In the region $\text{Star}(w_{i})+\mathbb{R}_{\geq 0}w_{i}\subset N_{\mathbb{R}}$, the directional derivative of the canonical extension $u=u^{**}$ satisfies $\langle w_{i},\nabla u\rangle=1.$ In particular, in this region, for any $m$ with $\langle m,w_{i}\rangle=1$, the function $u_{m}=u-m$ is constant upon translation in the $w_{i}$-direction.