Generate Bezier curves of any degree

GraphicsGrid[Partition[Table[With[{pts = Table[i{Cos[8 / n i], Sin[8 / n i]}, {i, n}]}, Graphics[{Green, Line[pts], Red, Point[pts], Thick, Blue, BezierCurve[pts, SplineDegree -> (n - 1)]}, PlotLabel -> Row[{"degree ", n - 1}]]], {n, 4, 16}], 4], Frame -> All, ImageSize -> {500, 500}]

-Graphics-