How to randomly plot circles on grid lines and determine coordinates of intersection?

I'm trying to create my own vertical and horizontal grid lines and then plot multiple circles randomly over it. I then want to determine the points where the grid lines and circles intersect. The diameter of the circle should not exceed the length of one grid. All circles should be of equal size to each other. This is the code that I have at the moment (that I took from other sources) does not output what I want and is completely wrong. I don't fully understand the code so any help would be great! Thanks in advance.

x = 0:30;                            
y = 0:30;                          
figure(1)                          
plot(repmat(x,2,length(x)), [0 length(y)-1])    
hold on
plot([0 length(x)-1], repmat(y,2,length(y)))    
hold on 
r=10;
center=[20,30]; 
t=-pi:0.001:pi;
x=r*cos(t)+center(1);
y=r*sin(t)+center(2);
plot(x,y)
hold off
axis equal

Answer 1

[KSSV]

N = 20 ;
x = linspace(0,30,N) ;
y = linspace(0,30,N) ;

[X,Y] = meshgrid(x,y) ;
figure
hold on
plot(X,Y,'r') ;
plot(Y,X,'r')

%%draw circles 
nc = 1 ;
R = 2. ;
th = linspace(0,2*pi) ;
iwant = cell(nc,1) ;
for i = 1:nc
    % get random centre of circle 
    cx0 = (max(x)-min(x)).*rand + min(x);
    cy0 = (max(y)-min(y)).*rand + min(y);
    % circle coordinates 
    cx = cx0+R*cos(th) ;
    cy = cy0+R*sin(th) ;
    plot(cx,cy,'k')
    % get intersection 
    P = InterX([cx ;cy],[X(:)' ; Y(:)']) ;
    iwant{i} = P ;
    plot(P(1,:),P(2,:),'.b')
end

download InterX from the link: https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections?focused=5165138&tab=function

[Atiqah Zakirah]

Thanks! But there's one tiny problem with the code. I ran it and it's generating points which aren't at the intersection. Why is it so? Is there a way to solve this?

[KSSV]

N = 20 ;
x = linspace(0,30,N) ;
y = linspace(0,30,N) ;
[X,Y] = meshgrid(x,y) ;
figure
hold on
plot(X,Y,'r') ;
plot(Y,X,'r')
%%draw circles
nc = 10 ;
R = 3. ;
th = linspace(0,2*pi) ;
iwant = cell(nc,1) ;
for i = 1:nc
    % get random centre of circle
    cx0 = (max(x)-min(x)).*rand + min(x);
    cy0 = (max(y)-min(y)).*rand + min(y);
    % circle coordinates
    cx = cx0+R*cos(th) ;
    cy = cy0+R*sin(th) ;
    plot(cx,cy,'k')
    % get intersection

      Q = cell(1,[]) ;
      count = 0 ;
      % loop along lines parallel to x-axes
      for j = 1:N
          P = InterX([cx ;cy],[X(j,:) ; Y(j,:)]) ;
          if ~isempty(P)
              count = count+1 ;
              Q{count} = P ;
          end
      end
      % loop along lines parallel to y-axes
      for k = 1:N
          P = InterX([cx ;cy],[X(:,k)' ; Y(:,k)']) ;
          if ~isempty(P)
              count = count+1 ;
              Q{count} = P ;           
          end
      end
      Q = cell2mat(Q) ;
      plot(Q(1,:),Q(2,:),'.b')
      iwant{i} = Q ;
  end

[Adam Podbielski]

how can this be incorporated with a circle in polar coordinates?