Rasterization and voxelization of two- and three-dimensional space partitionings

The paper presents a very straightforward and effective algorithm to convert a space partitioning, made up of polyhedral objects, into a 3D block of voxels, which is fully occupied, i.e. in which every voxel has a value. In addition to walls, floors, etc. there are 'air' voxels, which in turn may be distinguished as indoor and outdoor air. The method is a 3D extension of a 2D polygon-to-raster conversion algorithm. The input of the algorithm is a set of non-overlapping, closed polyhedra, which can be nested or touching. The air volume is not necessarily represented explicitly as a polyhedron (it can be treated as 'background', leading to the 'default' voxel value). The approach consists of two stages, the first being object (boundary) based, the second scan-line based. In addition to planar faces, other primitives, such as ellipsoids, can be accommodated in the first stage without affecting the second.