Let $V$ be a paracompact strictly $K$-analytic space with a line bundle $L$. A metric ${\|\hskip 4.30554pt\|}$ on $L$ is called piecewise ${\mathbb{Q}}$-linear if for every $x\in V$ there exists an open neighbourhood $W$ of $x$ and a non-zero $n\in{\mathbb{N}}$ such that ${\|\hskip 4.30554pt\|}^{\otimes n}_{|W}$ is a piecewise linear metric on $L^{\otimes n}_{|W}$. A function $\varphi\colon V\to{\mathbb{R}}$ is called a piecewise ${\mathbb{Q}}$-linear function if it induces a piecewise ${\mathbb{Q}}$-linear metric on the trivial line bundle $\mathcal{O}_{V}$.