Here's an example or two of using full-colour pigment functions. This
example shows how to do a fake MC Escher "Circle Limit" effect, using
stereographic projection. True "Circle Limit" pictures use hyperbolic


(angle-preserving), FWIW.

// Persistence of Vision Ray Tracer Scene Description File
// File: PigFunc.pov
// Vers: 3.6
// Desc: Pigment function demo
// Date: 2005.02.19
// Auth: PM 2Ring
//
//  -D +A0.1 +AM2 +R4
//  -F -A0.4 +AM2 +R1
//

#version 3.6;

global_settings {
  assumed_gamma 1
}

camera {
  location <0, 5, -1> * 2.4
  look_at  0
  direction z

  angle 40
}

light_source {
   <0, 2, -1> * 50
   rgb 1.75 // 2.25
}

//---Color Maps--------------------------------------------

//Make a color_map from a0 to a1
#macro CMRange(a0, a1)color_map{[0 a0][1 a1]}#end

//Make a color_map from Black to a
#macro CMFull(a)CMRange(rgb 0, a)#end

//---Stereographically projected
pigment!-----------------------------------------

#declare R2 = 8.8;
#declare f_proj = function(x,z){R2/sqrt(R2 - min(R2-1E-12, x*x+z*z))}

#declare TestPig = pigment{hexagon rgb<1 .9 .5>, rgb <.85 .5 .6>, rgb <0 0
...8>}

#declare f_Pig = function{pigment{TestPig}}
#declare f_Pig1 = f_Pig;

//Turn a pigment function into a real-live pigment!
#declare PigRGB0 =
pigment{
  average
  pigment_map {
    [1 function{f_Pig(x,y,z).red} CMFull(red 3)]
    [1 function{f_Pig(x,y,z).green} CMFull(green 3)]
    [1 function{f_Pig(x,y,z).blue} CMFull(blue 3)]
  }
}

//And now, with projection!

#declare f_X = function{x*f_proj(x,z)}
#declare f_Y = function{y}
#declare f_Z = function{z*f_proj(x,z)}

#declare PigRGB1 =
pigment{
  average
  pigment_map {
  #if(0)
    [1 function{f_Pig(f_X(x,y,z), f_Y(x,y,z), f_Z(x,y,z)).red} CMFull(red
3)]
    [1 function{f_Pig(f_X(x,y,z), f_Y(x,y,z), f_Z(x,y,z)).green}
CMFull(green 3)]
    [1 function{f_Pig(f_X(x,y,z), f_Y(x,y,z), f_Z(x,y,z)).blue} CMFull(blue
3)]
  #else
    [1 function{f_Pig(x*f_proj(x,z), y, z*f_proj(x,z)).red} CMFull(red 3)]
    [1 function{f_Pig(x*f_proj(x,z), y, z*f_proj(x,z)).green} CMFull(green
3)]
    [1 function{f_Pig(x*f_proj(x,z), y, z*f_proj(x,z)).blue} CMFull(blue 3)]
  #end
  }
}

//---Scene--------------------------------

cylinder{
  -.1*y, .1*y, 3
  //open
  pigment{
    PigRGB1
    //PigRGB0
    //TestPig
  }
}

background{
  //rgb<0.035, 0.27, 0.67>
  rgb 0
}

//-------------------------------------------------------

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Attachments:
Download 'pigfuncda0.jpg' (106 KB)

Preview of image 'pigfuncda0.jpg'

PM 2Ring wrote:
> Here's an example or two of using full-colour pigment functions.

Nice demo.  Note the mechsim include file coming with MegaPOV contains a 
generic Vector_Function() macro that can simplify this kind of thing. 
The version in MegaPOV 1.1 only supports positive function values - here 
is the improved, more universal version:


#ifndef (MSim_Fn_Range)
	#declare MSim_Fn_Range=1e6;
#end

#macro Vector_Function_Range(Fn_X, Fn_Y, Fn_Z, Range)

	#local PigX=
	pigment {
		function { 0.5+Fn_X(x, y, z)*(0.5/Range) }
		color_map {
			[0.0 color rgb -3*Range*x ]
			[0.5 color rgb 0 ]
			[1.0 color rgb  3*Range*x ]
		}
	}

