.  It is tempting to try to lift the restrictions of Corollary \[cor0\] to be able to compute, in polylogarithmic space, the area $A(c)$ defined by an arbitrary polygonal closed curve $c$ in the plane equipped with a tessellation ${\mathcal{T}}$ into unit squares. However, in the general situation, this idea would not work because the rational number $A(c)$ might have an exponentially large denominator, hence, $A(c)$ could take polynomial space just to store (let alone the computations)