Find close points in two matrices of coordinates

I have two different length matrices of 3D coordinates. I want to find all the unique coordinates in one matrix that are within a certain Euclidean distance of any of the coordinates in the other matrix. What is the most efficient way to do this?

Answer 1

[Torsten]

Use "pdist2" to calculate the distances of the sites of the first set to the sites of the second set.

Check which rows of the distance matrix D have an entry <= dmax where dmax is your prescribed maximum distance.

These are the sites of the first set you want to determine.

[Adam Fitchett]

But as i have said, the matrices are of different lengths

So I cannot directly measure the pairwise distance between elements in the two matrices

Also they are coordinates in 3D and pdist2 is only for 2D coordinates

Basically I want to know if I can do this without some complicated system of nested for loops

E.g. checking the distance between the first element of matrix1 with every element in matrix2 and then repeating that for each element of matrix1. That seems inelegant to me

[Torsten]

Works for me.

set1 = [0,1,4;
       2 5 8];
set2 = [-1,3,6 ;...
        4,2,7 ;...
        -2 6 9];
dmax = 3;
distance_set1_set2 = pdist2(set1,set2)

distance_set1_set2 = 2×3

3.0000 5.0990 7.3485 4.1231 3.7417 4.2426

indices = any(distance_set1_set2 <= dmax,2)

indices = 2×1 logical array
   1
   0

set1(indices==1,:)

ans = 1×3

0 1 4

[Adam Fitchett]

This worked thanks, although it turned out to be very memory-hungry for my large matrices

Used 98% of the RAM on a workstation with 256 GB of RAM!