# ... intro stuff...

labent($frm, 'X1',     \$x1,   8);
labent($frm, 'Y1',     \$y1,   8);
labent($frm, 'X2',     \$x2,   8);
labent($frm, 'Y2',     \$y2,   8);
labent($frm, 'Start',  \$deg,  8);
labent($frm, 'Extent', \$ext,  8);

#------------------------------------
#PATCH 1
my $normal = 0;
labent($frm, 'Normal', \$normal, 8);
#------------------------------------

# ... more stuff ...

sub random_args {
    $x1  = random_value(0, $cw);
    $x2  = random_value(0, $cw);
    $y1  = random_value(0, $ch);
    $y2  = random_value(0, $ch);
    $deg = random_value(0, 360);

    #------------------------------------
    #PATCH 2
    if ($normal) {
       $x2 = 2*$x1 - $x2 if $x2 < $x1;
       $y2 = 2*$y1 - $y2 if $y2 < $y1;
    }
    #------------------------------------
}

##</code><code>##

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) ];
}