Let $V$ be a paracompact strictly $K$-analytic space with a line bundle $L$. A metric ${\|\hskip 4.30554pt\|}$ on $L$ is called piecewise linear if there is a ${\rm G}$-covering $(V_{i})_{i\in I}$ and frames $s_{i}$ of $L$ over $V_{i}$ for every $i\in I$ such that $\|s_{i}\|=1$ on $V_{i}$. A function $\varphi\colon V\to{\mathbb{R}}$ is called a piecewise linear function if it induces a piecewise linear metric on the trivial line bundle $\mathcal{O}_{V}$. Note that these are ${\rm G}$-local definitions (see [GK15, Proposition 5.10] for the argument).