#!/opt/local/bin/perl

# change path to fit your system
#	usage: $ perl infinitile.pl

# can generate SVG files containing puzzle pieces in a tile

#	Copyright (C) 2010  Robert Flannery

# version 1.0
# Thu Jul 29 06:14:26 PDT 2010

#    This program is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, either version 3 of the License, or
#    (at your option) any later version.

#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.

#    You should have received a copy of the GNU General Public License
#    along with this program.  If not, see <http://www.gnu.org/licenses/>.

# I used regular_polygon.pl by GustavB to create a decagon.
# http://commons.wikimedia.org/wiki/User:Gustavb/regular_polygon.pl

# Daud Sutton explains how to use a few pieces to create an indefinitely large 
# puzzle, inspired by Islamic Design, which is the name of his book.
# http://www.powells.costarm/biblio?isbn=9780802716354

# Squiggle is what I've been using to convert SVG to PNG
# http://xmlgraphics.apache.org/batik/tools/browser.html

# points
@star = ();
$#star = 19; # array length of 20
$star_length = $#star + 1;
$pindex = 0; # point index

# Presentation parameters

$stroke = 0.1;
$draw_border = 1;
$border_color = "#777";
$star_color = "#AAA";
$kite_color = "#887";
$pentagon_color = "#444";
$bottle_color = "#755";
$doublepentagon_color = "#666";

# Constants 
$pi = 3.14159265358979323846264338327950288419717;

# Derived measures
$d = 2*$pi/10;
$a = ($pi - $d) / 2;
$radius = 36;
$centerX = 0;
$centerY = 0;

#default
$dim =  800;
$vdim = 800;

$Elmer = '<defs>' . "\n\n"; # definitions for SVG file


for($v=$a; $v <= 2*$pi+$a-$d; $v+=$d) 
{
    $x = $centerX + $radius*cos($v); 
    $y = $centerY + $radius*sin($v);
    $star[$pindex] = [$x, $y];    
    $pindex += 2; # 2 increment
    if($pindex > $#star)
    {
    	$pindex = $pindex % ($star_length); # modulo
    }
}

for($pindex=1; $pindex<$star_length; $pindex += 2) #$pindex is calculated value
{
	$p1_index = $pindex + 1;
	if($p1_index > $#star)
  {
  	$p1_index = $p1_index % $star_length; # modulo
  }
	$p1ref = $star[$p1_index];
	
	$p2_index = $p1_index + 4;
  if($p2_index > $#star)
  {
  	$p2_index = $p2_index % $star_length; # modulo
  }
	$p2ref = $star[$p2_index];
	$line1ref = [$p1ref, $p2ref];

	$p3_index = $pindex + 3;
	if($p3_index > $#star)
  {
  	$p3_index = $p3_index % $star_length; # modulo
  }
	$p3ref = $star[$p3_index];
	
	$p4_index = $p3_index + 4;
  if($p4_index > $#star)
  {
  	$p4_index = $p4_index % $star_length; # modulo
  }
	$p4ref = $star[$p4_index];
	$line2ref = [$p3ref, $p4ref];
	
	$pointref = find_intersection_point( [$line1ref, $line2ref] );
	($xi, $yi) = @{$pointref};
	
	$inter_index = $pindex + 4;
	if($inter_index > $#star)
  {
  	$inter_index = $inter_index % $star_length; # modulo
  }
	$star[$inter_index] = [$xi, $yi];
}

define_pieces( [ @star ], "star", "$star_color" );

($star_0x, $star_0y) = @{ $star[0] };
($star_1x, $star_1y) = @{ $star[1] };
($star_2x, $star_2y) = @{ $star[2] };
($star_3x, $star_3y) = @{ $star[3] };
($star_4x, $star_4y) = @{ $star[4] };
($star_5x, $star_5y) = @{ $star[5] };
($star_6x, $star_6y) = @{ $star[6] };
($star_7x, $star_7y) = @{ $star[7] };
($star_8x, $star_8y) = @{ $star[8] };
($star_9x, $star_9y) = @{ $star[9] };
($star_10x, $star_10y) = @{ $star[10] };
($star_11x, $star_11y) = @{ $star[11] };
($star_12x, $star_12y) = @{ $star[12] };
($star_13x, $star_13y) = @{ $star[13] };
($star_14x, $star_14y) = @{ $star[14] };
($star_15x, $star_15y) = @{ $star[15] };
($star_16x, $star_16y) = @{ $star[16] };
($star_17x, $star_17y) = @{ $star[17] };
($star_18x, $star_18y) = @{ $star[18] };
($star_19x, $star_19y) = @{ $star[19] };

@half_star = ();
for($pindex=1; $pindex < 12; $pindex++) 
{
	push @half_star, $star[$pindex];
}

$old_draw_border = $draw_border;
$draw_border = 0;
define_pieces( [ @half_star ], "half_star_core", "$star_color" );
$draw_border = $old_draw_border;
$Elmer = $Elmer .   '<g id="half_star"  >' . "\n"; # draw needed lines
$Elmer = $Elmer .   '<use xlink:href="#half_star_core"/>' . "\n";
if($draw_border == 1)
{
	$Elmer = $Elmer . '<line x1="' . $star_1x . '" y1="' . $star_1y . '" x2="' . $star_2x . '" y2="' . $star_2y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_2x . '" y1="' . $star_2y . '" x2="' . $star_3x . '" y2="' . $star_3y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_3x . '" y1="' . $star_3y . '" x2="' . $star_4x . '" y2="' . $star_4y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_4x . '" y1="' . $star_4y . '" x2="' . $star_5x . '" y2="' . $star_5y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_5x . '" y1="' . $star_5y . '" x2="' . $star_6x . '" y2="' . $star_6y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_6x . '" y1="' . $star_6y . '" x2="' . $star_7x . '" y2="' . $star_7y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_7x . '" y1="' . $star_7y . '" x2="' . $star_8x . '" y2="' . $star_8y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_8x . '" y1="' . $star_8y . '" x2="' . $star_9x . '" y2="' . $star_9y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_9x . '" y1="' . $star_9y . '" x2="' . $star_10x . '" y2="' . $star_10y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $star_10x . '" y1="' . $star_10y . '" x2="' . $star_11x . '" y2="' . $star_11y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
}
$Elmer = $Elmer .   '</g>' . "\n\n";

@rising_star = ();
for($pindex=1; $pindex < 12; $pindex++) 
{
	$star_index = $pindex + 5;
	$star_index = $star_index % $star_length; # modulo
	push @rising_star, $star[$star_index];
}
$old_draw_border = $draw_border;
$draw_border = 0;
define_pieces( [ @rising_star ], "rising_star", "$star_color" );
$draw_border = $old_draw_border;

######### additional points
$p1ref = $star[9];
$p2ref = $star[10];
$p3ref = $star[12];
$p4ref = $star[13];
$line1ref = [$p1ref, $p2ref];
$line2ref = [$p3ref, $p4ref];
$top_point = find_intersection_point( [$line1ref, $line2ref] );
($topX, $topY) = @{ $top_point };


$p1ref = $star[2];
$p2ref = $star[3];
$p3ref = $star[0];
$p4ref = $star[19];
$line1ref = [$p1ref, $p2ref];
$line2ref = [$p3ref, $p4ref];
$bottom_point = find_intersection_point( [$line1ref, $line2ref] );
($bottomX, $bottomY) = @{ $bottom_point };

@k_star = (); # 10 k_star points
for($pindex=1; $pindex<$star_length; $pindex += 2) #$pindex is calculated value
{
	$p1ref = $star[$pindex];
	
