How to choose the middle of a random cell in a 2D grid

Hi all,

I have a 2D grid that has 25 points equally spaced in both axes dividing the grid into little boxes/cells/pixels. Is there a way to choose the middle of a random box in this grid. My code is the follwoing:

Any help would be appreciated.

Thanks.

[Scott MacKenzie]

Please clarify what you mean by "random box". You've got a 25x25 grid. To select a random point in this grid is easy enough, but that doesn't seem to be what you are after. More details, please.

[Lama Hamadeh]

You are correct. Choosing a random"point" is rather easy to do. However, based on the sketch below, I want to specifiy the middle point of a random cell of this grid.

Hopefully this is clear!?

Thanks

[Scott MacKenzie]

It's still not clear - to me, anyway. In your sketch you have a 5x6 grid of cells within your overall 25x25 grid. No mention of this in your question. So you want a random cell within this inner grid, but it's not clear what the inner grid is.

[Lama Hamadeh]

The sketch is just an illustration. Sorry for that! suppose the drawn grid is 25x25 and the red cell is the one I want to pick randomly from it. So it's a cell out of the 25x25 overall grid.

[Scott MacKenzie]

Ok, so we're kinda back where we started. If you just want a random cell from the 25x25 grid, can't you just pick the cell at x=randi(25) and y=randi(25)?

[Lama Hamadeh]

But would that give me a point rather than a cell?

Answer 1

[Scott MacKenzie]

OK, thanks for the clarification. I think this achieves what you are after. The added code randomly chooses vertices (points) but highlights in red the face (box) that is bounded on the lower-left by the point. The demo repeats ten times with a half-second pause to show each randomly selected box. An example screen ship is also shown.

%x axis
smin = 0; 
L = 4; 
ns = 25; 
s = linspace(smin,L,ns); 

%y axis
pmin = -1;
pmax = 1;
np = 25;
p = linspace(pmin,pmax,np); 

%construct coordinates meshgrid
[S,P] = meshgrid(s,p); 
%Each point in the grid represents a position on the boundary and a
%direction of travel.
% mesh needs X,Y and Z so create z
Z = zeros(size(S));
%Visualise the grid
figure;
m = mesh(S,P,Z,'Marker','.','MarkerFaceColor','k','EdgeColor',"k", 'facecolor', 'w')
axis equal tight
view(2);
xlabel('$S$','Interpreter','latex');
ylabel('$P$','Interpreter','latex');
set(gca,'TickLabelInterpreter','latex');
set(gca,'FontSize',16);
set(gcf, 'color', 'w');
hold on

% set color map to gray+red and make all faces gray
colormap([1 0 0; .9 .9 .9]);
m.FaceColor = 'flat';
m.CData(:,:) = 2;

for i=1:10
    % pick a vertex at random
    x = randi([1 24]);
    y = randi([1 24]);
    
    % show the corresponding face in red
    m.CData(x,y) = 1;
    
    % pause briefly, then restore color to gray
    pause(.5);
    m.CData(x,y) = 2; 
end

[Lama Hamadeh]

Many thanks for this. It truly helps. One question though, what does

m.CData(:,:) = 2;

mean? What does the number 2 refer to? And then again when you assign the cell colour to be equal to 1. Do they refer to the first and the second rows of the Colormap array?

Thanks.

[Scott MacKenzie]

Setting faceColor of 'flat' overrides the default color mapping for mesh graphs and allows you to customize the mapping. The code creates a color map with just two colors, red (1st entry) and gray (2nd entry). The line m.CData(:,:) = 2 makes all the 25x25 faces gray. The "2" refers to the 2nd entry in the color map. In the loop, indices are selected at random with the color of corresponding face changed to red (1) for half a second. The loop repeats 10x, just as a demo.

[Scott MacKenzie]

@Lama Hamadeh Thanks. I just posted another solution that you can consider as well. It does basically the same thing but is simpler. Instead of setting up the grid using mesh, the grid is created just as a series of x-lines and y-lines. The highlighting of cells is done by defining a rectangle of the correct size and changing its position at randon within the grid.

Answer 2

[Scott MacKenzie]

This solution is simpler. It creates the grid using lines instead of a mesh.

% x axis
smin = 0; 
L = 4; 
ns = 25; 
s = linspace(smin,L,ns); 

% y axis
pmin = -1;
pmax = 1;
np = 25;
p = linspace(pmin,pmax,np); 

% width and height of each cell in grid
w = (L-smin) / ns;
h = (pmax-pmin) / np;

% set up figure and axes
figure;
set(gcf, 'color', 'w');
ax = gca;
ax.Color = [.9 .9 .9];
ax.XTick = smin:L;
ax.YTick = pmin:0.5:pmax;
ax.XLabel.String = '{\itS}';
ax.XLabel.FontSize = 12;
ax.YLabel.String = '{\itP}';
ax.YLabel.FontSize = 12;

% create grid as series of x/y lines
xline(s);
yline(p);

% define a rectangle, but set x-y coordinates and color in loop
r = rectangle('position', [0 0 w h], 'facecolor', 'none', 'edgecolor', 'none');

% pick cells at random and highlight in red for half second (10x)
for i=1:10
    x = s(randi([1 length(s)-1]));
    y = p(randi([1 length(p)-1]));
    r.Position(1:2) = [x y];
    r.FaceColor = 'r';
    pause(0.5);
    r.FaceColor = 'none'; 
end