Calculating Euclidean distance of pairs of 3D points.

I have an Nx3 array that contains N 3D points

 a1 b1 c1 
 a2 b2 c2 
 .... 
 aN bN cN

I want to calculate Euclidean distance in a NxN array that measures the Euclidean distance between each pair of 3D points. (i,j) in result array returns the distance between (ai,bi,ci) and (aj,bj,cj). Is it possible to write a code for this without loop ?

Answer 1

[Andrei Bobrov]

use Statistics Toolbox:

out = squareform(pdist(Nm)); % here Nm - your matrix [Nx3]

one variant without Statistics Toolbox:

nc = num2cell(Nm,2);
[x,y] = ndgrid(1:N);
out = cellfun(@(x,y)sqrt(sum((x-y).^2)),nc(x),nc(y));

other variant

out = squeeze(sqrt(sum(bsxfun(@minus,Nm,permute(Nm,[3,2,1])).^2,2)));

[Josh Wiley]

regarding the last variant, when I use this with a 2x3 matrix, the output is a 2x2 matrix with the distance appearing twice, what might be the cause of that?

Answer 2

[Roger Stafford]

Use matlab's 'pdist' and 'squareform' functions