An integral affine function on an open subset of $\mathbb{R}^{n}$ is a continuous real-valued function locally of the form $f(x_{1},\ldots,x_{n})=a_{1}x_{1}+\ldots+a_{n}x_{n}+b$, with $a_{i}\in\mathbb{Z}$ and $b\in\mathbb{R}$. We denote by $\textrm{Aff}_{\mathbb{R}^{n}}$ the sheaf of integral affine functions on $\mathbb{R}^{n}$.