	$pindex2 = $pindex + 1;
	if($pindex2 > $#star)
	{
 	 $pindex2 = $pindex2 % $star_length; # modulo
	}
	$p2ref = $star[$pindex2];
	
	$pindex3 = $pindex + 3;
	if($pindex3 > $#star)
	{
 	 $pindex3 = $pindex3 % $star_length; # modulo
	}
	$p3ref = $star[$pindex3];
	
	$pindex4 = $pindex + 4;
	if($pindex4 > $#star)
	{
 	 $pindex4 = $pindex4 % $star_length; # modulo
	}
	$p4ref = $star[$pindex4];
	
	$line1ref = [$p1ref, $p2ref];
	$line2ref = [$p3ref, $p4ref];

	$point_point = find_intersection_point( [$line1ref, $line2ref] );
	push @k_star, $point_point;
}

($k_star_0x, $k_star_0y) = @{ $k_star[0] };
($k_star_1x, $k_star_1y) = @{ $k_star[1] };
($k_star_2x, $k_star_2y) = @{ $k_star[2] };
($k_star_3x, $k_star_3y) = @{ $k_star[3] };
($k_star_4x, $k_star_4y) = @{ $k_star[4] };
($k_star_5x, $k_star_5y) = @{ $k_star[5] };
($k_star_6x, $k_star_6y) = @{ $k_star[6] };
($k_star_7x, $k_star_7y) = @{ $k_star[7] };
($k_star_8x, $k_star_8y) = @{ $k_star[8] };
($k_star_9x, $k_star_9y) = @{ $k_star[9] };


@long_star = (); # 10 long_star points

for($pindex=1; $pindex<$star_length; $pindex += 2) #$pindex is calculated value
{
	$p1ref = $star[$pindex];

	$pindex2 = $pindex + 2;
	if($pindex2 > $#star)
	{
 	 $pindex2 = $pindex2 % $star_length; # modulo
	}
	$p2ref = $star[$pindex2];

	$pindex8 = $pindex + 8;
	if($pindex8 > $#star)
	{
  	$pindex8 = $pindex8 % $star_length; # modulo
	}
	$p3ref = $star[$pindex8];

	$pindex10 = $pindex + 10;
	if($pindex10 > $#star)
	{
  	$pindex10 = $pindex10 % $star_length; # modulo
	}
	$p4ref = $star[$pindex10];

	$line1ref = [$p1ref, $p2ref];
	$line2ref = [$p3ref, $p4ref];
	$point_point = find_intersection_point( [$line1ref, $line2ref] );
	($pointX, $pointY) = @{$point_point};
	push @long_star, $point_point;
}
($long_star_0x, $long_star_0y) = @{ $long_star[0] };
($long_star_1x, $long_star_1y) = @{ $long_star[1] };
($long_star_2x, $long_star_2y) = @{ $long_star[2] };
($long_star_3x, $long_star_3y) = @{ $long_star[3] };
($long_star_4x, $long_star_4y) = @{ $long_star[4] };
($long_star_5x, $long_star_5y) = @{ $long_star[5] };
($long_star_6x, $long_star_6y) = @{ $long_star[6] };
($long_star_7x, $long_star_7y) = @{ $long_star[7] };
($long_star_8x, $long_star_8y) = @{ $long_star[8] };
($long_star_9x, $long_star_9y) = @{ $long_star[9] };

# kite
@kite = (); #empty array
$pindex=1;
$p1_index = $pindex + 1;
if($p1_index > $#star)
{
  $p1_index = $p1_index % $star_length; # modulo
}
$p1ref = $star[$p1_index];
	
$p2_index = $p1_index + 3;
if($p2_index > $#star)
{
  $p2_index = $p2_index % $star_length; # modulo
}
$p2ref = $star[$p2_index];
$line1ref = [$p1ref, $p2ref];

$p3_index = $pindex + 19;
if($p3_index > $#star)
{
  $p3_index = $p3_index % $star_length; # modulo
}
$p3ref = $star[$p3_index];
	
$p4_index = $p3_index + 17;
if($p4_index > $#star)
{
  $p4_index = $p4_index % $star_length; # modulo
}
$p4ref = $star[$p4_index];
$line2ref = [$p3ref, $p4ref];
	
$pointref = find_intersection_point( [$line1ref, $line2ref] );

	($xi, $yi) = @{ $pointref };
		
	$p1_index = $pindex + 19;
	if($p1_index > $#star)
	{
  	$p1_index = $p1_index % $star_length; # modulo
  }
  	
	$trough_index = $p1_index + 1;
	if($trough_index > $#star)
	{
  	$trough_index = $trough_index % $star_length; # modulo
  }
		
	$point_four_index = $p1_index + 2;
	if($point_four_index > $#star)
	{
  	$point_four_index = $point_four_index % $star_length; # modulo
  }
	push @kite, $pointref;
	push @kite, $star[$p1_index];
	push @kite, $star[$trough_index];
	push @kite, $star[$point_four_index];
		
	define_pieces( [ @kite ], "kite", "$kite_color" );
	
	($kite_0x, $kite_0y) = @{ $kite[0] };
	($kite_1x, $kite_1y) = @{ $kite[1] };
	($kite_2x, $kite_2y) = @{ $kite[2] };
	($kite_3x, $kite_3y) = @{ $kite[3] };
	
	@half_kite = ();
	for($pindex=0; $pindex < 3; $pindex++) 
	{
		push @half_kite, $kite[$pindex];
	}

$old_draw_border = $draw_border;
$draw_border = 0;
define_pieces( [ @half_kite ], "half_kite_core", "$kite_color" );
$draw_border = $old_draw_border;
$Elmer = $Elmer .   '<g id="half_kite"  >' . "\n"; # add needed lines
$Elmer = $Elmer .   '<use xlink:href="#half_kite_core"/>' . "\n";
if($draw_border == 1)
{
	$Elmer = $Elmer .   '<line x1="' . $kite_1x . '" y1="' . $kite_1y . '" x2="' . $kite_2x . '" y2="' . $kite_2y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
}
$Elmer = $Elmer .   '</g>' . "\n\n";

# pentagon
@pentagon = ();

($star_9x, $star_9y) = @{ $star[9] };
($star_3x, $star_3y) = @{ $star[3] };

($star_11x, $star_11y) = @{ $star[11] };
($star_17x, $star_17y) = @{ $star[17] };

($star_7x, $star_7y) = @{ $star[7] };

($star_13x, $star_13y) = @{ $star[13] };

$pentagon[0] = [$star_9x, $star_9y];
$pentagon[1] = [$star_11x, $star_11y];
$pentagon[2] = find_intersection_point( [ [ [$star_3x, $star_3y], [$star_13x, $star_13y] ], [ [$star_11x, $star_11y], [$star_17x, $star_17y] ] ] );
$pentagon[3] = find_intersection_point( [ [ [$star_3x, $star_3y], [$star_13x, $star_13y] ], [ [$star_17x, $star_17y], [$star_7x, $star_7y] ] ] );
$pentagon[4] = find_intersection_point( [ [ [$star_17x, $star_17y], [$star_7x, $star_7y] ], [ [$star_9x, $star_9y], [$star_3x, $star_3y] ] ] );
define_pieces( [ @pentagon ], "pentagon", "$pentagon_color" );

($pentagon_0x, $pentagon_0y) = @{ $pentagon[0] };
($pentagon_1x, $pentagon_1y) = @{ $pentagon[1] };
($pentagon_2x, $pentagon_2y) = @{ $pentagon[2] };
($pentagon_3x, $pentagon_3y) = @{ $pentagon[3] };
($pentagon_4x, $pentagon_4y) = @{ $pentagon[4] };


