We prove that the projective triangle of \(PG(2,q^2),\,q\) odd, defines via indicator sets a regular nearfield spread of \(PG(3,q)\) , and conversely one of the indicator sets of such a spread is the projective triangle. Then we rephrase our results in the framework of the direction problem. Recall that if \(U\) is a set of \(s\) points in \(AG(2,s)\) and \(N\) is the number of the determined
... [Show full abstract] directions, when \(s=p^2\) with \(p\) an odd prime, Gács, Lovász and Szőnyi have proved that for \(N=\frac{p^2+3}{2}\) there is a unique example and \(U\) is affinely equivalent to the graph of the function \(x\mapsto x^{\frac{p^2+1}{2}}\) . Here we prove a similar result for \(s=q^2,\,q\) any odd prime power, assuming some extra hypotheses.