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

Question

Xiaohan Du 2017-11-9

1
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/366165-group-3-3-2d-or-3-3-3-3d-coordinates-into-square-blocks

评论： Xiaohan Du 2017-11-10

采纳的回答： Matt J

在 MATLAB Online 中打开

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     0    -1
  -1     1    -1
   0    -1    -1
   0     0    -1
   0     1    -1
   1    -1    -1
   1     0    -1
   1     1    -1
  -1    -1     0
  -1     0     0
  -1     1     0
   0    -1     0
   0     0     0
   0     1     0
   1    -1     0
   1     0     0
   1     1     0
  -1    -1     1
  -1     0     1
  -1     1     1
   0    -1     1
   0     0     1
   0     1     1
   1    -1     1
   1     0     1
   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!

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Answer 1

Matt J 2017-11-10

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/366165-group-3-3-2d-or-3-3-3-3d-coordinates-into-square-blocks#answer_290293

编辑：Matt J 2017-11-10

在 MATLAB Online 中打开

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