#!/usr/bin/perl
use strict;
use warnings;
use POSIX qw/floor/;

my $max = 19;                                       #from OP  
my @aoa = map { [ ( 'o' ) x ($max + 1) ] } 0..$max; #from OP

my $max_x_grid = @{$aoa[0]};
my $max_xi = $max_x_grid-1;   #range 0..$max_xi
my $max_y_grid = @aoa;
my $max_yi = $max_y_grid-1;   #range 0..$max_yi

print "grid size is $max_x_grid x $max_y_grid\n";
print "max x index is $max_xi, max y index is $max_yi (zero based indicies)\n";

# Choice of coordinate system:
#   Lower left hand corner of grid is (0,0)
#   This could be upper left hand corner or other point
#   But with this choice:
#          no negative x or y indicies are allowed

my ($circle_x, $circle_y) =(8,9);   #Center of Circle
print "Circle Center = ($circle_x, $circle_y)\n";
my $circle_radius = 5.6;
print "Circle radius in fractions: $circle_radius\n";
my $max_radius_on_axis = floor($circle_radius); #"round down" is part of spec


my $top_y_index    = $circle_y + $max_radius_on_axis;
my $bottom_y_index = $circle_y - $max_radius_on_axis;
my $left_x_index   = $circle_x - $max_radius_on_axis;
my $right_x_index  = $circle_x + $max_radius_on_axis;

print "imagine a box containing the circle using tangential lines:\n";
print "coordinates top of box:    ($left_x_index,$top_y_index) to ($right_x_index,$top_y_index)\n";
print "coordinates bottom of box:($left_x_index,$bottom_y_index) to ($right_x_index,$bottom_y_index)\n";
print "the circle is contained within the above box!\n";

# Circle in cartesian coordinates
#(x - a)**2 + (y - b)**2 = r**2 where a and b are the coordinates of the center (a, b) and r is the radius.

for (my $y=$top_y_index; $y >= $bottom_y_index; $y--)
{
   for (my $x=$left_x_index; $x <= $right_x_index; $x++)
   {
      $aoa[$x][$y] = 'X' if ( (($x-$circle_x)**2 + ($y-$circle_y)**2 <= ($circle_radius**2) )
                            and $x >=0 and $y >=0)
   }
}

foreach my $row_ref ( @aoa)
{
    print "@$row_ref\n";   
}
    
__END__
grid size is 20 x 20
max x index is 19, max y index is 19 (zero based indicies)
Circle Center = (8, 9)
Circle radius in fractions: 5.6
imagine a box containing the circle using tangential lines:
coordinates top of box:    (3,14) to (13,14)
coordinates bottom of box:(3,4) to (13,4)
the circle is contained within the above box!
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