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Group 3 * 3 (2d) or 3 * 3 * 3 (3d) coordinates into square blocks?

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Hi all,
This question might be quite complex. Imagine there is a 3D block like this with the Cartesian coordinates:
There are 27 nodes, corresponding coordinates are (first column denotes a linear index):
K>> coords
coords =
1 -1 -1 -1
2 -1 0 -1
3 -1 1 -1
4 0 -1 -1
5 0 0 -1
6 0 1 -1
7 1 -1 -1
8 1 0 -1
9 1 1 -1
10 -1 -1 0
11 -1 0 0
12 -1 1 0
13 0 -1 0
14 0 0 0
15 0 1 0
16 1 -1 0
17 1 0 0
18 1 1 0
19 -1 -1 1
20 -1 0 1
21 -1 1 1
22 0 -1 1
23 0 0 1
24 0 1 1
25 1 -1 1
26 1 0 1
27 1 1 1
Now I'd like to group these 27 coordinates into small sub-blocks. I labelled these sub-blocks with red numbers, but it's not a must to follow the label sequence. The results should be:
block1:
-1 -1 -1
0 -1 -1
0 -1 0
-1 -1 0
-1 0 -1
0 0 -1
0 0 0
-1 0 0
block2
0 -1 -1
1 -1 -1
1 -1 0
0 -1 0
0 0 -1
1 0 -1
1 0 0
0 0 0
block3
......
Also, the code should work for any dimension, i.e. if there is a 2D square:
The code should be able to sort the coordinates into 4 sub-squares.
Can anyone help me with it? Or is there a toolbox developed for this kind of problem? Really appreciate it!

Risposta accettata

Matt J
Matt J il 10 Nov 2017
Modificato: Matt J il 10 Nov 2017
The result is the cell array "blocks":
dim=size(coords,2)-1;
L=(dec2bin(0:2^dim-1)-'0')*2-1;
N=size(L,1);
blocks=cell(1,N);
T=coords(:,2:end);
for i=1:N
idx=all(bsxfun(@times,T,L(i,:))>=0,2);
blocks{i}=T(idx,:);
end
  3 Commenti
Matt J
Matt J il 10 Nov 2017
Modificato: Matt J il 10 Nov 2017
In each block, you could compute the angle of the points using atan2() and then sort them according to that.

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