Consider $\mathcal A=(u_i)_{i=1}^m $ to be a set of hyperplanes in $\mathbb R^d$, such that for every $1\leq i \leq m$: $u_i \in \mathbb R^d$.

These hyperplanes are disconnecting $\mathbb R^d$ to convex polyhedra that are called regions. My question is the following: is there a way to find a representative from each such region?

Thanks!