arrays - Calculating Euclidean distance of pairs of 3D points in matlab

Question

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 in matlab without loop ?

Answer 1

Use pdist and squareform:

D = squareform( pdist(X, 'euclidean' ) ); 

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For beginners, it can be a nice exercise to compute the distance matrix D using bsxfun (hover to see the solution).

elemDiff = bsxfun( @minus, permute(X,[ 1 3 2 ]), permute(X, [ 3 1 2 ]) );
D = sqrt( sum( elemDiff.^2, 3 ) );