Challenge for forumers, Animation of Polyhedrons

Code:
// POV-Ray 3.6 / 3.7 Scene File "Regulare_Tetrahedron_Vectors_1.pov"

// author: Friedrich A. Lohmueller, Dec-2009/Jan-2011

// email: Friedrich.Lohmueller_at_t-online.de

// homepage: http://www.f-lohmueller.de

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

#version 3.6; // 3.7;

global_settings{ assumed_gamma 1.0 }

#default{ finish{ ambient 0.1 diffuse 0.9 }}

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

#include "colors.inc"

#include "textures.inc"

#include "glass.inc"

#include "metals.inc"

#include "golds.inc"

#include "stones.inc"

#include "woods.inc"

#include "shapes.inc"

#include "shapes2.inc"

#include "functions.inc"

#include "math.inc"

#include "transforms.inc"

//--------------------------------------------------------------------------------------------------------<<<<

#declare Camera_Number = 1 ;

//--------------------------------------------------------------------------------------------------------<<<<

#switch ( Camera_Number )

#case (0)

  #declare Camera_Position = < 0.00, 0.00, -2.80> ;  // front view

  #declare Camera_Look_At  = < 0.00, 0.00,  0.00> ;

  #declare Camera_Angle    =   40 ;

#break

#case (1)

  #declare Camera_Position = < 3.20, 2.00, -2.70> ;  // diagonal view

  #declare Camera_Look_At  = < 0.00, 0.10,  0.00> ;

  #declare Camera_Angle    =  20 ;

#break

#case (2)

  #declare Camera_Position = < 0.00, 0.00, -2.50> ;  // right side view

  #declare Camera_Look_At  = < 0.00, 0.00,  0.00> ;

  #declare Camera_Angle    =  45 ;

#break

#case (3)

  #declare Camera_Position = < 0.00, 3.00, -0.01> ;  // top view

  #declare Camera_Look_At  = < 0.00, 0.00,  0.00> ;

  #declare Camera_Angle    =  45 ;

#break

#else

  #declare Camera_Position = < 3.20, 2.00, -2.70> ;  // diagonal view

  #declare Camera_Look_At  = < 0.00, 0.10,  0.00> ;

  #declare Camera_Angle    =  20 ;

#break

#end // of "#switch ( Camera_Number )" -----------------------------

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

//-------------------------------------------------------------------------------------------------------<<<<

camera{ location Camera_Position

        right    x*image_width/image_height

        angle    Camera_Angle

        look_at  Camera_Look_At

      }

//------------------------------------------------------------------------------------------------------<<<<<

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

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

// sun -------------------------------------------------------------------

light_source{<-500,1500,-1500> color White*0.9}           // sun light

light_source{ Camera_Position  color rgb<0.9,0.9,1>*0.1}  // flash light



// sky -------------------------------------------------------------------

sky_sphere{ pigment{ gradient <0,1,0>

                     color_map{ [0   color rgb<1,1,1>         ]//White

                                [0.5 color rgb<0.14,0.14,0.56>*0.7]//~Navy

                                [0.5 color rgb<0.14,0.14,0.56>*0.7]//~Navy

                                [1.0 color rgb<1,1,1>         ]//White

                              }

                     scale 2 }

           } // end of sky_sphere

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



//------------------------------ the Axes --------------------------------

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

#macro Axis_( AxisLen, Dark_Texture,Light_Texture)

 union{

    cylinder { <0,-AxisLen,0>,<0,AxisLen,0>,0.05

               texture{checker texture{Dark_Texture }

                               texture{Light_Texture}

                       translate<0.1,0,0.1>}

             }

    cone{<0,AxisLen,0>,0.2,<0,AxisLen+0.7,0>,0

          texture{Dark_Texture}

         }

     } // end of union

#end // of macro "Axis()"

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

#macro AxisXYZ( AxisLenX, AxisLenY, AxisLenZ, Tex_Dark, Tex_Light)