@half_pentagon = ();

($star_0x, $star_0y) = @{ $star[0] };
($star_10x, $star_10y) = @{ $star[10] };

$p1 = find_intersection_point( [ [ [$star_9x, $star_9y], [$star_11x, $star_11y] ], [ [$star_0x, $star_0y], [$star_10x, $star_10y] ] ] ); 

push @half_pentagon, $p1;
push @half_pentagon, $pentagon[0];
push @half_pentagon, $pentagon[4];
push @half_pentagon, $pentagon[3];

($half_pentagon_0x, $half_pentagon_0y) = @{ $half_pentagon[0] };
($half_pentagon_1x, $half_pentagon_1y) = @{ $half_pentagon[1] };
($half_pentagon_2x, $half_pentagon_2y) = @{ $half_pentagon[2] };
($half_pentagon_3x, $half_pentagon_3y) = @{ $half_pentagon[3] };

$old_draw_border = $draw_border;
$draw_border = 0;
define_pieces( [ @half_pentagon ], "half_pentagon_core", "$pentagon_color" );
$draw_border = $old_draw_border;
$Elmer = $Elmer .   '<g id="half_pentagon"  >' . "\n"; 
$Elmer = $Elmer .   '<use xlink:href="#half_pentagon_core"/>' . "\n";
if($draw_border == 1)
{
	$Elmer = $Elmer .   '<line x1="' . $half_pentagon_0x . '" y1="' . $half_pentagon_0y . '" x2="' . $half_pentagon_1x . '" y2="' . $half_pentagon_1y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $half_pentagon_1x . '" y1="' . $half_pentagon_1y . '" x2="' . $half_pentagon_2x . '" y2="' . $half_pentagon_2y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $half_pentagon_2x . '" y1="' . $half_pentagon_2y . '" x2="' . $half_pentagon_3x . '" y2="' . $half_pentagon_3y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
}
$Elmer = $Elmer .   '</g>' . "\n\n";

@half_pentagon2 = ();
push @half_pentagon2, $p1;
push @half_pentagon2, $pentagon[1];
push @half_pentagon2, $pentagon[2];
push @half_pentagon2, $pentagon[3];

($half_pentagon2_0x, $half_pentagon2_0y) = @{ $half_pentagon2[0] };
($half_pentagon2_1x, $half_pentagon2_1y) = @{ $half_pentagon2[1] };
($half_pentagon2_2x, $half_pentagon2_2y) = @{ $half_pentagon2[2] };
($half_pentagon2_3x, $half_pentagon2_3y) = @{ $half_pentagon2[3] };

$old_draw_border = $draw_border;
$draw_border = 0;
define_pieces( [ @half_pentagon2 ], "half_pentagon2_core", "$pentagon_color" );
$draw_border = $old_draw_border;
$Elmer = $Elmer .   '<g id="half_pentagon2"  >' . "\n"; 
$Elmer = $Elmer .   '<use xlink:href="#half_pentagon2_core"/>' . "\n";
if($draw_border == 1)
{
	$Elmer = $Elmer .   '<line x1="' . $half_pentagon2_0x . '" y1="' . $half_pentagon2_0y . '" x2="' . $half_pentagon2_1x . '" y2="' . $half_pentagon2_1y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $half_pentagon2_1x . '" y1="' . $half_pentagon2_1y . '" x2="' . $half_pentagon2_2x . '" y2="' . $half_pentagon2_2y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $half_pentagon2_2x . '" y1="' . $half_pentagon2_2y . '" x2="' . $half_pentagon2_3x . '" y2="' . $half_pentagon2_3y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
}
$Elmer = $Elmer .   '</g>' . "\n\n";

# bottle

$p1 = $star[9]; # point reference
$p10 = $star[11]; # point reference

$p6 = $star[19]; # point reference
($star_19x, $star_19y) = @{ $p6 };

$p5 = $star[1]; # point reference
($star_1x, $star_1y) = @{ $p5 };

$p3 = find_intersection_point( [ [ [$star_9x, $star_9y], [$star_3x, $star_3y] ], [ [$star_1x, $star_1y], [$star_7x, $star_7y] ] ] ); # 9 - 3 and 7 - 1

($l5x1, $l5y1) = @{ $p3 };
($star_12x, $star_12y) = @{ $star[12] };

$p8 = find_intersection_point( [ [ [$star_11x, $star_11y], [$star_17x, $star_17y] ], [ [$star_19x, $star_19y], [$star_13x, $star_13y] ] ] ); # 11 - 17 and 19 - 13

($l6x1, $l6y1) = @{ $p8 };
($star_8x, $star_8y) = @{ $star[8] };

($l7x1, $l7y1) = @{ $p3 };
($star_18x, $star_18y) = @{ $star[18] };

($l8x1, $l8y1) = @{ $p8 };
($star_2x, $star_2y) = @{ $star[2] };

($star_9x, $star_9y) = @{ $star[9] };
($star_19x, $l9y2) = @{ $star[19] };

$p2 = find_intersection_point( [ [ [$star_9x, $star_9y], [$star_19x, $star_19y] ], [ [$l5x1, $l5y1], [$star_12x, $star_12y] ] ] ); 
$p4 = find_intersection_point( [ [ [$l7x1, $l7y1], [$star_18x, $star_18y] ], [ [$star_11x, $star_11y], [$star_1x, $star_1y] ] ] ); 
$p7 = find_intersection_point( [ [ [$star_9x, $star_9y], [$star_19x, $star_19y] ], [ [$l8x1, $l8y1], [$star_2x, $star_2y] ] ] ); 
$p9 = find_intersection_point( [ [ [$l6x1, $l6y1], [$star_8x, $star_8y] ], [ [$star_11x, $star_11y], [$star_1x, $star_1y] ] ] ); 

@bottle = ($p1, $p2, $p3, $p4, $p5, $p6, $p7, $p8, $p9, $p10);

define_pieces( [ @bottle ], "bottle", "$bottle_color"  );

($bottle_0x, $bottle_0y) = @{ $p1 };
($bottle_1x, $bottle_1y) = @{ $p2 };
($bottle_2x, $bottle_2y) = @{ $p3 };
($bottle_3x, $bottle_3y) = @{ $p4 };
($bottle_4x, $bottle_4y) = @{ $p5 };
($bottle_5x, $bottle_5y) = @{ $p6 };
($bottle_6x, $bottle_6y) = @{ $p7 };
($bottle_7x, $bottle_7y) = @{ $p8 };
($bottle_8x, $bottle_8y) = @{ $p9 };
($bottle_9x, $bottle_9y) = @{ $p10 };

@half_bottle = ();

$p0 = find_intersection_point( [ [ [$star_0x, $star_0y], [$star_10x, $star_10y] ], [ [$star_9x, $star_9y], [$star_11x, $star_11y] ] ] ); 

push @half_bottle, $p0;
push @half_bottle, $p1;
push @half_bottle, $p2;
push @half_bottle, $p3;
push @half_bottle, $p4;
push @half_bottle, $p5;
$p11 = find_intersection_point( [ [ [$star_0x, $star_0y], [$star_10x, $star_10y] ], [ [$star_1x, $star_1y], [$star_19x, $star_19y] ] ] ); 
push @half_bottle, $p11;

$old_draw_border = $draw_border;
$draw_border = 0;
define_pieces( [ @half_bottle ], "half_bottle_core", "$bottle_color" );
$draw_border = $old_draw_border;

