MATLAB: Are there any known algorithms for identifying the coordinates of the nearest neighbours of a 2D square lattice

nearest neighbours

I'm looking for a code that takes these inputs: (i) 2D lattice in x,y coordinates (ii) coordinate of interest (iii) integer n, and outputs the coordinates of the n-th nearest neighbours.
For example:
  • Input (i) some arbitrary lattice (ii) (0,0) as coordinate of interest (iii) 2 – for next nearest neighbours.
  • Output (-1,0), (0,1), (1,0), (0,-1) for nearest neighbours, (-1,1), (1,1), (1,-1), (-1,-1) for next nearest neighbours.
If there is no code around, I will write one up.
Thanks a bunch!

Best Answer

Assuming the lattice is not too huge, can't you just calculate the distance from your point to every lattice point, sort the distances and pick the nth first points (watching out for equality)? E.g.:
lattice = [];
[lattice(:, :, 1), lattice(:, :, 2)] = ndgrid(-10:10);  
lattice = reshape(lattice, [], 2) %demo lattice as Nx2 matrix, each row is a lattice point
querypoint = [0 0]
neighbours = 2 
distances = hypot(querypoint(:, 1) - lattice(:, 1), querypoint(:, 2) - lattice(:, 2));
[d, ~, order] = unique(distances);  %sort the distance and get unique id for each distance
rows = (1:numel(order)).';
if d(1) == 0
   %point on lattice coincide with query point, remove from result
   order = order - 1;
   rows(order == 0) = [];
   order(order == 0) = [];
end
result = accumarray(order(order <= neighbours), rows(order <= neighbours), [],@(v) {lattice(v, :)});
celldisp(result)
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