#!/lusr/bin/perl
# Author: V. B. Balayoghan (vbb@cs.utexas.edu)
# Given sizes of 2 squares, generate their dissection into a single square

$areaUsed= 0.85; $lineWidthFigure= 1.3; $lineWidthCuts= 0.7;

die("Usage:\n\t$0 <size of square 1> <size of square 2>") if ($#ARGV < 1);
$a= shift; $b= shift;
die("Sizes cannot be negative") if ($a < 0 || $b < 0);
die("At least one size must be non-zero") if (($s= $a+$b) == 0);

if ($a < $b) {$a= $b; $b= $s-$a;}
$scale= 792*$areaUsed/(3*$a+$b); $dash= 2.0/$scale;
$flw= $lineWidthFigure/$scale; $clw= $lineWidthCuts/$scale;
$xmargin= (612/$scale-(1.5*$a+$b))/2;
$ymargin= (792/$scale-($a>2*$b ? 2.5*$a+$b : 2*$a+2*$b))/3;

# ps preamble and some macros
print "%!PS-Adobe-2.0\n%%Pages: 1\n%%BoundingBox: 0 0 612 792\n",
    "/slw {setlinewidth} bind def /n {newpath} bind def /m {moveto} bind def\n",
    "/l {lineto} bind def /s {stroke} bind def\n",
    "/sl {[] 0 setdash} bind def /dl {[$dash] 0 setdash} bind def\n\n";
print "%%Page: 1 1\n$scale $scale scale\n";

# 3+2 dissection (bottom of the page)
printf "%g %g translate\n", $xmargin, $ymargin;
print "$flw slw n $a 0 m $a $a l 0 $a l 0 0 l $s 0 l $s $b l $a $b l s\n";
print "$clw slw n 0 $a m $b 0 l $s $b l s dl n $s $b m $a $s l 0 $a l s\n";
printf "n $a $a m $a $s l s n %g %g m %g %g l s sl\n",
    $a, 2*$b, $a+$b*($a-$b)/$a, 2*$b;

# 4+1 dissection (top of the page)
printf "%g %g translate\n", 0, $ymargin+1.5*$a+$b;
print "$flw slw n $a 0 m $a $a l 0 $a l 0 0 l $s 0 l $s $b l $a $b l s\n";
printf "%g slw n %g %g m %g %g l s n %g %g m %g %g l s\n", $clw,
    0, .5*$a-.5*$b, $a, .5*$s, .5*$a-.5*$b, $a, .5*$s, 0;
printf "dl n %g %g m %g %g l %g %g l %g %g l %g %g l s\n", .5*$s, 0,
    .5*$a+$b, -.5*$a, 1.5*$a+$b, -.5*$a+$b, 1.5*$a, .5*$a+$b, $a, .5*$s;
printf "n %g %g m %g %g l s\n", $s, $b, 1.5*$a+.5*$b, $b;
printf "n %g %g m %g %g l s\n", $s, 0, $s, -.5*$a+.5*$b;

print "showpage clear\n";