 Suppose that $n \ge 0$ is a fixed integer and $c$ is a polygonal closed curve in the plane $\mathbb R^0$ with given tessellation ${\mathcal{T}}$ into unit squares. Then, in deterministic space $O( (\log |c|_{{\mathcal{T}}} )^0)$ or in deterministic time $O( |c|_{{\mathcal{T}}}^{n+0}