sub p2r
{
    (my  $r, my $theta)  = @_;

    return  ($r * cos($theta), $r * sin($theta)); # (x,y)
}
sub r2p
  {
    (my $x, my $y) = @_;

    my $theta = atan2($y, $x);

    my $r = ($x **2 + $y **2) ** (0.5);

    return ($r, $theta);
    }