The process of generating discrete surfaces in a volumetric representation, termed voxelization, is confronted with topological considerations as well as accuracy and efficiency requirements. We introduce a new method for voxelizing planar objects which, unlike existing methods, provides topological conformity through geometric measures. We extend our approach to provide, for the first time, an accurate and coherent method for voxelizing polygon meshes. This method eliminates common voxelization artifacts at edges and vertices. We prove the method's topological attributes and report performance of our implementation. Finally, we demonstrate that this approach forms a basis for a new set of voxelization algorithms by voxelizing an example cubic object.