$Elmer = $Elmer .   '<g id="half_bottle"  >' . "\n"; 
$Elmer = $Elmer .   '<use xlink:href="#half_bottle_core"/>' . "\n";
if($draw_border == 1)
{
	($half_bottle_0x, $half_bottle_0y) = @{ $p0 };
	$Elmer = $Elmer .   '<line x1="' . $half_bottle_0x . '" y1="' . $half_bottle_0y . '" x2="' . $bottle_0x . '" y2="' . $bottle_0y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $bottle_0x . '" y1="' . $bottle_0y . '" x2="' . $bottle_1x . '" y2="' . $bottle_1y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $bottle_1x . '" y1="' . $bottle_1y . '" x2="' . $bottle_2x . '" y2="' . $bottle_2y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $bottle_2x . '" y1="' . $bottle_2y . '" x2="' . $bottle_3x . '" y2="' . $bottle_3y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer .   '<line x1="' . $bottle_3x . '" y1="' . $bottle_3y . '" x2="' . $bottle_4x . '" y2="' . $bottle_4y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	($half_bottle_6x, $half_bottle_6y) = @{ $p11 };
	$Elmer = $Elmer .   '<line x1="' . $half_bottle_6x . '" y1="' . $half_bottle_6y . '" x2="' . $bottle_4x . '" y2="' . $bottle_4y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";

}
$Elmer = $Elmer .   '</g>' . "\n\n";

# doublepentagon 

($l2x1, $l2y1) = @{ $star[15] };
($l2x2, $l2y2) = @{ $star[1] };

($l3x1, $l3y1) = @{ $star[15] };
($l3x2, $l3y2) = @{ $star[9] };

($l4x1, $l4y1) = @{ $star[11] };
($l4x2, $l4y2) = @{ $star[5] };

($l5x1, $l5y1) = @{ $star[9] };
($l5x2, $l5y2) = @{ $star[19] };

($l6x1, $l6y1) = @{ $star[7] };
($l6x2, $l6y2) = @{ $star[1] };

$p1 = find_intersection_point( [ [ [$star_17x, $star_17y], [$star_11x, $star_11y] ], [ [$l2x1, $l2y1], [$l2x2, $l2y2] ] ] ); 
$p2 = find_intersection_point( [ [ [$l3x1, $l3y1], [$l3x2, $l3y2] ], [ [$star_17x, $star_17y], [$star_11x, $star_11y] ] ] ); 
($l7x1, $l7y1) = @{ $p2 };
($l7x2, $l7y2) = @{ $star[6] };
$p4 = find_intersection_point( [ [ [$l5x1, $l5y1], [$l5x2, $l5y2] ], [ [$l4x1, $l4y1], [$l4x2, $l4y2] ] ] ); 
($l8x1, $l8y1) = @{ $star[16] };
($l8x2, $l8y2) = @{ $p4 };

$p3 = find_intersection_point( [ [ [$l8x1, $l8y1], [$l8x2, $l8y2] ], [ [$l7x1, $l7y1], [$l7x2, $l7y2] ] ] ); 
$p5 = find_intersection_point( [ [ [$l6x1, $l6y1], [$l6x2, $l6y2] ], [ [$l4x1, $l4y1], [$l4x2, $l4y2] ] ] ); 

($l9x1, $l9y1) = @{ $star[5] };
($l9x2, $l9y2) = @{ $star[19] };

$p6 = find_intersection_point( [ [ [$l6x1, $l6y1], [$l6x2, $l6y2] ], [ [$l9x1, $l9y1], [$l9x2, $l9y2] ] ] ); 

$p8 = find_intersection_point( [ [ [$l5x1, $l5y1], [$l5x2, $l5y2] ], [ [$l2x1, $l2y1], [$l2x2, $l2y2] ] ] ); 

($l10x1, $l10y1) = @{ $star[16] };
($l10x2, $l10y2) = @{ $p6 };

($l11x1, $l11y1) = @{ $star[6] };
($l11x2, $l11y2) = @{ $p8 };

$p7 = find_intersection_point( [ [ [$l10x1, $l10y1], [$l10x2, $l10y2] ], [ [$l11x1, $l11y1], [$l11x2, $l11y2] ] ] ); 

@doublepentagon = ($p1, $p2, $p3,  $p4, $p5, $p6, $p7, $p8);
define_pieces( [ @doublepentagon ], "doublepentagon", "$doublepentagon_color"  );

#points
($l12x1, $l12y1) = @{ $doublepentagon[0] };
($l12x2, $l12y2) = @{ $doublepentagon[1] };
($l13x1, $l13y1) = @{ $doublepentagon[2] };
($l13x2, $l13y2) = @{ $doublepentagon[3] };

$p9 = find_intersection_point( [ [ [$l12x1, $l12y1], [$l12x2, $l12y2] ], [ [$l13x1, $l13y1], [$l13x2, $l13y2] ] ] ); 

($l14x1, $l14y1) = @{ $doublepentagon[4] };
($l14x2, $l14y2) = @{ $doublepentagon[5] };
($l15x1, $l15y1) = @{ $doublepentagon[7] };
($l15x2, $l15y2) = @{ $doublepentagon[0] };
$p10 = find_intersection_point( [ [ [$l14x1, $l14y1], [$l14x2, $l14y2] ], [ [$l15x1, $l15y1], [$l15x2, $l15y2] ] ] ); 

@half_doublepentagon = ();

push @half_doublepentagon, $p3;
push @half_doublepentagon, $p2;
push @half_doublepentagon, $p1;
push @half_doublepentagon, $p8;
push @half_doublepentagon, $p7;

($half_doublepentagon_0x, $half_doublepentagon_0y) = @{ $half_doublepentagon[0] };
($half_doublepentagon_1x, $half_doublepentagon_1y) = @{ $half_doublepentagon[1] };
($half_doublepentagon_2x, $half_doublepentagon_2y) = @{ $half_doublepentagon[2] };
($half_doublepentagon_3x, $half_doublepentagon_3y) = @{ $half_doublepentagon[3] };
($half_doublepentagon_4x, $half_doublepentagon_4y) = @{ $half_doublepentagon[4] };

$old_draw_border = $draw_border;
$draw_border = 0;
define_pieces( [ @half_doublepentagon ], "half_doublepentagon_core", "$doublepentagon_color"  );
$draw_border = $old_draw_border;
$Elmer = $Elmer .   '<g id="half_doublepentagon"  >' . "\n"; # draw needed lines
$Elmer = $Elmer .   '<use xlink:href="#half_doublepentagon_core"/>' . "\n";
if($draw_border == 1)
{
	$Elmer = $Elmer . '<line x1="' . $half_doublepentagon_0x . '" y1="' . $half_doublepentagon_0y . '" x2="' . $half_doublepentagon_1x . '" y2="' . $half_doublepentagon_1y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $half_doublepentagon_1x . '" y1="' . $half_doublepentagon_1y . '" x2="' . $half_doublepentagon_2x . '" y2="' . $half_doublepentagon_2y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $half_doublepentagon_2x . '" y1="' . $half_doublepentagon_2y . '" x2="' . $half_doublepentagon_3x . '" y2="' . $half_doublepentagon_3y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";
	$Elmer = $Elmer . '<line x1="' . $half_doublepentagon_3x . '" y1="' . $half_doublepentagon_3y . '" x2="' . $half_doublepentagon_4x . '" y2="' . $half_doublepentagon_4y . '" stroke="' . $border_color . '" stroke-width="' . $stroke . '"  />' . "\n";

}
$Elmer = $Elmer .   '</g>' . "\n\n";

