Plotting a circle and finding intersections

I am trying to plot a circle using existing data I have and find the points where the circle intersect grid lines. I randomly picked a set of coordinates from the data to be used as the center point of the circle. However, the code I have isn't displaying the circle. When I run the code, it says there is an error in the line "plot(Q(1,:),Q(2,:),'.b')". Can anyone solve this problem? Thanks in advance!

 nc = 1; % number of circle 
 r = 10; % radius
 th = linspace(0,2*pi);
 iwant = cell(nc,1);

 for i = i:nc
    % get center of circle
    x = center(:,2); % x coordinate  
    y = center(:,3); % y coordinate 

    % circle coordinates
    cx = x+r*cos(th);
    cy = y+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

[KSSV]

Here is complete code which is working https://in.mathworks.com/matlabcentral/answers/340636-how-to-randomly-plot-circles-on-grid-lines-and-determine-coordinates-of-intersection. YOu have missed many variables in the above code.

[Atiqah Zakirah]

Thank you for the help! I made some changes to the code. I have troubling integrating my code with the code you provided. Instead of getting random center of the circle, I'm getting random coordinates from my data set to be the center of my circle this time. When I make this change to the code, it presents me with an error.

Index exceeds matrix dimensions error: P = InterX([cx ;cy],[X(:,k)' ; Y(:,k)']) ; Error: plot(Q(1,:),Q(2,:),'g');

 %%create grid 
 N = 30;
xgrid = linspace(103.6,104,N);
ygrid = linspace(1.25,1.5,N);
[X,Y] = meshgrid(xgrid,ygrid);
figure 
hold on
plot(X,Y,'r');
plot(X',Y','r');
xlim([103.6 104])
ylim([1.25 1.5])

 %%plot points
plot(coordinates(:,2),coordinates(:,3),'.');
plot (train(:,1),train(:,2),'x');

 %%obtaining random coordinates
row = randi(size(coordinates,1),1); % generates random row number 
% obtain x and y coordinates from selected row 
center = coordinates(row,:); 

 %%create a circle using center 
nc = 1; % number of circle 
R = 30; % radius
th = linspace(0,2*pi);
iwant = cell(nc,1); 

 for i = i:nc
    % get center of circle
    x = center(:,2); % x coordinate  
    y = center(:,3); % y coordinate 

    % circle coordinates
    cx = x+R*cos(th);
    cy = y+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,:),'g');
      iwant{i} = Q ;

 end

[KSSV]

coordinates and train are missing..

Answer 1

[TED MOSBY]

Hi @Atiqah Zakirah,

To find the points of intersection of a circle with the gridlines of the plot area you can use the “InterX” function of MATLAB.

Here is an example code to find the points of intersection of the circle with the grid lines:

% Example dataset: Replace this with your actual data 
data = [1, 2; 3, 4; 5, 6; 7, 8; 9, 10]; % Each row is a point [x, y] 

% Randomly select a point from the dataset to be the center 
numPoints = size(data, 1); % Number of points in the dataset 
randomIndex = randi(numPoints); % Randomly select an index 
center = data(randomIndex, :); % Get the [x, y] coordinates of the center 

% Display the chosen center 
disp(['Chosen center: (', num2str(center(1)), ', ', num2str(center(2)), ')']); 

% Define circle parameters 
nc = 1; % number of circles 
r = 10; % radius 
th = linspace(0, 2*pi); 
iwant = cell(nc, 1); 

% Define grid 
gridSize = 20; % Size of the grid 
N = 10; % Number of grid lines 
xGrid = linspace(-gridSize, gridSize, N); 
yGrid = linspace(-gridSize, gridSize, N); 
[X, Y] = meshgrid(xGrid, yGrid); 
figure; % Create a new figure 
hold on; % Ensure all plots are on the same figure 

% Plot grid lines 
for j = 1:N 
    plot([xGrid(1), xGrid(end)], [yGrid(j), yGrid(j)], 'g--'); % Horizontal lines 
    plot([xGrid(j), xGrid(j)], [yGrid(1), yGrid(end)], 'g--'); % Vertical lines 
end 
for i = 1:nc 
    % Get center of circle 
    x = center(1); % x coordinate   
    y = center(2); % y coordinate  
    % Circle coordinates 
    cx = x + r * cos(th); 
    cy = y + 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 
hold off; % Release the hold on the plot 

% Display intersection points 
disp('Intersection points:'); 
disp(Q); 

Below is the output of the above code in my MATLAB R2023b:

Here is the documentation on the "interX" function:

www.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections?s_tid=srchtitle_support_results_1_interx

Hope your query is resolved!