On the graph of a function in two variables over a finite field

We show that if the number of directions determined by a pointset $\W$ of $\AG(3,q)$, $q=p^h$, of size $q^2$ is less than $q^2+2$, then every plane intersects $\W$ in $0$ modulo $p$ points, and apply the result to ovoids of the generalized quadrangles $T_2(\O)$ and $T_2^*(\O)$