How to obtain possible combinations of adjacent points with coordinates?

Hi all,

I am trying to obtain all possible combinations of adjacent points in combinations of 2, 3, 4, 5,...n number.

Example, I have 9 points, and I would like to get all the possible combinations shown below:

If I do it with the combination function, I will get combinations that will not work for me, therefore a lot of noise will be introduced into my analysis. Also, the points are not always aligned and most of the time they look something like this:

I do have all the x and y coordinates of each point. Anyone can give me a hand on this please??

Thank you in advance!

[Walter Roberson]

Your first part of your question is dealing with rectangular cells, and none of the desired combinations have points that are only diagonally connected.

Your second part has cells that are diagonally connected, with diagonal walls between them. It is not clear whether connections between those are to be accepted or rejected.

It might be reasonable to say that you want to permit connections between any two cells that share a line boundary. You mention that you have the X Y coordinates of the points -- but you do not mention whether you have the coordinates of the boundaries. Are there strict rules about how to calcuate where the boundaries are given X Y coordinates?

I don't think "rows" and "columns" are well defined for this situation. For example where you have three points arranged like

A

B

C

then are all three to be considered in the same column ?

[Manuel Matus]

Thanks for your reply!

There are cases in which the tributary areas of each point are rectangular cells, but some others become like cells diagonally connected. Both are correct.

We have the X and Y coordinates of each point (always located within each cell - see figure below). We do not have the coordinates of the boundaries (I am using VORONOI matlab function to create the tributary areas of the points - cells). The only rule to estimate the boundaries between two points is the midpoint between them.

In regards to the "rows" and "columns" not being well defined for this situation, I showed it to more or less give a simpler example of what the main point is when finding possible combinations. In addition, there might be times in which the placement of points end upt with rectangular cells next to each other, as shown below. Again, here the main point is to find combinations, lets say 2, 3, 4 until a single combination covers all 24 points.

Example :

combinations of 2:

1 2 ; 2 3 ; 3 4 ; 5 6 ; . . . ; 23 34 ; 1 5 ; 5 9 ; ..... ; 20 24

combinations of 4:

1 2 3 4 ; 5 6 7 8 ; 9 10 11 12 ; 13 14 15 16 ; 17 18 19 20 ; 21 22 23 24 ;

1 5 9 13 ; 5 9 13 17 ; 9 13 17 21 ; ..... ; 12 16 20 24 ;

1 2 5 6 ; 2 3 6 7 ; 3 4 7 8 ; ..... ; 19 20 23 24.

[Walter Roberson]

It is not obvious why 1 2 6 10 would be excluded? In the case of purely rectangular boundaries would could guess about that... but especially as soon as you introduce diagonal connections as being permitted sometimes, then the rules become very unclear.