  Let $S$ be a set of $n$ points in general position in $\mathbb{R}^d$. The
order-$k$ Voronoi diagram of $S$, $V_k(S)$, is a subdivision of $\mathbb{R}^d$
into cells whose points have the same $k$ nearest points of $S$.
  Sibson, in his seminal paper from 1980 (A vector identity for the Dirichlet
tessellation), gives a formula to express a point $Q$ of $S$ as a convex
combination of other points of $S$ by using ratios of volumes of the
intersection of cells of $V_2(S)$ and the cell of $Q$ in $V_1(S)$. The natural
neighbour interpolation method is based on Sibson's formula. We generalize his
result to express $Q$ as a convex combination of other points of $S$ by using
ratios of volumes from Voronoi diagrams of any given order.
