Finite sets of points in ${\mathbb{P}}^4$ with special projection properties

In this note we introduce the notion of $(b,d)$-geprofi sets and study their basic properties. These are sets of $bd$ points in ${\mathbb{P}}^4$ whose projection from a general point to a hyperplane is a full intersection, i.e., the intersection of a curve of degree $b$ and a surface of degree $d$. We show that such nontrivial sets exist if and only if $b\ge 4$ and $d\ge 2$. Somewhat surprisingly, for infinitely many values of $b$ and $d$ there exist such sets in linear general position. The note contains open questions and problems.