PoV-ray illustration of the theorem of Desargues in 3D

desargues-labeled.svg

<?xml version="1.0"?>
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         "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">

<svg width="400px" height="400px" viewBox="-200 -200 400 400"
  overflow="hidden" version="1.1" xmlns="http://www.w3.org/2000/svg">

<style type="text/css">
line { stroke-linecap: round; stroke-linejoin: round; }
.uvw { stroke: rgb(0,0,128); stroke-width: 1.2px; }
.uvw-point { stroke: rgb(0,0,255); stroke-width: 5px; }
.lo { stroke: rgb(0,128,0); stroke-width: 1.2px; }
.lo-point { stroke: rgb(0,255,0); stroke-width: 5px; }
.tri1 { stroke: rgb(128,0,64); stroke-width: 0.6px; }
.tri1-point { stroke: rgb(255,0,128); stroke-width: 5px; }
.tri1-poly { fill: rgb(128,0,64); fill-opacity: 0.3; }
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.tri2-point { stroke: rgb(255,128,0); stroke-width: 5px; }
.tri2-poly { fill: rgb(128,64,0); fill-opacity: 0.3; }
text { font-size: 15px;  font-style: italic;  font-family: "New Century Schoolbook", "Century Schoolbook", "TeX Gyre Schola", serif; }
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<polygon class="tri1-poly" points="0.000,58.462 -66.667,106.667 -100.000,20.000" />
<polygon class="tri2-poly" points="0.000,-25.000 -33.937,-19.344 -25.685,-106.336" />
<line class="lo" x1="-0.000" y1="-200.000" x2="0.000" y2="200.000" />
<line class="lo" x1="12.987" y1="-200.000" x2="-90.909" y2="200.000" />
<line class="lo" x1="-200.000" y1="190.000" x2="29.412" y2="-200.000" />
<line class="uvw" x1="200.000" y1="-100.000" x2="-100.000" y2="200.000" />
<line class="tri1" x1="-100.000" y1="20.000" x2="-50.000" y2="150.000" />
<line class="tri1" x1="-100.000" y1="20.000" x2="30.000" y2="70.000" />
<line class="tri1" x1="-66.667" y1="106.667" x2="150.000" y2="-50.000" />
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<line class="tri2" x1="-33.937" y1="-19.344" x2="150.000" y2="-50.000" />
<line class="lo-point" x1="0.000" y1="-150.000" x2="0.000" y2="-150.000" />
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<line class="uvw-point" x1="30.000" y1="70.000" x2="30.000" y2="70.000" />
<line class="uvw-point" x1="150.000" y1="-50.000" x2="150.000" y2="-50.000" />
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<line class="tri1-point" x1="-66.667" y1="106.667" x2="-66.667" y2="106.667" />
<line class="tri1-point" x1="-100.000" y1="20.000" x2="-100.000" y2="20.000" />
<line class="tri2-point" x1="0.000" y1="-25.000" x2="0.000" y2="-25.000" />
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<line class="tri2-point" x1="-25.685" y1="-106.336" x2="-25.685" y2="-106.336" />
<text text-anchor="start" x="5.000" y="-145.000">O</text>
<text text-anchor="start" x="5.000" y="53.462">A₁</text>
<text text-anchor="end" x="-71.667" y="106.667">B₁</text>
<text text-anchor="end" x="-105.000" y="20.000">C₁</text>
<text text-anchor="start" x="5.000" y="-30.000">A₂</text>
<text text-anchor="end" x="-38.937" y="-19.344">B₂</text>
<text text-anchor="end" x="-30.685" y="-106.336">C₂</text>
<text text-anchor="start" x="-45.000" y="165.000">U</text>
<text text-anchor="start" x="35.000" y="85.000">V</text>
<text text-anchor="start" x="155.000" y="-35.000">W</text>

</svg>

desargues.pov

#include "consts.inc"
#include "colors.inc"
#include "woods.inc"
#include "stones.inc"
#include "metals.inc"
#include "skies.inc"

// povray +Idesargues.pov final.ini -W800 -H800
// convert desargues.png -quality 98 ~/public_html/images/geom/desargues3d.jpg
// convert desargues.png -resize 300x300 -quality 98 ~/public_html/images/geom/desargues3d-small.jpg

global_settings {
  photons { count 100000 }
  assumed_gamma 1.0
}

// Memento: POV-Ray uses a left-handed coordinate system.
// Here, x points right, y points down and z points toward camera.

