use GD; 

my $size=500; 
my $scale=20;
my $yinvert=-1; 
my ($xcenter,$ycenter)=(19.5,-5); 



my $i = new GD::Image($size,$size);

  $white  = $i->colorAllocate(255,255,255);
  $black  = $i->colorAllocate(0,0,0);       
  $blue   = $i->colorAllocate(0,0,255);
  $dred   = $i->colorAllocate(128,0,0);      
  $bred   = $i->colorAllocate(255,0,0);      
  $green  = $i->colorAllocate(0,255,0); 


sub scaled # scale distances
{ 
	my (@xyus)=@_;  # unscaled xy pairs or distances. 
	my @xys;        # scaled xy pairs
	while (@xyus)
	{
		my $x=$xyus[0]; 
        push(@xys, $x*$size/$scale); 
		shift(@xyus); 
	}
	return (@xys); 
} 
sub scale
{
	
	my (@xyus)=@_;  # unscaled xy pairs or distances. 
	my @xys;        # scaled xy pairs
	while (@xyus)
	{
		my $x=$xyus[0]-$xcenter; 
		my $y=$xyus[1]-$ycenter*$yinvert;
        push(@xys, $x*$size/$scale+$size/2,$y*$size/$scale*$yinvert+$size/2); 
		shift(@xyus); shift(@xyus); 
	}
	return (@xys); 
}

# first draw some radial lines at 0.25 degree intervals. 
# the lines are 1 unit long and centered at the point 20,0. 

my $pi=4.0 * atan2(1, 1);
my $rad=$pi/180.0;  # to radions convert factor
my $deg=180.0/$pi; #  to degrees convert factor. 

my $v1=19;  # vector lengths of lines being drawn from v1 to v2. 
my $v2=21; 

my $astep=10; 
my $oldangle; 
for my $j (0..4)
{ 

  my $angle=$astep*$j; 

  my $startx=$v1*cos($angle*$rad); 
  my $starty=$v1*sin($angle*$rad); 
  my $endx=$v2*cos($angle*$rad); 
  my $endy=$v2*sin($angle*$rad); 
  $i->line(scale($startx,$starty,$endx,$endy),$blue); # radial lines
  
  # now we draw some arcs, always 1 degree long, but starting at steps of 0.1 degree
  # we draw the lowest arc nearest the center, ie 1 to 2 deg, then 1.1 to 2.1 deg further out and so on. 
  # angles are clockwise, and our +ve direction is acw, so in fact we start at 
  # 359 to 360, then further out 359.1 to 360.1, and so on 
  for my $k (0..10)
  {  
     my $kstep=1; 
     my $kmove=0.2; 
     $i->arc(scale(0,0),scaled(2*$v1+$k*$kmove,2*$v1+$k*$kmove),360-$angle-$k*$kstep,360-$oldangle-$k*$kstep,$bred) if ($j%8==1);
  }
  $oldangle=$angle;  
} 



my $file="gdbug1.png"; 
open(F,">".$file) or die "Cannot open file ".$file; 
binmode F; 
print F $i->png; 
close F; 


##</code><code>##

use GD; 

my $size=500; 
my $scale=4.5;
my $yinvert=-1; 
my ($xcenter,$ycenter)=(19.5,-1.5); 



my $i = new GD::Image($size,$size);

  $white  = $i->colorAllocate(255,255,255);
  $black  = $i->colorAllocate(0,0,0);       
  $blue   = $i->colorAllocate(0,0,255);
  $dred   = $i->colorAllocate(128,0,0);      
  $bred   = $i->colorAllocate(255,0,0);      
  $green  = $i->colorAllocate(0,255,0); 


sub scaled # scale distances
{ 
	my (@xyus)=@_;  # unscaled xy pairs or distances. 
	my @xys;        # scaled xy pairs
	while (@xyus)
	{
		my $x=$xyus[0]; 
        push(@xys, $x*$size/$scale); 
		shift(@xyus); 
	}
	return (@xys); 
} 
sub scale
{
	
	my (@xyus)=@_;  # unscaled xy pairs or distances. 
	my @xys;        # scaled xy pairs
	while (@xyus)
	{
		my $x=$xyus[0]-$xcenter; 
		my $y=$xyus[1]-$ycenter*$yinvert;
        push(@xys, $x*$size/$scale+$size/2,$y*$size/$scale*$yinvert+$size/2); 
		shift(@xyus); shift(@xyus); 
	}
	return (@xys); 
}

# first draw some radial lines at 0.25 degree intervals. 
# the lines are 1 unit long and centered at the point 20,0. 

my $pi=4.0 * atan2(1, 1);
my $rad=$pi/180.0;  # to radions convert factor
my $deg=180.0/$pi; #  to degrees convert factor. 

my $v1=19;  # vector lengths of lines being drawn from v1 to v2. 
my $v2=20; 

my $astep=1; 
my $oldangle; 
for my $j (0..7)
{ 

  my $angle=$astep*$j; 

  my $startx=$v1*cos($angle*$rad); 
  my $starty=$v1*sin($angle*$rad); 
  my $endx=$v2*cos($angle*$rad); 
  my $endy=$v2*sin($angle*$rad); 
  $i->line(scale($startx,$starty,$endx,$endy),$blue); # radial lines
  
  # now we draw some arcs, always 1 degree long, but starting at steps of 0.1 degree
  # we draw the lowest arc nearest the center, ie 1 to 2 deg, then 1.1 to 2.1 deg further out and so on. 
  # angles are clockwise, and our +ve direction is acw, so in fact we start at 
  # 359 to 360, then further out 359.1 to 360.1, and so on 
  for my $k (0..20)
  {  
     my $kstep=0.1; 
     my $kmove=0.1; 
     $i->arc(scale(0,0),scaled(2*$v1+$k*$kmove,2*$v1+$k*$kmove),360-$angle-$k*$kstep,360-$oldangle-$k*$kstep,$bred) if ($j%8==1);
  }
  $oldangle=$angle;  
} 



my $file="gdbug2.png"; 
open(F,">".$file) or die "Cannot open file ".$file; 
binmode F; 
print F $i->png; 
close F;