##################### group definitions

# b - bottle
# s - star
# k - kite
# p - pentagon
# d - doublepentagon
 
#define group: kited_star
$Elmer = $Elmer .  '<g id="kited_star">' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#star"/>' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#kite"/>' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(36 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(72 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(108 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(144 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(180 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(216 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(252 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(288 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(324 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '</g>' . "\n\n";

#define group: k_rising_star
$Elmer = $Elmer .  '<g id="k_rising_star">' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#rising_star"/>' . "\n";
($x2, $y2) = @{ $pentagon[3] };
$x_translation = $star_10x - $x2;
$y_translation = $star_10y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(324 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(36 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(72 ' . $centerX . " $centerY" . ')" />' . "\n";

$Elmer = $Elmer .  '<use xlink:href="#half_pentagon2" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(288 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#half_pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(108 ' . $centerX . " $centerY" . ')" />' . "\n";

$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(108 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(144 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(180 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(216 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(252 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '</g>' . "\n\n";

#define group: k_half_star
$Elmer = $Elmer .  '<g id="k_half_star">' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#half_star"/>' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(36 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(72 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(108 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$Elmer = $Elmer .  '<use xlink:href="#kite" transform="rotate(144 ' . $centerX . " $centerY" . ')" />' . "\n"; 
$x_translation = $star_11x - $kite_2x;
$y_translation = $star_11y - $kite_2y;
$Elmer = $Elmer .  '<use xlink:href="#half_kite" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $star_11x . " $star_11y" . ')" />' . "\n";
$x_translation = $star_2x - $kite_2x;
$y_translation = $star_2y - $kite_2y;
$Elmer = $Elmer .  '<use xlink:href="#half_kite" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(324 ' . $star_2x . " $star_2y" . ')"  />' . "\n";

($star_2x, $star_2y) =  @{ $star[2] };
($x2, $y2) = @{ $pentagon[2] };
$x_translation = $star_2x - $x2;
$y_translation = $star_2y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(288 ' . $star_2x . " $star_2y" . ')" />' . "\n";

($star_4x, $star_4y) =  @{ $star[4] };
($x2, $y2) = @{ $pentagon[3] };
$x_translation = $star_4x - $x2;
$y_translation = $star_4y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(252 ' . $star_4x . " $star_4y" . ')" />' . "\n";

($star_6x, $star_6y) =  @{ $star[6] };
($x2, $y2) = @{ $pentagon[2] };
$x_translation = $star_6x - $x2;
$y_translation = $star_6y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

($x2, $y2) = @{ $pentagon[2] };
$x_translation = $star_8x - $x2;
$y_translation = $star_8y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(36 ' . $star_8x . " $star_8y" . ')" />' . "\n";

($x2, $y2) = @{ $pentagon[2] };
$x_translation = $star_10x - $x2;
$y_translation = $star_10y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(72 ' . $star_10x . " $star_10y" . ')" />' . "\n";
$Elmer = $Elmer .  '</g>' . "\n\n";

# define group: pentabottle
$Elmer = $Elmer .   '<g id="pentabottle">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#pentagon"/>' . "\n";
($x1, $y1) = @{ $bottle[0] };
($x2, $y2) = @{ $bottle[4] };
$x_translation = $x1 - $x2; 
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#bottle" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

# define group: fivepentabottle
$Elmer = $Elmer .   '<g id="fivepentabottle">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#pentabottle"/>' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#pentagon" transform="rotate(180 ' . $pentagon_0x . " $pentagon_0y" . ')"/>' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#pentagon" transform="rotate(180 ' . $pentagon_1x . " $pentagon_1y" . ')"/>' . "\n";

$x_translation = $bottle_9x - $bottle_4x;
$y_translation = $bottle_9y - $bottle_4y;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";

$x_translation = $bottle_0x - $bottle_5x;
$y_translation = $bottle_0y - $bottle_5y;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";

$Elmer = $Elmer .   '</g>' . "\n\n";

# define group: capped_bottle
$Elmer = $Elmer .   '<g id="capped_bottle">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#bottle"/>' . "\n";
($x1, $y1) = @{ $bottle[0] };
($x2, $y2) = @{ $half_pentagon[1] };
$x_translation = $x1 - $x2; 
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#half_pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(252 ' . $x1 . " $y1" . ')" />' . "\n";
($x1, $y1) = @{ $bottle[1] };
($x2, $y2) = @{ $pentagon[2] };
$x_translation = $x1 - $x2; 
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";
($x1, $y1) = @{ $bottle[4] };
($x2, $y2) = @{ $pentagon[0] };
$x_translation = $x1 - $x2; 
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";
($x1, $y1) = @{ $bottle[6] };
($x2, $y2) = @{ $pentagon[0] };
$x_translation = $x1 - $x2; 
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(324 ' . $x1 . " $y1" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

# define group: pentabottle2
$Elmer = $Elmer .   '<g id="pentabottle2">' . "\n";
($x1, $y1) = @{ $pentagon[0] };
$Elmer = $Elmer .   '<use xlink:href="#pentagon" transform="rotate(252 ' . $x1 . " $y1" . ')" />' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#bottle" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

# define group: pentangledbottle
$Elmer = $Elmer .   '<g id="pentangledbottle">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#bottle"/>' . "\n";
($x1, $y1) = @{ $bottle[4] };
($x2, $y2) = @{ $pentagon[0] };
$x_translation = $x1 - $x2;
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
($x1, $y1) = @{ $bottle[1] };
($x2, $y2) = @{ $pentagon[2] };
$x_translation = $x1 - $x2;
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
($x1, $y1) = @{ $bottle[8] };
($x2, $y2) = @{ $pentagon[4] };
$x_translation = $x1 - $x2;
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: kdk
$Elmer = $Elmer .   '<g id="kdk">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#doublepentagon"/>' . "\n";
($x1, $y1) = @{ $doublepentagon[2] };
$x_translation = $x1 - $kite_2x;
$y_translation = $y1 - $kite_2y;
$Elmer = $Elmer .   '<use xlink:href="#kite"  x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $x1 . " $y1" . ')" />' . "\n";
($x1, $y1) = @{ $doublepentagon[6] };
$x_translation = $x1 - $kite_2x;
$y_translation = $y1 - $kite_2y;
$Elmer = $Elmer .   '<use xlink:href="#kite"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: kdk_up
$Elmer = $Elmer .   '<g id="kdk_up">' . "\n";
$x_translation = $kite_2x - $kite_0x;
$y_translation = $kite_2y - $kite_0y;
$Elmer = $Elmer .   '<use xlink:href="#kdk"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: kdk_down
$Elmer = $Elmer .   '<g id="kdk_down">' . "\n";
$x_translation = $kite_0x - $kite_2x;
$y_translation = $kite_0y - $kite_2y;
$Elmer = $Elmer .   '<use xlink:href="#kdk"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: diamond
$Elmer = $Elmer .   '<g id="diamond">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#doublepentagon"/>' . "\n";

($x1, $y1) = @{ $doublepentagon[6] };
$x_translation = $x1 - $kite_2x;
$y_translation = $y1 - $kite_2y;
$Elmer = $Elmer .   '<use xlink:href="#kite" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
($kite_1x, $kite_1y) = @{ $kite[1] };
($x1, $y1) = @{ $doublepentagon[3] };
$x_translation = $x1 - $kite_1x;
$y_translation = $y1 - $kite_1y;
$Elmer = $Elmer .   '<use xlink:href="#kite" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $x1 . " $y1" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: half_diamond
$Elmer = $Elmer .   '<g id="half_diamond">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#half_doublepentagon"/>' . "\n";

