MATLAB: Locate particles in squares (combinatorics)

combinatoricsMATLAB

I have a problem: I have a lot of particles with given coordinates (x,y). My (x,y) plane is divided into a bunch of squares 32×32. I need a fast way to identify, which particles belongs to which square.
Input data: data(Nx3)=(x1,y1,id1;x2,y2,id2,….) – array with particles coordinates and id's. Also could have array with id's of squares, like: (x1,y1,x2,y2,id#; …)
What I want on output is array out(Nx2) containing id of particle and corresponding square id.
I don't need you to write a code for me. I want just idea -how to do it in the most fast and convinient way. Thanks

Best Answer

If you divide the x and y coordinates of your particles by your square size, you get in which column/row square your particles are in. Then just convert that into linear indexing with sub2ind (assuming you use the same column-major ordering as matlab). You can do the calculation on all particles at once, something like:
colsquare = floor(data(:, 1) / 32) + 1;
rowsquare = floor(data(:, 2) / 32) + 1;
squareidx = sub2ind([numsquarey numsquarex], rowsquare, colsquare);
out = [data(:, 3) squareidx];
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