3D line voxelization and connectivity control

Voxelization algorithms that convert a 3D continuous line representation into a discrete line representation have a dual role in graphics. First, these algorithms synthesize voxel-based objects in volume graphics. The 3D line itself is a fundamental primitive, also used as a building block for voxelizing more complex objects. For example, sweeping a 3D voxelized line along a 3D voxelized circle generates a voxelized cylinder. The second application of 3D line voxelization algorithms is for ray traversal in voxel space. Rendering techniques that cast rays through a volume of voxels are based on algorithms that generate the set of voxels visited (or pierced) by the continuous ray. Discrete ray algorithms have been developed for traversing a 3D space partition or a 3D array of sampled or computed data. These algorithms produce one discrete point per step, in contrast to ray casting algorithms for volume rendering, which track a continuous ray at constant intervals, and to voxelization algorithms that generate nonbinary voxel values (for example, partial occupancies). Before considering algorithms for generating discrete lines, we introduce the topology and geometry of discrete lines.