($x1, $y1) = @{ $half_doublepentagon[4] };
$x_translation = $x1 - $kite_2x;
$y_translation = $y1 - $kite_2y;

$Elmer = $Elmer .   '<use xlink:href="#half_kite" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
($kite_1x, $kite_1y) = @{ $kite[1] };
($x1, $y1) = @{ $half_doublepentagon[0] };
$x_translation = $x1 - $kite_1x;
$y_translation = $y1 - $kite_1y;

$Elmer = $Elmer .   '<use xlink:href="#half_kite" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(144 ' . $x1 . " $y1" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: half_diamond_plus
$Elmer = $Elmer .   '<g id="half_diamond_plus">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#half_diamond" />' . "\n";
($x1, $y1) = @{ $half_doublepentagon[1] };
($x2, $y2) = @{ $bottle[0] };
$x_translation = $x1 - $x2;
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#bottle" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";

($x1, $y1) = @{ $half_doublepentagon[1] };
($x2, $y2) = @{ $half_pentagon2[2] };
$x_translation = $x1 - $x2;
$y_translation = $y1 - $y2;
$Elmer = $Elmer .   '<use xlink:href="#half_pentagon2" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(108 ' . $x1 . " $y1" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: core_wheel
$Elmer = $Elmer .  '<g id="core_wheel">' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#kited_star"/>' . "\n";
($x2, $y2) = @{ $pentagon[3] };
$x_translation = $star_10x - $x2;
$y_translation = $star_10y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(36 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(72 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(108 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(144 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(216 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(252 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(288 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(324 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: wheel
$Elmer = $Elmer .  '<g id="wheel">' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#kited_star"/>' . "\n";
($x2, $y2) = @{ $pentagon[3] };
$x_translation = $star_10x - $x2;
$y_translation = $star_10y - $y2;
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(36 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(72 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(108 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(144 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(216 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(252 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(288 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#pentabottle" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(324 ' . $centerX . " $centerY" . ')" />' . "\n";

$x_translation = $topX - $star_1x;
$y_translation = $topY - $star_1y;
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(36 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(72 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(108 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(144 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(216 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(252 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(288 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(324 ' . $centerX . " $centerY" . ')" />' . "\n";


$x_translation = ($long_star_6x - $pentagon_2x);
$y_translation = ($long_star_6y - $pentagon_2y);
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(144 ' . $x_translation . " $y_translation" . ')"  />' . "\n";

$x_translation = ($long_star_7x - $pentagon_0x);
$y_translation = ($long_star_7y - $pentagon_0y);
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(36 ' . $x_translation . " $y_translation" . ')"  />' . "\n";
$Elmer = $Elmer .  '</g>' . "\n\n";

#define group: turned_wheel
$Elmer = $Elmer .  '<g id="turned_wheel">' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#wheel" transform="rotate(72 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '</g>' . "\n\n";

#define group: turnedagain_wheel
$Elmer = $Elmer .  '<g id="turnedagain_wheel">' . "\n";
$Elmer = $Elmer .  '<use xlink:href="#wheel" transform="rotate(252 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .  '</g>' . "\n\n";

#define group: upsidedown_half_star
$Elmer = $Elmer .   '<g id="upsidedown_half_star">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#k_rising_star"  transform="rotate(180 ' . $centerX . " $centerY" . ')"  />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: half_stars_p
$Elmer = $Elmer .   '<g id="half_stars_p">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#pentagon"    />' . "\n";
($x1, $y1) = @{ $pentagon[1] };
$x_translation = $x1 - $star_2x;
$y_translation = $y1 - $star_2y;
$Elmer = $Elmer .   '<use xlink:href="#k_half_star"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
($x1, $y1) = @{ $pentagon[3] };
$x_translation = $x1 - $star_10x;
$y_translation = $y1 - $star_10y;
$Elmer = $Elmer .   '<use xlink:href="#k_half_star"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: bottle36
$Elmer = $Elmer .   '<g id="bottle36">' . "\n";
($bottle_3x, $bottle_3y) = @{ $bottle[3] };
$Elmer = $Elmer .   '<use xlink:href="#capped_bottle"  transform="rotate(36 ' . $bottle_3x . " $bottle_3y" . ')"  />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

######### two_andahalf_bottles
$Elmer = $Elmer .   '<g id="two_andahalf_bottles">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#bottle"    />' . "\n";
($bottle_6x, $bottle_6y) = @{ $bottle[6] };
($doublepentagon_4x, $doublepentagon_4y) = @{ $doublepentagon[4] };
$x_translation = $bottle_6x - $doublepentagon_4x;
$y_translation = $bottle_6y - $doublepentagon_4y;
$Elmer = $Elmer .   '<use xlink:href="#diamond"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

($doublepentagon_0x, $doublepentagon_0y) = @{ $doublepentagon[0] };
($bottle_3x, $bottle_3y) = @{ $bottle[3] };
$x_translation = ($bottle_6x - $doublepentagon_4x) + ($doublepentagon_0x - $bottle_3x);
$y_translation = ($bottle_6y - $doublepentagon_4y) + ($doublepentagon_0y - $bottle_3y);
$Elmer = $Elmer .   '<use xlink:href="#bottle36"   x="' . $x_translation . '" y="' .  $y_translation .'"   />' . "\n";

($bottle_9x, $bottle_9y) = @{ $bottle[9] };
($half_bottle_1x, $half_bottle_1y) = @{ $half_bottle[1] };
$x_translation = $bottle_9x - $half_bottle_1x;
$y_translation = $bottle_9y - $half_bottle_1y;
$Elmer = $Elmer .   '<use xlink:href="#half_bottle"   x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(288 ' . $bottle_9x . " $bottle_9y" . ')"  />' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#pentagon"  x="' . $x_translation . '" y="' .  $y_translation .'"   />' . "\n";

($bottle_0x, $bottle_0y) = @{ $bottle[0] };
($half_pentagon2_2x, $half_pentagon2_2y) = @{ $half_pentagon2[2] };
$x_translation = $bottle_0x - $half_pentagon2_2x;
$y_translation = $bottle_0y - $half_pentagon2_2y;
$Elmer = $Elmer .   '<use xlink:href="#half_pentagon2"  x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(108 ' . $bottle_0x . " $bottle_0y" . ')"  />' . "\n";

$x_translation = $bottle_3x - $pentagon_2x;
$y_translation = $bottle_3y - $pentagon_2y;
$Elmer = $Elmer .   '<use xlink:href="#pentagon"  x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(324 ' . $bottle_3x . " $bottle_3y" . ')" />' . "\n";

$x_translation = $bottle_5x - $pentagon_1x;
$y_translation = $bottle_5y - $pentagon_1y;
$Elmer = $Elmer .   '<use xlink:href="#pentagon" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

#define group: tile
$Elmer = $Elmer .   '<g id="tile">' . "\n";
$updown = ($centerY - $star_11y);

($xk1, $yk1) = @{ $kite[2] };
($xk2, $yk2) = @{ $kite[0] };

$corner1X = $centerX + ($long_star_1x - $long_star_6x) + ($kite_2x - $xk2);
$corner1Y = $centerY + ($long_star_1y - $long_star_6y) + ($kite_2y - $yk2) - $updown;

$x_translation = $corner1X - $xk2;
$y_translation = $corner1Y - $yk2 - ($yk1 - $yk2) + $star_1y - $star_11y;
$Elmer = $Elmer .   '<use xlink:href="#half_diamond" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";

