Spherical Lissajous Curves using POVRay

Some examples of spherical Lissajous curves created with POVRay.

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# This program created by Hans Mikelson February 1998

# 

# This program generates a POV file so that 3D graphs can be

# rendered using the POV ray tracing package.  The surface is mapped

# as a sphere for each data point sampled.  This was configured for

# use on a Win95 computer.  Some changes may need to be made for use on

# other systems.  This program assumes that POVRay has been installed

# and that there is a path to it.

##############################################################################

# Define files for the template (header/footer), the data and the POV file.

$povfile="plotter.pov";

$scale   =.25;

$radius  = $scale;

# open the POV file.

open (POV, ">$povfile");

# Print the header

print POV "#version 3.0\n";

print POV "global_settings { assumed_gamma 2.2 }\n\n";

print POV "#include \"colors.inc\"\n";

print POV "#include \"shapes.inc\"\n";

print POV "#include \"textures.inc\"\n";

print POV "#include \"glass.inc\"\n";

print POV "#include \"stones.inc\"\n\n";

print POV "#include \"metals.inc\"\n\n";

print POV "camera {\n";

print POV "location <-2,-9,-2>\n";

print POV "  look_at <-2,0,-2>}\n\n";

print POV "// Light sources \n";

print POV "light_source {<-30, 21,  40> color White}\n";

print POV "light_source {< 0, -8, -4> color White}\n";

print POV "light_source {< 2,  30,  3> color White}\n";

print POV "background { color rgb <1, 1, 1> }\n\n";

@ul = (.3,.3,.6);

@vl = (.2,.2,.9);

for ($j=0; $j<1; $j++)

 {

  for ($k=0; $k<1; $k++)

   {

$u = $ul[$j];

$v = $vl[$k];

$rad = 2;

# Print the data.

for ($i=0; $i<800; $i++)

 {

  $t = $i * .1;

  # Cosines

  $cosu = cos($u*$t);

  $cosv = cos($v*$t);

  # Sines

  $sinu = sin($u*$t);

  $sinv = sin($v*$t);

  # Compute X and Y

  $xval = $rad*$sinu*$cosv;

  $yval = $rad*$sinu*$sinv;

  $zval = $rad*$cosu;

  $colr=1/(1+$xval*$xval);

  $colg=1/sqrt(1+abs($yval));

  $colb=1/(1+$zval*$zval*$zval*$zval);

  

  $xval += $j*5; $yval += $k*5;

  print POV "sphere { <$xval, $zval, $yval>, $radius\n";

  print POV "    texture { pigment {color rgb <$colr, $colg, $colb>}}\n";

  print POV "    finish {caustics 1.0 phong 1 phong_size 300 reflection 0.15}\n";

  print POV "}\n\n";

  if ($i>0)

   {

    print POV "cylinder { <$xval, $zval, $yval>, <$xold, $zold, $yold> $radius\n";

    print POV "    texture { pigment {color rgb <$colr, $colg, $colb>}}\n";

    print POV "    finish {caustics 1.0 phong 1 phong_size 300 reflection 0.15}\n";

    print POV "}\n\n";

   }

  $xold = $xval;

  $yold = $yval;

  $zold = $zval;

 }

}}

close(POV);

# End of script