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[2k Pi/13],Sin[2 k Pi/13]},{k,0,156,4}]]],
Graphics3D[BezierCurve[Table[{Cos[2k Pi/13],Sin[2 k Pi/13],k /156},{k,0,156,4}]]]}}]