An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.

The large size of many volume data sets often prevents visualization algorithms from providing interactive rendering. The use of hierarchical data structures can ameliorate this problem by storing summary information to prevent useless exploration of regions of little or no current interest within the volume. This paper discusses research into the use of the octree hierarchical data structure when the regions of current interest can vary during the application, and are not known a priori. Octrees are well suited to the six-sided cell structure of many volumes. A new space-efficient design is introduced for octree representations of volumes whose resolutions are not conveniently a power of two; octrees following this design are called branch-on-need octrees (BONOs). Also, a caching method is described that essentially passes information between octree neighbors whose visitation times may be quite different, then discards it when its useful life is over. Using the application of octrees to isosurface generation as a focus, space and time comparisons for octree-based versus more traditional "marching" methods are presented.

The mapping of images onto surfaces may substantially increase the realism and information content of computer-generated imagery. The projection of a flat source image onto a curved surface may involve sampling difficulties, however, which are compounded as the view of the surface changes. As the projected scale of the surface increases, interpolation between the original samples of the source image is necessary; as the scale is reduced, approximation of multiple samples in the source is required. Thus a constantly changing sampling window of view-dependent shape must traverse the source image. To reduce the computation implied by these requirements, a set of prefiltered source images may be created. This approach can be applied to particular advantage in animation, where a large number of frames using the same source image must be generated. This paper advances a "pyramidal parametric " prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images. Although the mapping of texture onto surfaces is an excellent example of the process and provided the original motivation for its development, pyramidal parametric data structures admit of wider application. The aliasing of not only surface texture, but also highlights and even the surface representations themselves, may be minimized by pyramidal parametric means.

VR-based rendering of large-scale data sets is typically limited by timing and complexity constraints of the rendering engine. Decentralized rendering, such as accessing a large data repository over a network and rendering the image on the client side, causes problems due to the limited bandwidth of existing networks. We present a combination of octree space subdivision and wavelet compression techniques to store large volumetric data sets in a hierarchical fashion, and we incorporate a unique numbering scheme, so that subvolumes (regions-of-interest) can be extracted efficiently at different levels of resolution.