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Say I have a Voronoi diagram of some points $p_1,\dots,p_n\in\mathbb{R}^d$, which tesselates $\mathbb{R}^d$ into cells $V_1,\dots,V_n$. Within each cell $V_i$, the pole is defined as the vertex of $...

Consider the following problem: Given an $\mathcal{H}$-polytope $P$ in $\mathbb{R}^d$ and $4$ orthogonal vectors $v_1, ..., v_4 \in \mathbb{R}^d$, compute the projection of $P$ to the subspace ...