How to determine blocks in mesh grid?

Hello guys,

I have a matrix representing a grid, say

A = [-1 -1; -1 1; 1 -1; 1 1; -1 0; 0 -1; 0 0; 0 1; 1 0];

Every row of A is a Cartesian coordinate. Therefore if you plot a scatter, you'll find that A is a square. My question is: clearly there are four blocks in A: left upper, right upper, left lower, right lower. How can I write a code to generate 4 matrices which each of them represents one block? The result should be something like:

A1 = [-1 -1; 0 -1; -1 0; 0 0], 
A2 = [0 -1; 1 -1; 0 0; 1 0], 
A3 = [-1 0; 0 0; -1 1; 0 1], 
A4 = [0 0; 1 0; 0 1; 1 1].

Thanks!

[Image Analyst]

I think you just did it.

[Xiaohan Du]

Hi Image Analyst,

Thanks for the reply!

I know what the answer should be like, and I can do it manually. But with the given matrix, what is the algorithm behind it? What if I have a finer grid? I cannot do it manually forever, it needs to be automatic.

Answer 1

[Guillaume]

This should work:

A = [-1 -1; -1 1; 1 -1; 1 1; -1 0; 0 -1; 0 0; 0 1; 1 0];
%get the sorted unique x and y coordinates:
xy = cellfun(@unique, num2cell(A, 1), 'UniformOutput', false);
x = xy{1};
y = xy{2};
%create output
Agrid = cell(numel(y) - 1, numel(x) - 1);
%iterate through the grid and fill output
for xidx = 1 : numel(x) - 1
   for yidx = 1 : numel(y) - 1
      Agrid{yidx, xidx} = [repmat(x(xidx:xidx+1), 2, 1), repelem(y(yidx:yidx+1), 2)];
   end
end

[Xiaohan Du]

Hi Guillaume,

Thanks for the reply!

Before testing this script, mind if I ask will it work for square grid with any size?

[Xiaohan Du]

Hi Guillaume,

I just tested, this works for a finer grid as well! Thank you so much!

[Guillaume]

This works for grids of any size, square or non-square and uniform or non-uniform.