use strict;
use Math::VectorReal;

sub Intersection {
   my( $x0, $y0, $x1, $y1, $x2, $y2, $x3, $y3) = @_;

   my $v0 = vector($x1 - $x0, $y1 - $y0, 0);
   my $v1 = vector($x2 - $x0, $y2 - $y0, 0);
   my $v2 = vector($x3 - $x2, $y3 - $y2, 0);

   # Take vector cross products.  Only Z is nonzero.
   my $a = ($v0 x $v1)->z();
   my $b = ($v2 x $v0)->z();

   # If |beta| > 1, line intersection outside segment.
   # Test it this way to avoid division by zero.
   return undef if abs($a) > abs($b);

   my $beta;
   if ($b == 0.0) {
      # 0/0 case
      $beta = 0.0;
   } else {
      $beta = $a/$b;
   }

   # Line intersection outside segment
   return undef if ($beta < 0.0); 

   # Now check in the other direction
   $a = ($v2 x $v1)->z();

   # |beta| > 1, line intersection outside segment
   return undef if abs($a) > abs($b);

   if ($b == 0) { 
      # 0/0 case
      $beta = 0.0;
   } else {
      $beta = $a/$b;
   }

   # line intersection outside other side
   return undef if ($beta < 0.0); 

   # find  by parametric equation
   $px = $x2 + $beta*($x3 - $x2); 
   $py = $y2 + $beta*($y3 - $y2); 

   return [$px, $py];
}
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