//--------------------- drawing of 3 Axes --------------------------------

#declare Text_Rotate = < 20,-45,0>; // rotate Text_Rotate 



union{

#if (AxisLenX != 0)

 object { Axis_(AxisLenX, Tex_Dark, Tex_Light)   rotate< 0,0,-90>}// x-Axis

 text   { ttf "arial.ttf",  "x",  0.15,  0  texture{Tex_Dark}

          rotate Text_Rotate scale 0.5 translate <AxisLenX+0.05,0.4,-0.10>}

#end // of #if

#if (AxisLenY != 0)

 object { Axis_(AxisLenY, Tex_Dark, Tex_Light)   rotate< 0,0,  0>}// y-Axis

 text   { ttf "arial.ttf",  "y",  0.15,  0  texture{Tex_Dark}

          rotate Text_Rotate scale 0.5 translate <-0.75,AxisLenY+0.20,-0.10>}

#end // of #if

#if (AxisLenZ != 0)

 object { Axis_(AxisLenZ, Tex_Dark, Tex_Light)   rotate<90,0,  0>}// z-Axis

 text   { ttf "arial.ttf",  "z",  0.15,  0  texture{Tex_Dark}

          rotate Text_Rotate  scale 0.75 translate <-0.75,0.2,AxisLenZ+0.10>}

#end // of #if

} // end of union

#end// of macro "AxisXYZ( ... )"

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



#declare Texture_A_Dark  = texture {

                               pigment{ color rgb<1,0.4,0>}

                               finish { phong 1}

                             }

#declare Texture_A_Light = texture {

                               pigment{ color rgb<1,1,1>}

                               finish { phong 1}

                             }



// axes ------------------------------------------------------------------- 

object{ AxisXYZ( 6.2, 5.2, 7.2, Texture_A_Dark, Texture_A_Light) scale 0.15 no_shadow }

//-------------------------------------------------- end of coordinate axes



/*

// ground -----------------------------------------------------------------

//---------------------------------<<< settings of squared plane dimensions

#declare RasterScale = 0.1;

#declare RasterHalfLine  = 0.035;

#declare RasterHalfLineZ = 0.035;

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

#macro Raster(RScale, HLine)

       pigment{ gradient x scale RScale

                color_map{[0.000   color rgbt<1,1,1,0>*0.7]

                          [0+HLine color rgbt<1,1,1,0>*0.7]

                          [0+HLine color rgbt<1,1,1,1>]

                          [1-HLine color rgbt<1,1,1,1>]

                          [1-HLine color rgbt<1,1,1,0>*0.7]

                          [1.000   color rgbt<1,1,1,0>*0.7]} }

 #end// of Raster(RScale, HLine)-macro

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

plane { <0,1,0>, 0    // plane with layered textures

        texture { pigment{color White*1.1}

                  finish {ambient 0.45 diffuse 0.85}}

        texture { Raster(RasterScale,RasterHalfLine ) rotate<0,0,0> }

        texture { Raster(RasterScale,RasterHalfLineZ) rotate<0,90,0>}

        rotate< 0,0,0>

        translate<0,0,0> 

      }

//------------------------------------------------ end of squared plane XZ

*/



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

//---------------------------- objects in scene ----------------------------

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



 



// sizes of lines and points ----------------------------------------------- 

#declare Rl = 0.010; // lines radius

#declare Rp = 0.020; // points radius

// textures ---------------------------------------------------------------- 

#declare Edge_Texture = 

         texture { pigment{ color rgb< 0.75, 1.0, 0.0> } 

                   finish { phong 1 reflection 0.00}

                 } // end of texture 

#declare Corners_Texture = 

         texture { pigment{ color rgb<0.4,1,0>*0.35 } 

                   finish { phong 1 reflection 0.00}

                 } // end of texture 

#declare Surface_Texture = 

         texture { pigment{ color rgbt< 0.75, 1.0, 0.0, 0.75> }  

                   finish { phong 1 reflection 0.00}

                 } // end of texture 

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

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

//--------------------------------------------------------------------- macro "Vector(Start,End,Radius)"!

#macro Vector(P_start,P_end, R_Vector)  

union{



cylinder{ P_start, P_end - ( vnormalize(P_end - P_start)*9.5*R_Vector), R_Vector  }

cone    { P_end - ( vnormalize(P_end - P_start)*10*R_Vector), 3*R_Vector, P_end, 0 }

}// end of union

#end //------------------------------------------------------------------------------------- end of macro

// alternatively:   #include "analytical_g.inc"

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



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

#declare Side_a = 1; // length of a side of a regular tetrahedron

// ---- equilateral triangle -----------------------------------------------------------------------------

//#declare Th =  1/2*sqrt(3)*Side_a; // the height of an equilateral triangle

//#declare Sh =  1/6*sqrt(3)*Side_a; // the height of the incenter of an equilateral triangle

//#declare Rc =  1/3*sqrt(3)*Side_a; // radius of circumcircle of an equilateral triangle

// ---- regular tetrahedron ------------------------------------------------------------------------------ 

