xtik48T2
/* Isosurface of Alessandra Sarti (degree=6, type 2, 48 nodes) */
F(): (z-1+sqrt(2)*x)^6
   + (z-1-sqrt(2)*x)^6
   + (z+1+sqrt(2)*y)^6
   + (z+1-sqrt(2)*y)^6
+15*((z-1+sqrt(2)*x)^2 *(z-1-sqrt(2)*x)^2 *(z+1+sqrt(2)*y)^2
    +(z-1+sqrt(2)*x)^2 *(z-1-sqrt(2)*x)^2 *(z+1-sqrt(2)*y)^2
    +(z-1+sqrt(2)*x)^2 *(z+1+sqrt(2)*y)^2 *(z+1-sqrt(2)*y)^2
    +(z-1-sqrt(2)*x)^2 *(z+1+sqrt(2)*y)^2 *(z+1-sqrt(2)*y)^2)
-2/3*(4 +4*x^2 +4*y^2 +4*z^2)^3
[x]: -2.4 , 2.4
[y]: -2.4 , 2.4
[z]: -2.4 , 2.4
;


Code:
Name: AS_SartisOctic72
/* Isosurface of Alessandra Sarti (degree=8, 72 nodes) */
F():  64*
( x^8 +y^8 +z^8
 -12*(x^6 +y^6 +z^6)
 -18*(x^4 +y^4 +z^4)
 -12*(x^2 +y^2 +z^2)
 +28*(x^4 +y^4 +2*z^4)
 +38*x^4*y^4
 +10*x^4*z^4
 +10*y^4*z^4
 +12*
 (11*x^2*y^2
  -3*x^2*z^2
  -3*y^2*z^2
  +11*x^4*z^2
  -3*x^4*y^2
  +11*y^4*z^2
  -3*y^4*x^2
  -3*z^4*x^2
  -3*z^4*y^2
  +11*z^4*x^2*y^2
  -3*x^4*y^2*z^2
  -3*y^4*x^2*z^2
  -34*x^2*y^2*z^2
  -x^6*(y^2 +z^2)
  -y^6*(z^2 +x^2)
  -z^6*(x^2 +y^2)
))
[x]: -4.4 , 4.4
[y]: -4.4 , 4.4
[z]: -4.4 , 4.4
;


Code:
Name: AS_SartisOctic144
/* Isosurface of Alessandra Sarti (degree=8, 144 nodes) */
F(): -66
     -112*(x^8 +y^8 +z^8)
     +576*(x^6*y^2 +x^6*z^2 +x^2*y^6 +x^2*z^6 +y^6*z^2 +y^2*z^6 +x^6 +y^6 +z^6 +x^2 +y^2 +z^2)
     -928*(z^4*x^4 +z^4*y^4 +x^4 +y^4)
     -2720*(x^4*y^4 +z^4)
     +1728*(x^4*y^2*z^2 +x^2*y^4*z^2 +x^2*z^2 +y^2*z^2 +x^4*y^2 +x^2*y^4 +x^2*z^4 +y^2*z^4)
     -9024*(z^2*y^4 +x^2*y^2 +z^4*x^2*y^2 +z^2*x^4)
     +24960*z^2*x^2*y^2
[x]: -5.5 , 5.5
[y]: -5.5 , 5.5
[z]: -5.5 , 5.5
;


Some formulas can be written shorter and well-arranged if K3dSurf would be able to handle variable in the formula definition like ...
Code:
a=1+sqrt(2);
b=1-sqrt(2);
F(): z-a*x)^6 +(z-b*x)^6 +(z+a*y)^6 +(z+b*y)^6 ....
Soooo, lets see what the time will bring us...
Wink Gerd


Last edited by inode on Mon Feb 24, 2014 8:55 am; edited 2 times in total
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ufoace



