#!/usr/bin/perl
use strict;
use warnings;
use List::Util qw( max min );

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


my %illu = illuminate( 0,0,12 );
display(@aoa);

%illu = illuminate( 0,10,4 );
display(@aoa);

%illu = illuminate( 10,10,6 );
display(@aoa);

%illu = illuminate( 10,0,5.5 );
display(@aoa);

sub illuminate{	
	my $center_r = shift;
	my $center_c = shift;
	my $radius     = shift;
	my %ret;
	
	foreach my $row ( $center_r - $radius .. $center_r + $radius ){
		my $delta_x = $radius ** 2 - ($center_r - $row) ** 2;
		if( $delta_x >= 0 ){
				
				$delta_x = int sqrt $delta_x;			
				my $low = max 0, $center_c - $delta_x;
				my $high = min $#{ $aoa[$row] }, $center_c + $delta_x;
				map { $ret{ $row.'_'.$_ }++ } $low .. $high;
		  }
	}
	   return %ret;
}

sub display{
	print "\n";
    foreach my $row ( 0..$#aoa ){		
        foreach my $col ( 0..$#{$aoa[$row]} ){
            print  $illu{$row.'_'.$col} ? ' ' : $aoa[$row][$col] ;			
        }
    print "\n"
    }
}