# Finding distance through pair of points [closed]

I have 2 sets of data of points in 3D space. What I want to do is to find the minimum distance of pair of points from each set (so basically how close the sets can get to each other). For example, say

fst = {{2.22673,0.59492,2.6842},{3.13408,0.16181,1.63544},
{1.34213,-0.31185,3.25682},{3.11765,-1.15956,1.2044},
{3.21693,-1.46205,-0.21326},{3.25025,1.24013,0.66829},
{3.34529,0.95071,-0.68805},{3.32838,-0.43039,-1.13854},
{-0.45219,1.37427,3.23023},{0.47229,2.32191,2.63187}}
sec = {{9.22673,0.59492,2.6842},{10.1341,0.16181,1.63544},
{8.34213,-0.31185,3.25682},{10.1177,-1.15956,1.2044},
{10.2169,-1.46205,-0.21326},{10.2503,1.24013,0.66829},
{10.3453,0.95071,-0.68805},{10.3284,-0.43039,-1.13854},
{6.54781,1.37427,3.23023},{7.47229,2.32191,2.63187}}


What I did was to first create list of all pairs

perm = Outer[List, fst, sec]


Then I applied the list to function EuclideanDistance[]

Min[EuclideanDistance @@ perm]


This apparently didn't work, because the distance function doesn't know how to read the coordinates. Is there a way around this?

## closed as off-topic by Anton Antonov, user31159, bbgodfrey, m_goldberg, FeyreSep 13 '16 at 7:58

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Anton Antonov, Community, bbgodfrey, m_goldberg, Feyre
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• Min[Outer[EuclideanDistance, fst, sec, 1]] You need to specify the level (4th argument) in Outer. Check out the docs. – Quantum_Oli Aug 31 '16 at 16:05
• For large point sets it is more efficient to work with Nearest, like so. In[22]:= nf1 = Nearest[fst]; candidates = nf1[sec][[All, 1]]; mindist = Min[MapThread[EuclideanDistance, {sec, candidates}]] Out[24]= 3.95815195623 – Daniel Lichtblau Aug 31 '16 at 16:25
• Ah, good point. Thank you! – psimanjuntak Sep 1 '16 at 13:03
• Alternatively: Min@DistanceMatrix[fst, sec]. – user31159 Sep 12 '16 at 23:53