Split matrix into square cells

I have a matirx 2-d matix where 1st colum is x and 2nd colum is y

[1 2 
 3 12 
 56 7;
 4 5 
 6 5 
 6 8;
 7 8 
 93 43 
 65 3;
 7 8 
 93 43;]

I would like to spilt the data into square cells of 0.5m and know how many and what points are inside the cell

[Matt J]

What does "0.5m" signify? I suggest showing the desired output for your example.

[A]

0.5 is the dimenstions of the cell

Answer 1

[Voss]

% (x,y) in units of m, presumably
xy = [1 2 
 3 12 
 56 7;
 4 5 
 6 5 
 6 8;
 7 8 
 93 43 
 65 3;
 7 8 
 93 43;];

% define the grid starting at (min x, min y)-0.25, with spacing of 0.5:
x_grid = min(xy(:,1))-0.25:0.5:max(xy(:,1))+0.25;
y_grid = min(xy(:,2))-0.25:0.5:max(xy(:,2))+0.25;
% loop over grid cells:
for ii = 1:numel(x_grid)-1
    for jj = 1:numel(y_grid)-1
        % find points inside each cell:
        idx = xy(:,1) >= x_grid(ii) & xy(:,1) < x_grid(ii+1) ...
            & xy(:,2) >= y_grid(jj) & xy(:,2) < y_grid(jj+1);
        if ~any(idx)
            continue
        end
        % if some are found, print the info to the command line:
        fprintf(1,'grid cell: x=%.2f->%.2f, y=%.2f->%.2f:',x_grid(ii+[0 1]),y_grid(jj+[0 1]));
        fprintf(1,'%d point(s) inside: ',nnz(idx));
        fprintf(1,'(%d,%d) ',xy(idx,:).');
    end
end

grid cell: x=0.75->1.25, y=1.75->2.25:

1 point(s) inside: 

(1,2) 

grid cell: x=2.75->3.25, y=11.75->12.25:

1 point(s) inside: 

(3,12) 

grid cell: x=3.75->4.25, y=4.75->5.25:

1 point(s) inside: 

(4,5) 

grid cell: x=5.75->6.25, y=4.75->5.25:

1 point(s) inside: 

(6,5) 

grid cell: x=5.75->6.25, y=7.75->8.25:

1 point(s) inside: 

(6,8) 

grid cell: x=6.75->7.25, y=7.75->8.25:

2 point(s) inside: 

(7,8) (7,8) 

grid cell: x=55.75->56.25, y=6.75->7.25:

1 point(s) inside: 

(56,7) 

grid cell: x=64.75->65.25, y=2.75->3.25:

1 point(s) inside: 

(65,3) 

grid cell: x=92.75->93.25, y=42.75->43.25:

2 point(s) inside: 

(93,43) (93,43) 

[A]

Thank you so much! Just curious is there anyway to store the values into a matrix, like there are x points inside one matrix?

[Voss]

% (x,y) in units of m, presumably
xy = [1 2 
 3 12 
 56 7;
 4 5 
 6 5 
 6 8;
 7 8 
 93 43 
 65 3;
 7 8 
 93 43;];

% define the grid starting at (min x, min y)-0.25, with spacing of 0.5:
x_grid = min(xy(:,1))-0.25:0.5:max(xy(:,1))+0.25;
y_grid = min(xy(:,2))-0.25:0.5:max(xy(:,2))+0.25;
% initialize counts
Nx = numel(x_grid)-1;
Ny = numel(y_grid)-1;
counts = zeros(Ny,Nx);
% loop over grid cells:
for ii = 1:Nx
    for jj = 1:Ny
        % find points inside each cell:
        idx = xy(:,1) >= x_grid(ii) & xy(:,1) < x_grid(ii+1) ...
            & xy(:,2) >= y_grid(jj) & xy(:,2) < y_grid(jj+1);
        if ~any(idx)
            continue
        end
        % if some are found, update the counts:
        counts(jj,ii) = nnz(idx);
    end
end
disp(counts);

  Columns 1 through 37

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  Columns 75 through 111

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Alternatively, as another answer suggests, you can use histcounts2 to do the counting for you:

hist_counts = histcounts2(xy(:,1),xy(:,2),x_grid,y_grid);

isequal(counts.',hist_counts) % histcounts2 returns the counts transposed relative to how I've done it

ans = logical
   1

[A]

Thanks!, so with that comand it can show the number of point that are in each cell?

Also, what do the zeros mean, like how does this comand show that in one cell there are 2 points and next cell there are 5 and so on? Kinda like how 1 point(s) inside this line was used for each cell

[Voss]

Most of the cells have zero points inside. That's why there's so many zeros.

In this case with 11 points total and grid spacing of 0.5, that's what you get; most cells have zero points inside and occasionally there are one or two points inside a cell.

[A]

Okay that make senes, thank you so much

[Voss]

You're welcome!

[A]

Also, just curious why did you subtract by 0.25 for the xgrid?

[Voss]

That's to get the first grid cell centered on the min x and min y (and I added 0.25 on the end so the grid completely spans the points). Without that, the count missed a couple of points due to them being right on the last edge of the grid, if I recall correctly.

[A]

Okay that makes more sense, thank you!

Answer 2

[Steven Lord]

Use the histcounts2 function.