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June 30[edit]

Smallest hypersphere around a cloud of points[edit]

I've started wondering (for some hierarchical classification system) how to find the smallest hypersphere that encompasses a set of points in $R^{n}$ . For n=1, I can just take the two points that are furthest apart on the number line and get an interval (i.e. a 1-sphere ;-). For n=2, I think I need the two points that are farthest apart on the circle, but they don't uniquely define the circle (consider the case where three points form an equilateral triangle). On the other hand, the circle does not necessarily go through even 3 of the points - consider the case of all three on a line. I'm sure there is some smart approach someone already knows... --Stephan Schulz (talk) 10:09, 30 June 2019 (UTC)[reply]

I think you're referring to a bounding sphere - the article contains a few algorithms for finding either minimal or ε-minimal solutions. — crh23 (Talk) 11:52, 30 June 2019 (UTC)[reply]

Thanks, that is very useful! --Stephan Schulz (talk) 13:04, 30 June 2019 (UTC)[reply]