Allen Van Gelder

Octrees for faster isosurface generation

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.

Anatomically based modeling

We describe an improved, anatomically based approach to modeling and animating animals. Underlying muscles, bones, and generalized tissue are modeled as triangle meshes or ellipsoids. Muscles are deformable discretized cylinders lying between fixed origins and insertions on specific bones. Default rest muscle shapes can be used, or the rest muscle shape can be designed by the user with a small set of parameters. Muscles automatically change shape as the joints move. Skin is generated by voxelizing the underlying components, filtering, and extracting a polygonal isosurface. Isosurface skin vertices are associated with underlying components and move with them during joint motion. Skin motion is consistent with an elastic membrane model. All components are parameterized and can be reused on similar bodies with non-uniformly scaled parts. This parameterization allows a non-uniformly sampled skin to be extracted, maintaining more details at the head and extremities.

Direct volume rendering with shading via three-dimensional textures

A new and easy-to-implement method for direct volume rendering that uses 3D texture maps for acceleration, and incorporates directional lighting, is described. The implementation, called Voltx, produces high-quality images at nearly interactive speeds on workstations with hardware support for three-dimensional texture maps. Previously reported methods did not incorporate a light model, and did not address issues of multiple texture maps for large volumes. Our research shows that these extensions impact performance by about a factor of ten. Voltx supports orthographic, perspective, and stereo views. This paper describes the theory and implementation of this technique, and compares it to the shear-warp factorization approach. A rectilinear data set is converted into a three-dimensional texture map containing color and opacity information. Quantized normal vectors and a lookup table provide efficiency. A new tesselation of the sphere is described, which serves as the basis for normal-vector quantization. A new gradient-based shading criterion is described, in which the gradient magnitude is interpreted in the context of the field-data value and the material classification parameters, and not in isolation. In the rendering phase, the texture map is applied to a stack of parallel planes, which effectively cut the texture into many slabs. The slabs are composited to form an image.

A coherent projection approach for direct volume rendering

Direct volume rendering offers the opportunity to visualize all of a three-dimensional sample volume in one image. However, processing such images can be very expensive and good quality high-resolution images are far from interactive. Projection approaches to direct volume rendering process the volume region by region as opposed to ray-casting methods that process it ray by ray. Projection approaches have generated interest because they use coherence to provide greater speed than ray casting and generate the image in a layered, informative fashion. This paper discusses two topics: First, it introduces a projection approach for directly rendering rectilinear, parallel-projected sample volumes that takes advantage of coherence across cells and the identical shape of their projection. Second, it considers the repercussions of various methods of integration in depth and interpolation across the scan plane. Some of these methods take advantage of Gouraud-shading hardware, with advantages in speed but potential disadvantages in image quality.

Design Overview of the NAIL! System

We describe the design decisions made for the NAIL! (not another implementation of logic!) system, an advanced form of DBMS where queries may involve a large collection of Prolog-like rules used for query interpretation. A discussion of the ways NAIL! semantics differs from Prolog is followed by an exposition of the principal ideas in the system design. These points include the partition of predicates into strongly connected components to represent the structure of recursions and the “capture rule” organization for selecting query processing strategies. Other ideas include the way distinctions between bound and free arguments are capitalized upon and the persistence of previously discovered facts about the way to handle certain queries. We also survey the recent work on the processing of recursively defined queries conducted by the NAIL! group and others with similar computational models.

Efficient tests for top-down termination of logical rules

Considered is the question of whether top-down (Prolog-like) evaluation of a set of logical rules can be guaranteed to terminate. The NAIL! system is designed to process programs consisting of logical rules and to select, for each fragment of the program, the best from among many possible strategies for its evaluation. In the context of such a system, it is essential that termination tests be fast. Thus, the “uniqueness” property of logical rules is introduced. This property is satisfied by many of the common examples of rules and is easily recognized. For rules with this property, a set of inequalities, whose satisfaction is sufficient for termination of the rules, can be generated in polynomial time. Then a polynomial test for satisfaction of constraints generated by this process is given.

Parallel complexity of logical query programs

We consider the parallel time complexity of logic programs without function symbols, called logical query programs, or Datalog programs. We give a PRAM algorithm for computing the minimum model of a logical query program, and show that for programs with the “polynomial fringe property,” this algorithm runs in time that is logarithmic in the input size, assuming that concurrent writes are allowed if they are consistent. As a result, the “linear” and “piecewise linear” classes of logic programs are inNC. Then we examine several nonlinear classes in which the program has a single recursive rule that is an “elementary chain.” We show that certain nonlinear programs are related to GSM mappings of a balanced parentheses language, and that this relationship implies the “polynomial fringe property;” hence such programs are inNC Finally, we describe an approach for demonstrating that certain logical query programs are log space complete forP, and apply it to both elementary single rule programs and nonelementary programs.

SYSTEM/U: a database system based on the universal relation assumption

System/U is a universal relation database system under development at Standford University which uses the language C on UNIX. The system is intended to test the use of the universal view, in which the entire database is seen as one relation. This paper describes the theory behind System/U, in particular the theory of maximal objects and the connection between a set of attributes. We also describe the implementation of the DDL (Data Description Language) and the DML (Data Manipulation Language), and discuss in detail how the DDL finds maximal objects and how the DML determines the connection between the attributes that appear in a query.

Multi-dimensional trees for controlled volume rendering and compression

This paper explores the use of multi-dimensional trees to provide spatial and temporal efficiencies in imaging large data sets. Each node of the tree contains a model of the data in terms of a fixed number of basis functions, a measure of the error in that model, and a measure of the importance of the data in the region covered by the node. A divide-and-conquer algorithm permits efficient computation of these quantities at all nodes of the tree. The flexible design permits various sets of basis functions, error criteria, and importance criteria to be implemented easily. Selective traversal of the tree provides images in acceptable time, by drawing nodes that cover a large volume as single objects when the approximation error and/or importance are low, and descending to finer detail otherwise. Trees over very large datasets can be pruned by the same criterion to provide data representations of acceptable size and accuracy. Compression and traversal are controlled by a user-defined combination of modeling error and data importance. For imaging decisions additional parameters are considered, including grid location, allowed time, and projected screen area. To analyse results, two evaluation metrics are used: the first compares the hierarchical model to actual data values, and the second compares the pixel values of images produced by different parameter settings.

Safety and translation of relational calculus

Not all queries in relational calculus can be answered sensibly when disjunction, negation, and universal quantification are allowed. The class of relation calculus queries or formulas that have sensible answers is called the domain independent class which is known to be undecidable. Subsequent research has focused on identifying large decidable subclasses of domain independent formulas. In this paper we investigate the properties of two such classes: the evaluable formulas and the allowed formulas. Although both classes have been defined before, we give simplified definitions, present short proofs of their main properties, and describe a method to incorporate equality. Although evaluable queries have sensible answers, it is not straightforward to compute them efficiently or correctly. We introduce relational algebra normal form for formulas from which form the correct translation into relational algebra is trivial. We give algorithms to transform an evaluable formula into an equivalent allowed formula and from there into relational algebra normal form. Our algorithms avoid use of the so-called Dom relation, consisting of all constants appearing in the database or the query. Finally, we describe a restriction under which every domain independent formula is evaluable and argue that the class of evaluable formulas is the largest decidable subclass of the domain independent formulas that can be efficiently recognized.