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It's my first time here, so I appologise in advance if I break any rules through this post.

So I have a Cartesian Lattice spanning across the Euclidean plane and a unit square. The lattice points inside the square are highlighted in green and their coordinates are known. Each of them has around it an area of control or a Wigner Seitz cell, that I know how to calculate. How do I calculate how much of the square is covered by the Wigner-Seitz cells?