A Practical Volumetric System for Indirect Visualization

Uniform volumetric data contains values recorded at constant intervals in three dimensions of space. The time and space complexities of many algorithms for volumetric data are both O(n), where n is the number of cells in a three-dimensional array containing the data.;To store uniform volumetric data in memory, a data structure called a brick octree can be used. This structure reduces memory requirements by removing duplicate portions of the data. To store uniform volumetric data in files, we devised the Voxel Object Definition (VOD) file format, based on directly encoding a brick octree. The VOD file format has advantages over the RAW format on consumer level hardware, where memory and storage requirements are critical. It reduces these requirements through duplicate brick removal and inlined lossless compression. In our experiments, the method achieved compression ratios ranging from 1.58 : 1 to 52.18: 1.;To improve the speed of indirect visualization of uniform volumetric data, geometric mip mapping and parallel processing can be applied to the brick octree data structure in a system called Isovox. In our experiments, speed ups of between 2.41 and 2.96 were observed on a machine with a single processor comprised of four cores when extracting surfaces in parallel using the brick octree structure. Speed ups between 137.57 and 147.35 were observed when extracting a surface at a lower resolution than the original data.;Visualization is often applied to volumetric data to aid in understanding. To visualize volumetric data with an indirect approach, the Marching Cubes algorithm is used to produce a polygon model corresponding to every implicit surface in the data. Such models can be displayed quickly on consumer level hardware. We describe an algebra, algorithms and data structures suited to manipulating, storing and visualizing uniform volumetric data appropriately for indirect visualization. To enable manipulation of volumetric data, we introduce the Indirect Constructive Volume Geometry (ICVG) algebra and provide descriptions of primitives for volumetric data presented through indirect visualization. The concept of a volume sampling function is defined, and functions are provided for cuboids, ellipsoids, cylinders and cones. The algebra and associated primitives facilitate authoring of complicated volumetric content.