Joined: 11 Mar 2013
Posts: 46

PostPosted: Mon Apr 08, 2013 10:58 am    Post subject: Reply with quote

Thanks Inode. a couple of remixes of spiral, reminiscent of cymatics.

var a=Mathf.Sin((Mathf.Sqrt(x*x+y*y*.4) - .5*Mathf.Atan2(Mathf.Sin(y),Mathf.Cos(x*.3)) )) ;
var crd= 0.5 - z*z - a*a;

var b=Mathf.Sin((Mathf.Sqrt(x*x+z*z) - .5*Mathf.Atan2(Mathf.Sin(z),Mathf.Cos(x)) ));

var a=Mathf.Sin((Mathf.Sqrt(x*x+y*y) - .5*Mathf.Atan2(Mathf.Sin(y),Mathf.Cos(x)) )) ;
var crd= 0.3 - b*b - a*a;
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Fri Aug 16, 2013 1:17 pm    Post subject: DecicStar in Copper rendered with Maxwell Renderer Reply with quote

Hi all

Stefan has rendered my DedicStar with Maxwell in high polished copper...

Stefan, I never played around with the Maxwell Renderer. It would be nice if you would publish the source code of the decicStar as an example!
Thank you Wink Gerd
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Tue Oct 01, 2013 11:51 pm    Post subject: komplex formulas of Stephan Klaus Reply with quote

Please go to the link http://imaginary.org/es/node/68
and select suface "(2,5)-Torusknoten"
You'll see a red pentagonal knot with it's formula beneath.

Take a look at the appended formula - that's over my Surprised

Okay I know the parametric formula. It's very easy...
Code:
x=sin(2*u)*c
y=cos(2*u)*c
z=R*0.5*sin(5*u)+r*sin(v))
c=R*(2+0.3*cos(5*u))+r*cos(v)

The formula amuse me. Isn't it a little bit too excessive? Rolling Eyes
The algebraic surface may be builded 'simply' as a torus where the cone is replaced by a double helix.

have fun Wink Gerd


Last edited by inode on Sat Dec 07, 2013 2:08 pm; edited 1 time in total
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Furan



Joined: 05 Oct 2010
Posts: 64
Location: Prague, Czech Republic

PostPosted: Wed Oct 02, 2013 11:14 am    Post subject: Reply with quote

Their stupid "algebraic only" approach creates monsters like this with Taylor series. They should change profession. Rolling Eyes
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sun Dec 22, 2013 11:00 am    Post subject: The Evolution of Christmas Tree Decoration Reply with quote

Hi all,
IMAGINARY has created new decoration shapes for the christmas tree.
see http://www.imaginary.org/news/the-evolution-of-christmas-tree-decoration-and-a-happy-new-year

I also want to wish you a merry christmas
and if you have no star to decorate your chrismas tree use this one...


Code:
Name: PG_OctaStar_1
/* Isosurface: PG_OctaStar_1 9/2013 Gerd Platl */
F(): (x^2-1) *(y^2-1) *(z^2-0.9)*((x+y)^2-2) *((x-y)^2-2)-(4*z)^4-(x*x+y*y-3)^3
[x]: -8 , 8
[y]: -8 , 8
[z]: -0.6 , 0.6
;

Do you also have a star for christmas tree decoration?
If yes - let it see us. Wink
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denisc



Joined: 24 Apr 2013
Posts: 92

PostPosted: Tue Jan 14, 2014 2:51 pm    Post subject: Reply with quote

Hello inode

thanks for sharing. Smile
The probleme for your formula of pent torus is:
your tube is not perfectly round ,it's a ovoloide.

Your formula
X():sin(2*u)*6*(2+0.3*cos(5*u))+.2*cos(v)
Y():cos(2*u)*6*(2+0.3*cos(5*u))+.2*cos(v)
Z():6*0.5*(sin(5*u)+.2*sin(v))
[u]:-pi, pi
[v]:-pi, pi

try with k3dsurf.
cheers denisc
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