Computation of Rees algebra of polynomial ideal

Question

Let $R=k[x_{1},\ldots,x_{n}]$, $k$ be a field. Let $I$ be an ideal of $R$ and $f\in R$. If $R[It]$ is known, how to compute Rees algebra $R[(I+(f))t]$? Is there any algorithmic procedure? It is easy when $I$ and $(f)$ are insect transversally.