  Let $f$ be a generalized affine fractal interpolation function with vertical
scaling function $S$. In this paper, we study $\dim_B \Gamma f$, the box
dimension of the graph of $f$, under the assumption that $S$ is a Lipschtz
function. By introducing vertical scaling matrices, we estimate the upper bound
and the lower bound of oscillations of $f$. As a result, we obtain explicit
formula of $\dim_B \Gamma f$ under certain constraint conditions.
