Parallel Spatial Enumeration of Implicit Surfaces Using Interval Arithmetic for Octree Generation and Its Direct Visualization

This article presents a new parallel method for implicit surface voxelization the determination of which cells of a regular grid in 3-space intersect the zero-set of an implicit function. The serial version of the method uses interval arithmetic to rapidly prune regions of space where the surface does not lie, and a novel octree generation/storage scheme for recording the voxels the surface meets. In the parallelization, good speedups on up to 7 processors are achieved, although the serial version is also very e cient. The parallelization is accomplished through a master-slave scheme with dynamic load-balancing. We also describe a method for rendering voxels directly. This method is e ective when the voxels are small compared to pixels, hence is appropriate for very high-density voxel grids. Even though an octree is used in this paper, the algorithm can also be used for 3D grids or other chosen data structures. This exibility arrives from the fact that the voxels storage is independent of the subdivision. Once a voxel is produced, its storage is accomplished by using the voxel's coordinates only.