circular area in a coordinates grid (AoA)

[Discipulus]

Hello monks,

I have an array of arrays full of o and, given the coordinates of one element and a radius I want to change all elements around the center into x

My AoA can be eventually big so I do not want to process every element of the AoA.

The sub ( illuminate in the example below ) must not complain if a point is outside of the AoA (for example giving a corner as vertex).

A pure perl solution will be the best, but also using modules will be ok.

Sorry if I only have the below sketch but I'm very scarce in trig and until now I can only figure to hardcode series of coordinates relative to the vertex (that is silly..)

use strict;
use warnings;

my $max = 19;

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

display( @aoa );

# @to_change will contain [row1,col1],[row2,col2]...
my @to_change = illuminate( 5, 4, 6 );

sub illuminate{
    my $center_row = shift;
    my $center_col = shift;
    my $radius     = shift;    
    ...
}

sub display{
    foreach my $row ( @_ ){
        foreach my $col ( @$row ){
            print $col;
        }
    print "\n"
    }
}

Thanks

L*

PS the above code displays the AoA before the change: I want to be able to select into @to_change the serie of elements falling inside the circle.

minor changes to explain better

UPDATE June 24 2019 see also 2d field of view, vision algorithm in grid (ray casting)