$kstar_point = find_intersection_point( [ [ [$star_8x, $star_8y], [$star_7x, $star_7y] ], [ [$star_10x, $star_10y], [$star_11x, $star_11y] ] ] );

($kstar_pointX, $kstar_pointY) = @{ $kstar_point };
$x_translation = $corner1X - $kstar_pointX;
$y_translation = $corner1Y - $kstar_pointY;
$Elmer = $Elmer .   '<use xlink:href="#two_andahalf_bottles"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$y_translation = ($long_star_1y - $long_star_6y) + ($yk1 - $yk2) - $updown;
$Elmer = $Elmer .   '<use xlink:href="#upsidedown_half_star" x="' . 0 . '" y="' .  $y_translation .'"  />' . "\n";

$corner2X = $centerX + ($long_star_4x - $long_star_9x) + ($xk1 - $xk2);
$corner2Y = $centerY + ($long_star_4y - $long_star_9y) + ($yk1 - $yk2) - $updown;

$x_translation = $corner2X - $xk2;
$y_translation = $corner2Y - $yk2 + ($yk2 - $yk1);
$Elmer = $Elmer .   '<use xlink:href="#half_diamond"  x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $corner2X . " $corner2Y" . ')"  />' . "\n";

$x_translation = ($long_star_3x - $star_4x) + ($star_19x - $star_0x);
$y_translation = ($long_star_3y - $star_4y) + ($star_19y - $star_0y);
$Elmer = $Elmer .   '<use xlink:href="#two_andahalf_bottles" x="' . $x_translation . '" y="' .  $y_translation .'"/>' . "\n";

$corner3X = $centerX + ($long_star_6x - $long_star_1x) + ($xk2 - $xk1);
$corner3Y = $centerY + ($long_star_6y - $long_star_1y) + ($yk2 - $yk1) + $updown;

$x_translation = ($long_star_6x - $long_star_1x);
$y_translation = ($long_star_6y - $long_star_1y) + $star_1y - $star_11y + ($yk2 - $yk1);
$Elmer = $Elmer .   '<use xlink:href="#half_diamond"  x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $corner3X . " $corner3Y" . ')" />' . "\n";

($x1, $y1) = @{ $kstar_point };
$x_translation = $corner3X - $x1;
$y_translation = $corner3Y - $y1;
$Elmer = $Elmer .   '<use xlink:href="#two_andahalf_bottles"  x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $corner3X . " $corner3Y" . ')" />' . "\n";

($x1, $y1) = @{ $long_star[9] };
($x2, $y2) = @{ $long_star[4] };
$corner4X = $centerX + ($x1 - $x2) + ($xk2 - $xk1);
$corner4Y = $centerY + ($y1 - $y2) + ($yk2 - $yk1) + $updown;

$x_translation = $corner4X - $xk2;
$y_translation = $corner4Y - $yk2 - ($yk1 - $yk2);
$Elmer = $Elmer .   '<use xlink:href="#half_diamond" x="' . $x_translation . '" y="' .  $y_translation .'"  />' . "\n";

$y_translation = ($y1 - $y2) + ($yk2 - $yk1) + $updown;
$Elmer = $Elmer .   '<use xlink:href="#k_rising_star" x="' . 0 . '" y="' .  $y_translation .'"  />' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#wheel"/>' . "\n";

($pentagon_2x, $pentagon_2y) = @{ $pentagon[2] };
$x_translation = $corner2X - $centerX + ($centerX - $pentagon_2x);
$y_translation = ($centerY - $pentagon_2y);
$Elmer = $Elmer .   '<use xlink:href="#half_stars_p" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#half_stars_p" x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(180 ' . $centerX . " $centerY" . ')" />' . "\n";

($x1, $y1) = @{ $long_star[3] };
$x_translation = ($x1 - $star_4x) + ($star_19x - $star_0x);
$y_translation = ($y1 - $star_4y) + ($star_19y - $star_0y);
$Elmer = $Elmer .   '<use xlink:href="#two_andahalf_bottles" x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(180 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

# define group: bottled_wheel
$Elmer = $Elmer .  '<g id="bottled_wheel">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#core_wheel"/>' . "\n";
$x_translation = $k_star_7x - $bottle_0x;
$y_translation = $k_star_7y - $bottle_0y;
$Elmer = $Elmer .   '<use xlink:href="#bottle" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation = $k_star_6x - $bottle_4x + ($pentagon_3x - $pentagon_4x);
$y_translation = $k_star_6y - $bottle_4y + ($pentagon_3y - $pentagon_4y);
$Elmer = $Elmer .   '<use xlink:href="#tipped_bottle" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

# define group: v_bridge
$Elmer = $Elmer .  '<g id="v_bridge">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#wheel"/>' . "\n";

$x_translation = 0;
$y_translation = $star_1y - $star_11y;
$y_translation  += 4 * ($kite_0y - $kite_2y);
$y_translation  +=  ($half_doublepentagon_4y - $half_doublepentagon_0y);

$v_edge_centerY = $y_translation;

$Elmer = $Elmer .   '<use xlink:href="#bottled_wheel" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

# define group: v_edge
$Elmer = $Elmer .  '<g id="v_edge">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#v_bridge"/>' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#turned_wheel"  transform="rotate(180 ' . $centerX . " $v_edge_centerY" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

# define group grand_tile
$Elmer = $Elmer .  '<g id="grand_tile">' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#v_edge"/>' . "\n";

$x_translation = $long_star_4x;
$x_translation *= 2;

$h_edge_centerX = $x_translation;

$y_translation = $bottomY;
$Elmer = $Elmer .   '<use xlink:href="#core_wheel" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#turnedagain_wheel"  transform="rotate(180 ' . $x_translation . " $centerY" . ')" />' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#core_wheel" x="' . $x_translation . '" y="' .  $y_translation .'" transform="rotate(180 ' . $h_edge_centerX . " $v_edge_centerY" . ')" />' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#wheel"  transform="rotate(180 ' . $h_edge_centerX . " $v_edge_centerY" . ')" />' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#bottled_wheel" x="' . 0 . '" y="' .  $v_edge_centerY .'" transform="rotate(180 ' . $h_edge_centerX . " $v_edge_centerY" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";


# define group: tipped_bottle
$Elmer = $Elmer .  '<g id="tipped_bottle">' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#bottle" transform="rotate(36 ' . $centerX . " $centerY" . ')" />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";


# define group: center
$Elmer = $Elmer .  '<g id="center">' . "\n";
$x_translation = $h_edge_centerX;
$y_translation = $v_edge_centerY - $star_1y;
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$x_translation = $h_edge_centerX;
$y_translation = $v_edge_centerY - $star_11y;
$Elmer = $Elmer .  '<use xlink:href="#diamond" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$Elmer = $Elmer .   '<use xlink:href="#fivepentabottle" x="' . $h_edge_centerX . '" y="' .  $v_edge_centerY .'" transform="rotate(288 ' . $h_edge_centerX . " $v_edge_centerY" . ')"  />' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#fivepentabottle" x="' . $h_edge_centerX . '" y="' .  $v_edge_centerY .'" transform="rotate(108 ' . $h_edge_centerX . " $v_edge_centerY" . ')"  />' . "\n";

$x_translation = $h_edge_centerX - $kstar_pointX;
$y_translation = $v_edge_centerY - $kstar_pointY;
$Elmer = $Elmer .   '<use xlink:href="#bottle"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#bottle"  x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(180 ' . $h_edge_centerX . " $v_edge_centerY" . ')" />' . "\n";