//#declare Tetra_H = sqrt (2/3) * Side_a; // the height of a regular tetrahedron  

#declare R_circum  = sqrt( 3/8 ) * Side_a; // radius of the circumsphere of a regular tetrahedron 

//#declare R_in  = 1/3 * Rc ; //    or  = 1/sqrt(24) * A = Tetra_H-R_circum ; radius insphere

//#declare Face_Corner_Center_Angle =  degrees (  atan (  R_in / Rf ) );

//#declare Face_to_Face_Angle =  degrees( atan(2*sqrt(2))) ; // degrees (  atan (  Tetra_H/ Sh ) );  ~ 71

//#declare Edge_to_Face_Angle =  degrees( atan(sqrt(2))) ;  //   ~ 55    

#declare Vertex_Center_Vertex_Angle = degrees( acos( -1/3 ))    ;  //  ~ 109.471 

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





// caculation of the vectors ------------------------------------------ 

#declare V1 = <0,R_circum,0>; 

#declare V2 = vrotate ( V1, < Vertex_Center_Vertex_Angle,   0, 0> ); 

#declare V3 = vrotate ( V2, <   0, 120, 0> ); 

#declare V4 = vrotate ( V2, <   0,-120, 0> ); 



// vectors ------------------------------------------------------------ 

object{ Vector( o,V1, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow}

object{ Vector( o,V2, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow}

object{ Vector( o,V3, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow}

object{ Vector( o,V4, Rl) pigment{ color rgb<0.2,0.5,0.0> } no_shadow}





// corners ------------------------------------------------------------ 

sphere{ V1, Rp texture{ Corners_Texture } no_shadow }

sphere{ V2, Rp texture{ Corners_Texture } no_shadow }

sphere{ V3, Rp texture{ Corners_Texture } no_shadow }

sphere{ V4, Rp texture{ Corners_Texture } no_shadow }





// lettering ---------------------------------------------------------- 

text{ ttf "arial.ttf", "A", 0.02, 0.0  rotate<20,-40,0>  

      texture{ Corners_Texture }  

      scale<1,1,1>*0.10  translate V1 + <-0.10,0,-0.10>     no_shadow

    } // end of text object ------------------------------------------- 

text{ ttf "arial.ttf", "B", 0.02, 0.0  rotate<20,-40,0> 

      texture{ Corners_Texture } 

      scale<1,1,1>*0.12  translate V2 + < 0.00,-0.05, 0.15> no_shadow

    } // end of text object ------------------------------------------- 

text{ ttf "arial.ttf", "C", 0.02, 0.0  rotate<20,-40,0> 

      texture{ Corners_Texture } 

      scale<1,1,1>*0.09  translate V3 + < 0.00,-0.12,-0.05> no_shadow

    } // end of text object ------------------------------------------- 

text{ ttf "arial.ttf", "D", 0.02, 0.0  rotate<20,-40,0> 

      texture{ Corners_Texture }  

      scale<1,1,1>*0.10  translate V4 + <-0.15,-0.05,-0.10> no_shadow

    } // end of text object -------------------------------------------

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

#declare Point_A = V1; 

#declare Point_B = V2; 

#declare Point_C = V3; 

#declare Point_D = V4; 

// edges ---------------------------------------------------------

cylinder{ Point_A, Point_B, Rl  texture{ Edge_Texture } }

cylinder{ Point_B, Point_C, Rl  texture{ Edge_Texture } }

cylinder{ Point_C, Point_A, Rl  texture{ Edge_Texture } }

cylinder{ Point_A, Point_D, Rl  texture{ Edge_Texture } }

cylinder{ Point_B, Point_D, Rl  texture{ Edge_Texture } }

cylinder{ Point_C, Point_D, Rl  texture{ Edge_Texture } }



// surfaces-------------------------------------------------------

triangle{ Point_A, Point_B, Point_C texture{ Surface_Texture } } 

triangle{ Point_A, Point_B, Point_D texture{ Surface_Texture } } 

triangle{ Point_B, Point_C, Point_D texture{ Surface_Texture } } 

triangle{ Point_C, Point_A, Point_D texture{ Surface_Texture } } 

 

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

// The corners of a regular tetraeder based on x-axis:

//#declare Point_A = <-Side_a/2,      0, 0>;

//#declare Point_B = < Side_a/2,      0, 0>;

//#declare Point_C = <        0,      0,Th>;

//#declare Point_D = <        0,Tetra_H,Sh>; // "top"

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