Voxelization in common sampling lattices

In this paper, we introduce algorithms to voxelize polygonal meshes in common sampling lattices. In the case of Cartesian lattices, we complete the separability and minimality proof for the voxelization method presented by Huang et al. We extend the ideas to general 2D lattices, including hexagonal lattices, and 3D body-centred cubic lattices. The notion of connectedness in the two lattice structures is discussed along with a novel voxelization algorithm for such lattices. Finally, we present the proof that meshes voxelized with our proposed algorithm satisfy the separability and minimality criteria.