Last Update May 10, 1998

NUMERICAL SPACE / TETRA

    My favorite print artist M.C.Escher drew
    various polyhedrons in his works. So, I
    made some works using tetrahedrons for funs.

    For following M.C.Escher, I made the frame
    of tetrahedron mofifying POV-Ray standard
    include files' tetrahedron.
    Please see the right description;


    Stars. 1948 M.C.Escher

    // Shapes by Tom Price [75300,620]:
    #declare Tetrahedron =
    intersection {
    plane {-y,1}
    plane {-z,1 rotate <19.47, 0, 0>}
    plane {-z,1 rotate <19.47, -120, 0>}
    plane {-z,1 rotate <19.47, 120, 0>}
    }

    // Shapes by Tsutomu Higo :
    #declare Tetrahedrfm =
    merge {
    intersection {
    object { Tetrahedron }
    merge {
    plane {z,1.4 rotate <35.263, 180, 0>inverse}
    plane {z,1.4 rotate <35.263, -60, 0> inverse}
    plane {z,1.4 rotate <35.263, 60, 0> inverse}
    plane {-z,1.4 rotate <35.263, 180, 0>inverse}
    plane {-z,1.4 rotate <35.263, -60, 0> inverse}
    plane {-z,1.4 rotate <35.263, 60, 0> inverse}
    }
    }
    }


    merge {
    object { Tetrahedrfm }
    object { Tetrahedrfm rotate x*180 }
    }

    merge {
    object { Tetrahedrfm translate y*1 }
    object { Tetrahedrfm rotate x*180 rotate y*180 translate y*-1}
    }

    merge {
    object { Tetrahedrfm translate y*1 }
    object { Tetrahedrfm rotate x*180 rotate y*180 translate y*-1}
    object { Tetrahedrfm rotate <180,180,0> translate y*-2 rotate <-109.47,60,0> translate y*1 }
    object { Tetrahedrfm rotate <180,180,0> translate y*-2 rotate <-109.47,180,0> translate y*1 }
    object { Tetrahedrfm rotate <180,180,0> translate y*-2 rotate <-109.47,300,0> translate y*1 }
    }


Hedrons from Tetrahedron / 44k / Apr. 1998 / by Tsutomu Higo

    I simply arranged tetrahedrons regularly. But I see their various shapes with a fun.

Arranged Ttrahedrons / 61k / Apr. 1998 / by Tsutomu Higo

    I used this fog for showing the horizontal structure.

    #declare Orig_Fog = 1
    #declare Ground_Mist= 2
    fog{
    fog_type Ground_Mist fog_alt 0.5 fog_offset 0 distance 2
    color rgb <0.1, 0.2, 0.3>
    turbulence <0.05, 0.05, 0.05> omega 0.25 lambda 2.5 octaves 6
    }


Arranged Frames of Tetrahedrons / 66k / Apr. 1998 / by Tsutomu Higo

    I merely repeated several times like as follows.

    #declare Tetrahedrg = object { Tetrahedron }
    #declare Ct=1 #while ( Ct < 9 )
    #declare Tetrahedrg =
    union {
    object { Tetrahedrg translate < 0,0,2.8284*2> }
    object { Tetrahedrg translate <-2.4495*2,0,-1.4142*2> }
    object { Tetrahedrg translate < 2.4495*2,0,-1.4142*2> }
    object { Tetrahedrg translate <0,4*2,0> }
    }
    Ct=Ct*2 #end


Fractal Tetrahedron / 52k / Apr. 1998 / by Tsutomu Higo

    I put the blue or red fog as follows. Of course I put the tetrahedron in this cylinder with the texture like the fog.

    light_source {<0, 0.8, -10> rgb <0.6,1,1>}
    light_source {<0, 5.5, 0> rgb <1,0,0.5>}
    cylinder { <-1.5,0.8,0>,<1.5,0.8,0> 0.3
    texture { pigment {marble color_map {[0.3 color rgbt <0, 0, 1, 1.0>] [1.0 color rgb <0.7, 0, 1>]} turbulence 0.4 scale 0.23 rotate y*90 translate y*30 translate x*4} finish {ambient 0 diffuse 0.8 reflection 0.} }
    scale 8
    }


Illusion of a Tetrahedron / 32k / Apr. 1998 / by Tsutomu Higo

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