Let $\Psi$ be a virtual support function on $\Sigma$, $L=\mathcal{O}(D_{\Psi})$ and $s=s_{\Psi}$. Then the correspondence $\|\cdot\|\mapsto\psi_{\|\cdot\|}$ determines a bijection between the set of toric metrics on $L^{{\text{\rm an}}}$ and the set of continuous functions $\psi$ on $N_{\mathbb{R}}$ with the property that $\psi-\Psi$ can be extended to a continuous function on $N_{\Sigma}$. The metric associated to a function $\psi$ will be denoted $\|\cdot\|_{\psi}$.