# The advantage of B-spline compared to Bézier if the number of control points is very small

If the number of control points is n+1, and the degree of the basis function is p

If n = p, B-spline is as same as Bézier curve.

Suppose I have a chance to increase the number of control points say to be n+2; What advantage I can get by doing so compared to Bézier.

Thank you very much

With degree $p$, a bezier can only have $p+1$ control-points. For a composite bezier curve the number of control points must be a multiple $m$ of $p+1$.
With a B-spline you can increase the number of parameters by $1$.
When using $d$-dimensional composite bezier curves, the control points are usually constrained to obtain $G^1$-continuity. This reduces the dimension of the parameter space from $dm(p+1)$ to $dm(p-1)+m$.