#declare camera_dist = 12;

camera {
  location <0, 0, camera_dist>
  sky <0, -1, 0>
  right <image_width/image_height, 0, 0>
  look_at <0,0,0>
  angle 2*atan(2/camera_dist * image_width/image_height)*180/pi
}

sky_sphere {
  S_Cloud2
  rotate <0,0,180>
}

plane {
  <0,-1,0>,-1.5
  texture {
    T_Stone15
    scale 5
  }
}

light_source {
  <-2, -15, 30>
  color White
}

#declare point_O = <0,-3/2,0>;
#declare point_A1 = <0, 38/65, 0>;
#declare point_B1 = <-10/15 / (1 + (77/30)/camera_dist), 16/15 / (1 + (77/30)/camera_dist), 77/30 / (1 + (77/30)/camera_dist)>;
#declare point_C1 = <-10/10, 2/10, 0>;
#declare point_A2 = <0, -1/4, 0>;
#declare point_B2 = <-300/884 / (1 + (1155/884)/camera_dist), -171/884 / (1 + (1155/884)/camera_dist), 1155/884 / (1 + (1155/884)/camera_dist)>;
#declare point_C2 = <-150/584, -621/584, 0>;
#declare point_U = <-1/2 / (1 + (77/20)/camera_dist), 3/2 / (1 + (77/20)/camera_dist), 77/20 / (1 + (77/20)/camera_dist)>;
#declare point_V = <3/10, 7/10, 0>;
#declare point_W = <3/2 / (1 + (-231/40)/camera_dist), -1/2 / (1 + (-231/40)/camera_dist), -231/40 / (1 + (-231/40)/camera_dist)>;

sphere {
  // The point O
  point_O, 0.05
  texture {
    pigment { color red 0 green 1 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point A₁
  point_A1, 0.05
  texture {
    pigment { color red 1 green 0 blue 0.5 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point B₁
  point_B1, 0.05
  texture {
    pigment { color red 1 green 0 blue 0.5 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point C₁
  point_C1, 0.05
  texture {
    pigment { color red 1 green 0 blue 0.5 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point A₂
  point_A2, 0.05
  texture {
    pigment { color red 1 green 0.5 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point B₂
  point_B2, 0.05
  texture {
    pigment { color red 1 green 0.5 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point C₂
  point_C2, 0.05
  texture {
    pigment { color red 1 green 0.5 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point U
  point_U, 0.05
  texture {
    pigment { color red 0 green 0 blue 1 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point V
  point_V, 0.05
  texture {
    pigment { color red 0 green 0 blue 1 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

sphere {
  // The point W
  point_W, 0.05
  texture {
    pigment { color red 0 green 0 blue 1 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_O, 5*point_A1-4*point_O, 0.01
  texture {
    pigment { color red 0 green 0.5 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_O, 5*point_B1-4*point_O, 0.01
  texture {
    pigment { color red 0 green 0.5 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_O, 5*point_C1-4*point_O, 0.01
  texture {
    pigment { color red 0 green 0.5 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_C1, point_U, 0.01
  texture {
    pigment { color red 0.5 green 0 blue 0.25 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_C1, point_V, 0.01
  texture {
    pigment { color red 0.5 green 0 blue 0.25 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_B1, point_W, 0.01
  texture {
    pigment { color red 0.5 green 0 blue 0.25 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_C2, point_U, 0.01
  texture {
    pigment { color red 0.5 green 0.25 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_C2, point_V, 0.01
  texture {
    pigment { color red 0.5 green 0.25 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  point_B2, point_W, 0.01
  texture {
    pigment { color red 0.5 green 0.25 blue 0 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

cylinder {
  2*point_U-point_W, 101*point_W-100*point_U, 0.01
  texture {
    pigment { color red 0 green 0 blue 0.5 }
    finish { ambient .45 diffuse .6 phong .3 }
  }
}

triangle {
  point_A1, point_B1, point_C1
  texture {
    pigment { color red 0.5 green 0 blue 0.25 transmit 0.2 }
    finish { reflection { 0.1 } ambient .45 diffuse .6 phong .3 }
  }
}

triangle {
  point_A2, point_B2, point_C2
  texture {
    pigment { color red 0.5 green 0.5 blue 0.25 transmit 0.2 }
    finish { reflection { 0.1 } ambient .45 diffuse .6 phong .3 }
  }
}