B - splines

B-splines are defined over a knot sequence. The Bernstein basis is a special case:

n=3;
bezknot[n_]:=Join[Table[0,{i,0,n}],Table[1,{i,0,n}]];
bezknot[3];
bbasis[n_,t_]:=Table[BSplineBasis[{n,bezknot[n]},i,t],{i,0,n}];
Plot[bbasis[3,t],{t,0,1},PlotRange-> All,PlotStyle->Thick]

knot[n_,ll_]:=Join[Table[0,{i,0,n}],Table[i/ll,{i,1,ll-1}],Table[1,{i,0,n}]];

n=3;  (*degree *)
ll=8; (* number of intervals *)
knot[n,ll];
basis[n_,ll_,t_]:=Table[BSplineBasis[{n,knot[n,ll]},i,t],{i,0,n+ll-1}];

Plot[basis[n,ll,t],{t,0,1},PlotRange-> All,PlotStyle->Thick]

Manipulate[Plot[BSplineBasis[{n,knot[n,ll]},i,t],{t,0,1},PlotRange->All,PlotStyle->Thick],{i,0,ll+n-1,1}]