sub getArcEnd {
  my ($x, $y, $x2, $y2, $start, $extent) = @_;

  # --------------------------------------
  # PATCH

  # handle denormalized bounding boxes
  if ($x2 < $x) {
    my $tmp = $x;
    $x=$x2;
    $x2=$tmp;
  }
  if ($y2 < $y) {
    my $tmp = $y;
    $y=$y2;
    $y2=$tmp;
  }
  # --------------------------------------

  # $x, $y, $x2, $y2 can be the bounding box of an
  # ellipse (not just a circle) so calculate vertical
  # and horizontal radius separately

  my $radiusX = ($x2 - $x)/2;
  my $centerX = $x + $radiusX;
  my $radiusY = ($y2 - $y)/2;
  my $centerY = $y + $radiusY;

  # Tk expects the starting angle and length of the
  # arc (extent) to be in degrees but cos and sin expect
  # them in radian

  my $radians = deg2rad($start + $extent);

  # [ x coord of arc end point, y coord of arc end point ]
  # the coordinate system for Tk::Canvas makes "down"
  # positive so we need to subtract the Y component
  # rather than add it.

  return [ $centerX + $radiusX*cos($radians)
           , $centerY - $radiusY*sin($radians) ];
}