sub intersectLines {
    my( $ax, $ay, $bx, $by, $cx, $cy, $dx, $dy )= @_;
    my $d= ($ax-$bx)*($cy-$dy) - ($ay-$by)*($cx-$dx);
    die "Parallel lines"   if  0 == $d;
    my $p = ( (by-dy)*(cx-dx) - (bx-dx)*(cy-dy) ) / $d;
    my $px= $p*$ax + (1-$p)*$bx;
    my $py= $p*$ay + (1-$p)*$by;
    return( $px, $py );
}