$x_translation = $h_edge_centerX + $kstar_pointX + ($star_18x - $star_4x);
$y_translation = $v_edge_centerY + $kstar_pointY;
$Elmer = $Elmer .   '<use xlink:href="#tipped_bottle"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#tipped_bottle"  x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(180 ' . $h_edge_centerX . " $v_edge_centerY" . ')"  />' . "\n";

$x_translation = 0 - $long_star_0x;
$y_translation = $v_edge_centerY + $topY;
$Elmer = $Elmer .   '<use xlink:href="#diamond"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#diamond"  x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(180 ' . $h_edge_centerX . " $v_edge_centerY" . ')"  />' . "\n";

$x_translation = 0 - $long_star_0x;
$y_translation = $v_edge_centerY - $topY;
$Elmer = $Elmer .   '<use xlink:href="#diamond"  x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
$Elmer = $Elmer .   '<use xlink:href="#diamond"  x="' . $x_translation . '" y="' .  $y_translation .'"  transform="rotate(180 ' . $h_edge_centerX . " $v_edge_centerY" . ')"  />' . "\n";
$Elmer = $Elmer .   '</g>' . "\n\n";

$Elmer = $Elmer .   '</defs>' . "\n\n"; ############ end defs

###### tile


$Elmer = $Elmer .   '<use xlink:href="#grand_tile"/>' . "\n";
$dim =  2 * $h_edge_centerX;
$vdim = 2 * $v_edge_centerY;

$Elmer = $Elmer .   '<use xlink:href="#center"  />' . "\n";


##### alternate tiling
if(1 == 0)
{
$x_translation =  (2 * $corner2X) - $corner1X - 1;
$y_translation = 0;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation =  (4 * $corner2X) - $corner1X - 2;
$y_translation = 0;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation = 0 - $corner1X;
$y_translation = $corner4Y - $corner1Y - 1;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation =  (2 * $corner2X) - $corner1X - 1;
$y_translation = $corner4Y - $corner1Y - 1;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation =  (4 * $corner2X) - $corner1X - 2;
$y_translation = $corner4Y - $corner1Y - 1;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation = 0 - $corner1X;
$y_translation = (2 * $corner4Y) - $corner1Y - 2;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation =  (2 * $corner2X) - $corner1X - 1;
$y_translation = (2 * $corner4Y) - $corner1Y - 2;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";

$x_translation =  (4 * $corner2X) - $corner1X - 2;
$y_translation = (2 * $corner4Y) - $corner1Y - 2;
$Elmer = $Elmer .   '<use xlink:href="#tile" x="' . $x_translation . '" y="' .  $y_translation .'" />' . "\n";
}


$name = "infinitile.svg";

# Write SVG
open(FUDD, "> $name");

print FUDD <<ENDL;
<?xml version="1.0"  encoding="iso-8859-1" standalone="yes"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
ENDL

print FUDD '  <svg width="'.$dim.'px" height="'.$vdim.'px" viewBox="0 0 '.$dim.' '.$vdim.'"'."\n";
print FUDD '       xmlns="http://www.w3.org/2000/svg" version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink">'."\n\n";

print FUDD "$Elmer \n";

print FUDD '</svg>' . "\n";
close FUDD;

sub define_pieces
{
	my $polypointref = shift;
	my $poly_id = shift;
	my $fill_color = shift;
	my @polypoints = @{ $polypointref };
	my $pointref;
	my $x;
	my $y;
	my $polypointindex = 0;
	
	unless(defined($fill_color))
	{
			$fill_color = "none";
	}
	
	if($draw_border == 1)
	{
		$Elmer = $Elmer . '    <polygon   id="' . $poly_id . '" style="fill:' . $fill_color . ';stroke:' . $border_color . ';stroke-width:'.$stroke.'px"'."\n";
	} else {
		$Elmer = $Elmer . '    <polygon   id="' . $poly_id . '" style="fill:' . $fill_color . ';stroke:none"'."\n";
	}

	$Elmer = $Elmer .  '             points="';
	
	for($polypointindex = 0; $polypointindex <= $#polypoints; $polypointindex++)
	{
		$pointref = $polypoints[$polypointindex]; # point reference
		($x, $y) = @{ $pointref };
		$Elmer = $Elmer .  "$x,$y ";
	}
	
	$Elmer = $Elmer .  '" />' . "\n\n";
}

sub find_intersection_point
{
	my $crossref = shift; # get data
	my ($line1ref, $line2ref) = @{$crossref}; # unravel
	my ($p1ref, $p2ref) = @{$line1ref};
	my ($p3ref, $p4ref) = @{$line2ref};
	my @p1 = @{$p1ref}; my @p2 = @{$p2ref}; my @p3 = @{$p3ref}; my @p4 = @{$p4ref};
	my $xi;
	my $yi;
	my $slope1;
	my $slope2;
	
	unless(defined($p1[0]) && defined($p1[1]) && defined($p2[0]) && defined($p2[1]) && defined($p3[0]) && defined($p3[1]) && defined($p4[0]) && defined($p4[1]))
	{
		return 0; # no point
	}
	
	#$slope1 = ($p2[1] - $p1[1]) / ($p2[0] - $p1[0]);
	#$slope2 = ($p4[1] - $p3[1]) / ($p4[0] - $p3[0]);
	
	if( ( abs($p2[1] - $p1[1]) < 0.0000001) &&  (abs($p4[1] - $p3[1]) < 0.0000001) )
	{
		return 0; # no point
	}
	
	# if x's or y's are equal then solve for second coordinate

		# x's equal
	if( abs($p1[0] - $p2[0]) < 0.0000001 ) 
	{
			$xi = $p1[0];
			$slope2 = ($p4[1] - $p3[1]) / ($p4[0] - $p3[0]);
			$yi = $p3[1] + ( $slope2 * ($xi - $p3[0]) );
			return [$xi, $yi]; # return intersection point
	}
	elsif( abs($p3[0] - $p4[0]) < 0.0000001 )
	{
			$xi = $p3[0];
			$slope1 = ($p2[1] - $p1[1]) / ($p2[0] - $p1[0]);
			$yi = $p1[1] + ( $slope1 * ($xi - $p1[0]) );
			return [$xi, $yi]; # return intersection point
	}
	
	$slope1 = ($p2[1] - $p1[1]) / ($p2[0] - $p1[0]);
	$slope2 = ($p4[1] - $p3[1]) / ($p4[0] - $p3[0]);
	
	# y's are equal
	if( abs($p2[1] - $p1[1]) < 0.0000001 )
	{
		$yi = $p1[1];
		$slope2 = ($p4[1] - $p3[1]) / ($p4[0] - $p3[0]);
		$xi = ( ( $yi - $p3[1] ) + ($slope2 * $p3[0]) ) / $slope2;
		return [$xi, $yi]; # return intersection point
	}
	elsif( abs($p4[1] - $p3[1]) < 0.0000001 )
	{
		$yi = $p3[1];
		$xi = ( ( $yi - $p1[1] ) + ($slope1 * $p1[0]) ) / $slope1;
		return [$xi, $yi]; # return intersection point
	}
		
	#if slopes are parallel, bailout
	if( abs($slope1 - $slope2) < 0.0000001 ) 
	{
			return 0; # no point
	}
	
	$xi = ( ($slope1 * $p1[0]) - ($slope2 * $p3[0]) + $p3[1] - $p1[1] ) / ($slope1 - $slope2);
	
	$yi = $p1[1] + ($slope1 * ($xi - $p1[0]));

	return [$xi, $yi]; # return intersection point
}


print "\n\tThat's All, Folks!\n\n";