I am having a seemingly easy question as what follows. Suppose I am estimating a smooth function $f(x_i)$, with $i=1,...,n$ and $n$ is the sample size. Now, if I have the restriction on $f(\cdot)$ such that $f(x=0)=f(0)=0$ (i.e., passing through the origin), then a B-spline approximation of $f(x=0)$ is given by $f(0)\approx \phi(0)'\beta$, where $\phi(\cdot)=[\phi_1(\cdot),...,\phi_J(\cdot)]'$ and $J$ is the number of the basis function that goes to infinity when $n$ goes to infinity.
Question
Since $f(x=0)=f(0)=0$, then $f(0)\approx \phi(0)'\beta=0$, implying that $\phi(0)'=0$ for all J. However, the basis function of B-spline does not give zero when evaluating at zero, i.e., $\phi(0)\neq 0$. Is there any way I can center the basis function around zero such that $\phi(0)'=0$ for all J?
Thank you all in advance.