	#local PigY=
	pigment {
		function { 0.5+Fn_Y(x, y, z)*(0.5/Range) }
		color_map {
			[0.0 color rgb -3*Range*y ]
			[0.5 color rgb 0 ]
			[1.0 color rgb  3*Range*y ]
		}
	}

	#local PigZ=
	pigment {
		function { 0.5+Fn_Z(x, y, z)*(0.5/Range) }
		color_map {
			[0.0 color rgb -3*Range*z ]
			[0.5 color rgb 0 ]
			[1.0 color rgb  3*Range*z ]
		}
	}

	function {
		pigment {
			average
			pigment_map {
				[1 PigX]
				[1 PigY]
				[1 PigZ]
			}
		}
	}

#end

#macro Vector_Function(Fn_X, Fn_Y, Fn_Z)

Vector_Function_Range(
	function { Fn_X(x, y, z) },
	function { Fn_Y(x, y, z) },
	function { Fn_Z(x, y, z) },
	MSim_Fn_Range
)

#end

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 27 Feb. 2005 _____./\/^>_*_<^\/\.______

Post a reply to this message

Christoph Hormann <chr### [at] gmxde> wrote:
> PM 2Ring wrote:

Sorry about the delay replying, I've been unwell.

> > Here's an example or two of using full-colour pigment functions.
>
> Nice demo.

Thanks! It would be even better if I hadn't screwed up the algebra. :)
Fortunately, the error only gives an incorrect scale to the projection. See
the next message for a corrected version.

And BTW, thanks for all the helpful tutorials you've created over the years.

> Note the mechsim include file coming with MegaPOV contains a
> generic Vector_Function() macro that can simplify this kind of thing.
> The version in MegaPOV 1.1 only supports positive function values - here
> is the improved, more universal version:
>
>
> #ifndef (MSim_Fn_Range)
>  #declare MSim_Fn_Range=1e6;
> #end
>
> #macro Vector_Function_Range(Fn_X, Fn_Y, Fn_Z, Range)
>
>  #local PigX=
>  pigment {
>   function { 0.5+Fn_X(x, y, z)*(0.5/Range) }

If only POV would allow the passing of function names... I guess it can be
done in a roundabout way using Parse_String().

Post a reply to this message

Here's the mathematically correct version:

// Persistence of Vision Ray Tracer Scene Description File
// File: PigFunc.pov
// Vers: 3.5+
// Desc: Pigment function demo
// Date: 2005.02.19
// Auth: PM 2Ring
//
//  -D +A0.01 +AM2 +R4 +W640 +H640
//  -F -A0.4 +AM2 +R1
//

global_settings {assumed_gamma 1}

//---Color Maps--------------------------------------------

//Make a color_map from a0 to a1
#macro CMRange(a0, a1)color_map{[0 a0][1 a1]}#end

//Make a color_map from Black to a
#macro CMFull(a)CMRange(rgb 0, a)#end

//---Stereographically projected
pigment!-----------------------------------------

#declare R = 3;   //Radius of projection
#declare R2 = R*R;
#declare f_proj = function(x,z){1/sqrt(1 - (x*x+z*z)/R2)}

#declare TestPig = pigment{hexagon rgb<1 .9 .5>, rgb <.85 .5 .6>, rgb <0 0
...8> scale .5}

#declare f_Pig = function{pigment{TestPig}}
#declare Brite = 3;
#declare PigRGB =
pigment{
  average
  pigment_map {
    [1 function{f_Pig(x*f_proj(x,z), y, z*f_proj(x,z)).red} CMFull(red
Brite)]
    [1 function{f_Pig(x*f_proj(x,z), y, z*f_proj(x,z)).green} CMFull(green
Brite)]
    [1 function{f_Pig(x*f_proj(x,z), y, z*f_proj(x,z)).blue} CMFull(blue
Brite)]
  }
}

//---Scene--------------------------------

cylinder{
  -.1*y, .1*y, R

  pigment{
    PigRGB
    //TestPig
  }
  finish{ambient 1 diffuse 0}
}

camera {
  orthographic
  location y * R * 4
  look_at  0
  right x*image_width/image_height up y
  direction z

  angle 30
}

background{rgb .5}

//-------------------------------------------------------

Post a reply to this message

Attachments:
Download 'pigfuncha2.png' (139 KB)

Preview of image 'pigfuncha2.png'