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}]]]}}]