Fundamentals of surface voxelization

This paper presents the theoretical discrete geometry framework for the voxelization of surfaces. A voxelized object is a 3D discrete representation of a continuous object on a regular grid of voxels. Many important topological properties of a discrete surface cannot be stated solely in terms of connectivity, and thus the concepts of separating, coverage, and tunnel-freeness are introduced. These concepts form the basis for proper voxelization of surfaces.