A function smart enough to sort coordinates of block into sub-blocks?

Hi all,

Imagine there is a 2D shape made of randomly distributed square blocks, with Cartesian coordinates like this:

I can read the coordinates of the nodes, for this case it is:

>> coords
coords =
     1    -1    -1
     2    -1     1
     3     1    -1
     4     1     1
     5    -1     0
     6     0    -1
     7     0     0
     8     0     1
     9     1     0
    10     2     0
    11     2     1
    12     0     2
    13    -1     2
    14    -2     0
    15    -2    -1

I'd like to have a function which is able to read this coordinates data, and sort it into 4-points square blocks, with coordinates in counter-clockwise, so the output would be:

>> otpt{:}
ans =
     1    -1    -1
     5    -1     0
     6     0    -1
     7     0     0
ans =
     2    -1     1
     5    -1     0
     7     0     0
     8     0     1
ans =
     3     1    -1
     6     0    -1
     7     0     0
     9     1     0
ans =
     4     1     1
     7     0     0
     8     0     1
     9     1     0
and so on...... (7 cell blocks in this case)

Moreover, for 3D blocks, such as this case:

If I'm able to read the nodal coordinates, can the function also suit for sorting the sub-blocks in 3D? Results would be 9 cell blocks with 8 x-y-z coordinates.

Matt J was very kind to provide me this solution here,

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

but it only works for uniform shapes. Thanks for any help!

Answer 1

[David Goodmanson]

Hi Xiaohan,

Here is some code that creates a 4x3xn 3d matrix sqquares (misspelled on purpose) where each level of sqquares in the third dimension, i.e. (:,:,k) is one of the solutions. I did not want to deal with a connectivity matrix so this assumes that every pair of vertices that can be connected by a line is connected by a line. For example suppose you had two more vertices at (1,2) and (2,2) and they are connected with the vertices below them to make a square. You could also have a line from (0,2) to (1,2) to make another square, or not. This code presumes that that line is there.

I am not going for cubes, life is too short.

 coords = ...
    [1    -1    -1
     2    -1     1
     3     1    -1
     4     1     1
     5    -1     0
     6     0    -1
     7     0     0
     8     0     1
     9     1     0
    10     2     0
    11     2     1
    12     0     2
    13    -1     2
    14    -2     0
    15    -2    -1];

xtaxi = -coords(:,2)+coords(:,2)';         % taxi displacements
ytaxi = -coords(:,3)+coords(:,3)';
r = xtaxi==1&ytaxi==0;                     % point on right or not, etc.
rd = xtaxi==1&ytaxi==-1;
d = xtaxi==0&ytaxi==-1;
ulef = find(any(r,2)&any(rd,2)&any(d,2));  % upper left corner of squares
n = length(ulef);
sqquares = zeros(4,3,n);
for k=1:n
  ind = ulef(k);
  vtx = [ind find(r(ind,:)) find(rd(ind,:)) find(d(ind,:))];   % cw order
  sqquares(:,:,k) = coords(vtx,:)
end

if you don't have one of the later versions of Matlab with implicit expansion you can do

[temp1 temp2] = meshgrid(coords(:,2),coords(:,2));
xtaxi = temp1-temp2;

and similarly for ytaxi with coords(:,3)

[Xiaohan Du]

Hi David,

First thanks a lot for the solution, I'll have a look and give you some feedback.

What is taxi displacements and why do we need it?

[David Goodmanson]

Hi Xiaohan,

These are just the usual displacements in x and y from the point in question, to find nearby corners. Taxi is a reference to the the path that a taxi has to take on a grid of city streets, no cutting across the diagonal. See for example Taxicab Geometry in Wikipedia.