Divide the 3D feature space into grid and then get their labels

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Dear all,
I have 3D locations in three vectors, x, y, and z. I want to divide the space into fix numbe of grids lets say 2 x 2 x 2. Lets take example in 2D space. I have two vectors x, and y, as below;
x = [1 1 2 2 3 10];
y = [1 2 1 1 2 5];
plot(x,y, '+')
now I divide in to 2 x 2. So the interval for x would be 0-to-5 and then 5.1-to-10, and likewise for y(0-to-2.5, and 2.6-to-5). I have drawn the points and divided the space manually as shown below.
now the there are four cells. I have vector r that should be r = [3,3,3,3,3,2] where all points are in cell 3 and only point 5,10 is on cell 2.

Accepted Answer

Turlough Hughes
Turlough Hughes on 31 Jan 2022
Example in 2D
% Data
x = rand(1,100)*10;
y = rand(1,100)*5;
r = zeros(size(x)); % group index
r(x>0 & x<=5 & y>0 & y<=2.5) = 1;
r(x>5 & x<=10 & y>0 & y<=2.5) = 2;
r(x>0 & x<=5 & y>2.5 & y<=5) = 3;
r(x>5 & x<=10 & y>2.5 & y<=5) = 4;
figure(), gscatter(x,y,r)
hold on, axis padded, legend off
xline(5), yline(2.5)
Here I'm using conditions > as well as <= so that you can select one edge, eg 5 instead of switching between 5 and 5.1 etc, though if you need to modify from this then do so as required.
Example in 3D
% Additional data for z
z = rand(1,100)*5;
% E for Edges
xE = [0 5 10];
yE = [0 2.5 5];
zE = [0 2.5 5]; % You can see why just one value for the edge is useful.
% Group the data according to the edges (r gives the groups).
idx = 1;
for ii = 1:numel(xE)-1
for jj = 1:numel(yE)-1
for kk = 1:numel(zE)-1
r(x>xE(ii) & x<=xE(ii+1) & y>yE(jj) & y<=yE(jj+1) & z>zE(kk) & z<=zE(kk+1)) = idx;
idx = idx + 1;
end
end
end
cmap = jet(8);
figure(), scatter3(x,y,z,80,cmap(r,:),'filled')
Not the best visualisation but you can see that it does the job.
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