pts1 = Tuples[{Range[4], Range[4]}];
pts2 = Tuples[{Range[3], Range[3], Range[3]}];
Grid[{
  {Graphics[{Green, Line[pts1], Red, Point[pts1], Black, 
     BezierCurve[pts1, SplineDegree -> 5]}], 
   Graphics3D[{BezierCurve[pts2, SplineDegree -> 4], Green, 
     Opacity[.5], Line[pts2], Red, Point[pts2]}]}, {Graphics[
    BezierCurve[
     Table[{Cos[2 k Pi/13], Sin[2 k Pi/13]}, {k, 0, 156, 4}]]],
   Graphics3D[
    BezierCurve[
     Table[{Cos[2 k Pi/13], Sin[2 k Pi/13], k /156}, {k, 0, 156, 
       4}]]]}}]