sub intersectLines {
#working subroutine. thanks to the original poster.
    my( $ax, $ay, $bx, $by, $cx, $cy, $dx, $dy )= @_;
    my @rval=0;
    
    my $d1=($ax-$bx)*($cy-$dy);
    my $d2=($ay-$by)*($cx-$dx);
    
    my $dp = $d1 - $d2;
    my $dq = $d2 - $d1;
    
    if($dp!=0 && $dq!=0) {    
       my $p = ( ($by-$dy)*($cx-$dx) - ($bx-$dx)*($cy-$dy) ) / $dp;   
+ 
       my $q = ( ($dy-$by)*($ax-$bx) - ($dx-$bx)*($ay-$by) ) / $dq;
      if($p>0 && $p<=1 && $q>0 && $q<=1) {    
         my $px= $p*$ax + (1-$p)*$bx;
         my $py= $p*$ay + (1-$p)*$by;
         @rval=($px, $py);
      }
   }
    
   return(@rval);
}
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