Phillip J. Barry

Principles for information visualization spreadsheets

The visualization spreadsheet provides a framework for exploring large and complex data sets. Structuring user interactions using a spreadsheet paradigm creates a powerful tool for information visualization.

A spreadsheet approach to information visualization

In information visualization, as the volume and complexity of the data increases, researchers require more powerful visualization tools that enable them to more effectively explore multidimensional datasets. We discuss the general utility of a novel visualization spreadsheet framework. Just as a numerical spreadsheet enables exploration of numbers, a visualization spreadsheet enables exploration of visual forms of information. We show that the spreadsheet approach facilitates certain information visualization tasks that are more difficult using other approaches. Unlike traditional spreadsheets, which store only simple data elements and formulas in each cell, a visualization spreadsheet cell can hold an entire complex data set, selection criteria, viewing specifications, and other information needed for a full-fledged information visualization. Similarly, inter-cell operations are far more complex, stretching beyond simple arithmetic and string operations to encompass a range of domain-specific operators. We have built two prototype systems that illustrate some of these research issues. The underlying approach in our work allows domain experts to define new data types and data operations, and enables visualization experts to incorporate new visualizations, viewing parameters, and view operations.

de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves

The de Boor-Fix dual functionals are a potent tool for deriving results about piecewise polynomial B-spline curves. In this paper we extend these functionals to Tchebycheffian B-spline curves and then use them to derive fundamental algorithms that are natural generalizations of algorithms for piecewise polynomial B-spline algorithms. Then, as a further example of the utility of this approach, we introduce “geometrically continuous Tchebycheffian spline curves,” and show that a further generalization works for them as well.

A recursive evaluation algorithm for a class of Catmull-Rom splines

It is known that certain Catmull-Rom splines [7] interpolate their control vertices and share many properties such as affine invariance, global smoothness, and local control with B-spline curves; they are therefore of possible interest to computer aided design. It is shown here that another property a class of Catmull-Rom splines shares with B-spline curves is that both schemes possess a simple recursive evaluation algorithm. The Catmull-Rom evaluation algorithm is constructed by combining the de Boor algorithm for evaluating B-spline curves with Nevilles algorithm for evaluating Lagrange polynomials. The recursive evaluation algorithm for Catmull-Rom curves allows rapid evaluation of these curves by pipelining with specially designed hardware. Furthermore it facilitates the development of new, related curve schemes which may have useful shape parameters for altering the shape of the curve without moving the control vertices. It may also be used for constructing transformations to Bézier and B-spline form.

Flexible information visualization of multivariate data from biological sequence similarity searches

Information visualization faces challenges presented by the need to represent abstract data and the relationships within the data. Previously, we presented a system for visualizing similarities between a single DNA sequence and a large database of other DNA sequences (E.H. Chi et al., 1995). Similarity algorithms generate similarity information in textual reports that can be hundreds or thousands of pages long. Our original system visualized the most important variables from these reports. However, the biologists we work with found this system so useful they requested visual representations of other variables. We present an enhanced system for interactive exploration of this multivariate data. We identify a larger set of useful variables in the information space. The new system involves more variables, so it focuses on exploring subsets of the data. We present an interactive system allowing mapping of different variables to different axes, incorporating animation using a time axis, and providing tools for viewing subsets of the data. Detail-on-demand is preserved by hyperlinks to the analysis reports. We present three case studies illustrating the use of these techniques. The combined technique of applying a time axis with a 3D scatter plot and query filters to visualization of biological sequence similarity data is both powerful and novel.

Visualization of biological sequence similarity search results

Biological sequence similarity analysis presents visualization challenges, primarily because of the massive amounts of discrete, multi dimensional data. Genomic data generated by molecular biologists is analyzed by algorithms that search for similarity to known sequences in large genomic databases. The output from these algorithms can be several thousand pages of text, and is difficult to analyze because of its length and complexity. We developed and implemented a novel graphical representation for sequence similarity search results, which visually reveals features that are difficult to find in textual reports. The method opens new possibilities in the interpretation of this discrete, multidimensional data by enabling interactive investigation of the graphical representation.

Shape parameter deletion for Pólya curves

We present a simple change of basis technique for transforming one type of Pólya curve to another closely related Pólya curve form. Repeated use of this method yields algorithms for transforming one arbitrary Pólya form to another, as well as algorithms for evaluating, subdividing, and differentiating Pólya curves. These procedures can be applied to almost all Pólya curves, including Bézier curves and Lagrange interpolating polynomials.

Interpolation and approximation of curves and surfaces using Po´lya polynomials

Abstract A class of polynomial curves which is a generalization of the class of “Polya curves” studied by R. Goldman [9–11] is introduced. This new scheme contains not only Bezier curves (of which Polya curves are a generalization), but also Lagrange interpolating polynomials. Motives for studying this new class of curves are recounted and then the geometric properties of these curves are investigated. Surfaces are also briefly discussed.

Identities for piecewise polynomial spaces determined by connection matrices

SummaryTwoB-spline results — Marsdens identity and the de Boor-Fix dual functionals — are extended to geometrically continuous curves determined by connection matrices.

Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices

We show that many fundamental algorithms and techniques for B-spline curves extend to geometrically continuous splines. The algorithms, which are all related to knot insertion, include recursive evaluation, differentiation, and change of basis. While the algorithms for geometrically continuous splines are not as computationally simple as those for B-spline curves, they share the same general structure. The techniques we investigate include knot insertion, dual functionals, and polar forms; these prove to be useful theoretical tools for studying geometrically continuous splines.