Storing neighboring coordinates within a sphere from a 3D domain.

Hi,

I wish to be able to form connections between nodes that are within a specified distance apart in 3D space.

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So far I have created a script that generates coordinates for random nodes within a 3D domain. The coordinates are stored in an N x 3 array, where (:,1) refers to the x axis, (:,2) refers to the y axis, (:,3) refers to the z axis and N refers to the number of nodes.

I wish to take node 40 for example (see below), and identify all of the other nodes that are within a sphere (of radius r) that surrounds it. It can be seen that, to name a few, nodes 5, 7, 10, 15 and 51 lie within this region.

My ideal output would be an array with 2 columns that stores the node number of each of these nodes. For the given example, the desired output would be X = [40, 5; 40, 7; 40, 10; 40, 15; 40, 51 ...]

Any help would be appreciated, please find the code attached.

Sam

I have generated the sphere using the method suggested by 'Image Analyst'.

( https://uk.mathworks.com/matlabcentral/answers/154490-find-all-neighbors-near-the-specified-point-x-y-z-in-3d-matrix )

Answer 1

[Cedric]

Use PDIST2 and get points within a distance smaller (or equal) to the center (node) than the radius.

EDIT : here is a quick example, where we have 4 nodes and we are interested in building a cell array of nodes (IDs) that are within in radius 2 of two centers:

 >> dNodes2Centers = pdist2( [1,0,0; 0,2,0; 0,0,3; 1,1,0], [0,0,0; 0,1,0] )
 dNodes2Centers =
    1.0000    1.4142
    2.0000    1.0000
    3.0000    3.1623
    1.4142    1.0000

 >> [r, c] = find( dNodes2Centers < 2 ) ;                 % R = 2, exclude boundary (<).
 >> nodeIdsPerCenter = accumarray( c, r, [], @(x){x} ) ;  % Group per center.

which builds:

 >> celldisp( nodeIdsPerCenter )
 nodeIdsPerCenter{1} =
     1
     4
 nodeIdsPerCenter{2} =
     1
     2
     4

[Samuel Thompson]

Hi Cedric,

Thanks for your help, this method will definitely work and is much more straight forward than what I was trying to do!

Thanks for your time,

Sam

[Cedric]

My pleasure!