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  1. or download this
        P = (p-1)*A + p*B
  2. or download this
    P = p*A + (1-p)*B
Q = q*C + (1-p)*D
...

p*( (ax-bx)*(cy-dy) - (ay-by)*(cx-dx) )
  = (by-dy)*(cx-dx) - (bx-dx)*(cy-dy)
  3. or download this
    p = ( (by-dy)*(cx-dx) - (bx-dx)*(cy-dy) )
  / ( (ax-bx)*(cy-dy) - (ay-by)*(cx-dx) )

px= p*ax + (1-p)*bx
py= p*ay + (1-p)*by
  4. or download this
    sub intersectLines {
    my( $ax, $ay, $bx, $by, $cx, $cy, $dx, $dy )= @_;
...
    my $py= $p*$ay + (1-$p)*$by;
    return( $px, $py );
}