David T. Kao

A flow-guided streamline seeding strategy

The paper presents a seed placement strategy for streamlines based on flow features in the dataset. The primary goal of our seeding strategy is to capture flow patterns in the vicinity of critical points in the flow field, even as the density of streamlines is reduced. Secondary goals are to place streamlines such that there is sufficient coverage in non-critical regions, and to vary the streamline placements and lengths so that the overall presentation is aesthetically pleasing (avoid clustering of streamlines, avoid sharp discontinuities across several streamlines, etc.). The procedure is straightforward and non-iterative. First, critical points are identified. Next, the flow field is segmented into regions, each containing a single critical point. The critical point in each region is then seeded with a template depending on the type of critical point. Finally, additional seed points are randomly distributed around the field using a Poisson disk distribution to minimize closely spaced seed points. The main advantage of this approach is that it does not miss the features around critical points. Since the strategy is not image-guided, and hence not view dependent, significant savings are possible when examining flow fields from different viewpoints, especially for 3D flow fields.

Strategy for seeding 3D streamlines

This paper presents a strategy for seeding streamlines in 3D flow fields. Its main goal is to capture the essential flow patterns and to provide sufficient coverage in the field while reducing clutter. First, critical points of the flow field are extracted to identify regions with important flow patterns that need to be presented. Different seeding templates are then used around the vicinity of the different critical points. Because there is significant variability in the flow pattern even for the same type of critical point, our template can change shape depending on how far the critical point is from transitioning into another type of critical point. To accomplish this, we introduce the /spl alpha/-/spl beta/ map of 3D critical points. Next, we use Poisson seeding to populate the empty regions. Finally, we filter the streamlines based on their geometric and spatial properties. Altogether, this multi-step strategy reduces clutter and yet captures the important 3D flow features.

PLIC: bridging the gap between streamlines and LIC

This paper explores mapping strategies for generating LIC-like images from streamlines and streamline-like images from LIC. The main contribution of this paper is a technique which we call pseudo-LIC or PLIC. By adjusting a small set of key parameters, PLIC can generate flow visualizations that span the spectrum of streamline-like to LIC-like images. Among the advantages of PLIC are: image quality comparable with LIC, performance speedup over LIC, use of a template texture that is independent of the size of the flow field, handles the problem of multiple streamlines occupying the same pixel in image space, reduced aliasing, applicability to time varying data sets, and variable speed animation.

Visualizing spatially varying distribution data

Box plot is a compact representation that encodes the minimum, maximum, mean, median, and quartile information of a distribution. In practice, a single box plot is drawn for each variable of interest. With the advent of more accessible computing power, we are now facing the problem of visualizing data where there is a distribution at each 2D spatial location. Simply extending the box plot technique to distributions over 2D domain is not straightforward. One challenge is reducing the visual clutter if a box plot is drawn over each grid location in the 2D domain. This paper presents and discusses two general approaches, using parametric statistics and shape descriptors, to present 2D distribution data sets. Both approaches provide additional insights compared to the traditional box plot technique.

An Extended Schema Model for Scientific Data

The absence of a uniform and comprehensive representation for complex scientific data makes the adaptation of database technology to multidisciplinary research projects difficult. In this paper, we clarify the taxonomy of data representations required for scientific database systems. Then, based on our proposed scientific database environment, we present a scientific data abstraction at the conceptual level, a schema model for scientific data. This schema model allows us to store and manipulate scientific data in a uniform way independent of the implementation data model. We believe that more information has to be maintained as metadata for scientific data analysis than in statistical and commercial databases. Clearly, metadata constitutes an important part of our schema model. As part of the schema model, we provide an operational definition for metadata. This definition enables us to focus on the complex relationship between data and metadata.

Database Issues for Data Visualization: Developing a Data Model

The remainder of this paper discusses the major issues related to the development of data models for scientific visualization which were identified by the data model subgroup at the IEEE Workshop on Database Issues in Visualization held in October 1993 in San Jose, California. The issues include the need to develop a reasonable taxonomy to apply to data models, the definition of metadata (or ancillary data), the notion of levels of abstraction available for defining a data model, the nature and role of queries in a data model, and the effects of data errors on a data model.

Database Issues for Data Visualization: Scientific Data Modeling

Visualization is one of the most important activities involved in modern exploratory data analysis. Traditional database data models, in their current forms, are inadequate to satisfy the data modeling need of exploratory data analysis in general and visualization in particular. A comprehensive scientific data model is required for seamless integration of various components of a scientific database system which includes visualization, data analysis, and data management.

An algebraic approach to the prefix model analysis of binary tree structures and set intersection algorithms

Abstract The trie , or digital tree , is a standard data structure for representing sets of strings over a given finite alphabet. Since Knuths original work (1973) , these data structures have been extensively studied and analyzed. In this paper, we present an algebraic approach to the analysis of average storage and average time required by the retrieval algorithms of trie structures under the prefix model . This approach extends the work of Flajolet et al. for other models which, unlike the prefix model, assume that no key in a sample set is the prefix of another. As the main application, we analyze the average running time of two algorithms for computing set intersections.

A Uniform Approach to the Analysis of Trie Structures That Store Prefixing-Keys

Triesare data structures for storing sets where each element is represented by a key that can be viewed as a string of characters over a finite alphabet. These structures have been extensively studied and analyzed under several probability models. All of these models, however, preclude the occurrence of sets in which the key of one element is a prefix of that of another?such a key is called aprefixing-key. This paper presents an average case analysis of several trie varieties, which we generically calledprefixing-tries, for representing sets with “unrestricted” keys, that is, sets in which the key of one element may be a prefix of that of another. The underlying probability model, which we call theprefix model, Ph,n,massumes as equally likely alln-element sets whose keys are composed of at mosthcharacters from a fixed alphabet of sizem. For each of the trie varieties analyzed, we derive exact formulas for the expected space required to store such a set, and the average time required to retrieve an element given its key, as functions ofh,n, andm. Our approach to the analysis is of interest in its own right. It provides a unifying framework for computing the expectations of a wide class of random variables with respect to the prefix model. This class includes the cost functions of the trie varieties analyzed here.

A Uniform Analysis of Trie Structures that Store Prefixing-Keys with Application to Doubly-Chained Prefixing-Tries

Tries are data structures for storing sets where each element is represented by a key that can be viewed as a string of characters over a finite alphabet. These structures have been extensively studied and analyzed under several probability models. All of these models, however, preclude the occurrence of sets in which the key of one element is a prefix of that of another — such a key is called a prefixing-key.