In this work, we propose a new grid conversion algorithm between the hexagonal lattice and the orthogonal (a.k.a. Cartesian) lattice. The conversion process, named $ H _{ 2 } $ O, is easy to implement and is perfectly reversible using the same algorithm to return from one lattice to the other. The key observation of our approach is a decomposition of the lattice conversion as a sequence of shearing operations along three well-chosen directions. Hence, only 1-D fractional sample delay operators are required, which can be implemented by simple convolutions. The proposed algorithm combines reversibility and fast 1-D operations, together with high-quality resampled images.