Problem 45912. Bounding Circle

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The Bounding Circle is the smallest enclosing circle to a given set of points on a plane https://en.wikipedia.org/wiki/Smallest-circle_problem

Find the radius r and center coordinates x, y of the smallest enclosing circle to the points with coordinates Xp, Yp (both [n x 1] vectors).

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Last Solution submitted on Nov 08, 2023

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Rafael S.T. Vieira on 20 Jun 2020

I've implemented the Welzl's algorithm, but, please, be warned as I've learned later that sometimes the algorithm fails. Years later, Matoušek, Sharir, and Welzl seems to have fixed the problem, creating a new version of the algorithm (adding one additional test).

Are Mjaavatten on 18 Apr 2021

I think the tolerance in Test 3 is a bit too tight. My solution fails in about 28% of the cases because the numerical error max(D)-r is up to 8*eps.

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