File:Runde pixel.png

English: Approximation for the case of a circular cutter χ, Covering the layer with circular pixels. A solution of the round trip problem is shown in the graph ${\displaystyle S}$ . The optimal round trip provides an approximation to the lawnmower problem given a circular lawnmower. Circular cutters. We can further extend the method to the case of circular cutters. Assume that χ is a unit-radius disk that is allowed to move arbitrarily in the plane. In this case, we use another form of “pixel” — instead of tiling the plane with unit squares, we tile the plane with regular hexagons, each of diameter 2. The centerpoints of these hexagons lie on a regular lattice. We join two centerpoints by an edge if they lie at distance √3; this results in a planar graph whose faces are equilateral triangles of side length √ 3.