[?] Find the smallest circumsphere containing N points?

[yn (Nan Yang)]

How to draw the smallest Circumsphere containing N points?

[mthiel (Marco Thiel)]

Something like this?

M = 10; (*Number of points*)
data = RandomReal[1, {M, 2}]; (*Generate coords of points*)
Show[RegionPlot[BoundingRegion[data, "MinDisk"]], Graphics[{Red, Point /@ data}]] (*Calculate Circumdisk and plot*)

In 3D

data3d = RandomReal[1, {M, 3}];
Show[RegionPlot3D[BoundingRegion[data3d, "MinBall"], PlotStyle -> Directive[Yellow, Opacity[0.5]]], Graphics3D[{Red, Point /@ data3d}]]

Cheers,

Marco

[yn (Nan Yang)]

Thank you so much!
But my version is 10.2, so it seems that the “BoundingRegion” cannot work.
Do you know how to do with 10.2?

cheers,
YN