Ken Brodlie

Distributed and Collaborative Visualization

Visualization is a powerful tool for analyzing data and presenting results in science, engineering and medicine. This paper reviews ways in which it can be used in distributed and/or collaborative environments. Distributed visualization addresses a number of resource allocation problems, including the location of processing close to data for the minimization of data traffic. The advent of the Grid Computing paradigm and the link to Web Services provides fresh challenges and opportunities for distributed visualization—including the close coupling of simulations and visualizations in a steering environment. Recent developments in collaboration have seen the growth of specialized facilities (such as Access Grid) which have supplemented traditional desktop video conferencing using the Internet and multicast communications. Collaboration allows multiple users—possibly at remote sites—to take part in the visualization process at levels which range from the viewing of images to the shared control of the visualization methods. In this review, we present a model framework for distributed and collaborative visualization and assess a selection of visualization systems and frameworks for their use in a distributed or collaborative environment. We also discuss some examples of enabling technology and review recent work from research projects in this field.

Preserving positivity using piecewise cubic interpolation

Abstract We give a simple algorithm for generating a C 1 piecewise cubic Hermite interpolant that preserves positivity. Given two data points with positive values, and arbitrary slopes, a simple test determines whether the associated cubic Hermite interpolant is positive. If not, one or two knots are inserted so that the resulting piecewise cubic interpolant preserves positivity. Applying this in successive intervals gives an algorithm that is local in nature, and unlike other algorithms does not require modification of the slope data. The problem of positivity is extended to cover the more general constraint that the interpolant be greater than some linear function of the independent variable.

GRASPARC-A problem solving environment integrating computation and visualization

Visualization has proved an efficient tool in the understanding of large data sets in computational science and engineering. There is growing interest today in the development of problem solving environments which integrate both visualization and the computational process which generates the data. The GRASPARC project has looked at some of the issues involved in creating such an environment. An architecture is proposed in which tools for computation and visualization can be embedded in a framework which assists in the management of the problem solving process. This framework has an integral data management facility which allows an audit trail of the experiments to be recorded. This design therefore allows not only steering but also backtracking and more complicated problem solving strategies. A number of demonstrator case studies have been implemented.<<ETX>>

A Review of Uncertainty in Data Visualization

Most visualization techniques have been designed on the assumption that the data to be represented are free from uncertainty. Yet this is rarely the case. Recently the visualization community has risen to the challenge of incorporating an indication of uncertainty into visual representations, and in this article we review their work. We place the work in the context of a reference model for data visualization, that sees data pass through a pipeline of processes. This allows us to distinguish the visualization of uncertainty—which considers how we depict uncertainty specified with the data—and the uncertainty of visualization—which considers how much inaccuracy occurs as we process data through the pipeline. It has taken some time for uncertain visualization methods to be developed, and we explore why uncertainty visualization is hard—one explanation is that we typically need to find another display dimension and we may have used these up already! To organize the material we return to a typology developed by one of us in the early days of visualization, and make use of this to present a catalog of visualization techniques describing the research that has been done to extend each method to handle uncertainty. Finally we note the responsibility on us all to incorporate any known uncertainty into a visualization, so that integrity of the discipline is maintained.

Visualization in Grid Computing Environments

Grid computing provides a challenge for visualization system designers. In this research, we evolve the dataflow concept to allow parts of the visualization process to be executed remotely in a secure and seamless manner. We see dataflow at three levels: an abstract specification of the intent of the visualization; a binding of these abstract modules to a specific software system; and then a binding of software to processing and other resources. We develop an XML application capable of describing visualization at the three levels. To complement this, we have implemented an extension to a popular visualization system, IRIS Explorer, which allows modules in a dataflow pipeline to run on a set of grid resources. For computational steering applications, we have developed a library that allows a visualization system front-end to connect to a simulation running remotely on a grid resource. We demonstrate the work in two applications: the dispersion of a pollutant under different wind conditions; and the solution of a challenging numerical problem in elastohydrodynamic lubrication.

Visualization over the World Wide Web and its application to environmental data

Explores the way in which data visualization systems, in particular modular visualization environments, can be used over the World Wide Web. The conventional approach is for the publisher of the data also to be responsible for creating the visualization, and posting it as an image on the Web. This leaves the viewer in a passive role, with no opportunity to analyse the data in any way. We look at different scenarios that occur as we transfer more responsibility for the creation of the visualization to the viewer, allowing visualization to be used for analysis as well as presentation. We have implemented one particular scenario, where the publisher mounts the raw data on the Web, and the viewer accesses this data through a modular visualization environment-in this case, IRIS Explorer. The visualization system is hosted by the publisher, but its fine control is the responsibility of the viewer. The picture is returned to the viewer as VRML, for exploration via a VRML viewer such as Webspace. We have applied this to air quality data which is posted on the Web hourly: through our system, the viewer selects what data to look at (e.g. species of pollutant, location, time period) and how to look at it-at any time and from anywhere on the Web.

Preserving convexity using piecewise cubic interpolation

Abstract This paper considers the problem of drawing a smooth cubic through a set of data points (xi, yi), i = 1, 2, ..., N, where the y-values are dependent on the x-values—a common problem in scientific visualisation. A typical approach is to estimate the slope of the curve at each data point and construct a piecewise cubic interpolant which is then easy to plot. An additional requirement is often to preserve the inherent shape of the data. While monotonicity can be preserved by suitable slope selection, it is known that the same cannot be achieved in general for convexity. However, this paper shows that by allowing (if necessary) two cubic pieces in some data intervals rather than one, convexity can always be preserved. Two methods are presented and illustrated with example data.

Recent Advances in Volume Visualization

In the past few years, there have been key advances in the three main approaches to the visualization of volumetric data: isosurfacing, slicing and volume rendering, which together make up the field of volume visualization.

Gaining understanding of multivariate and multidimensional data through visualization

Abstract High dimensionality is a major challenge for data visualization. Parameter optimization problems require an understanding of the behaviour of the objective function in the n -dimensional space around the optimum—this is multidimensional visualization and is the traditional domain of scientific visualization. Large data tables require us to understand the relationship between attributes in the table—this is multivariate visualization and is an important aspect of information visualization. Common to both types of ‘high-dimensional’ visualization is a need to reduce the dimensionality for display. In this paper we present a uniform approach to the filtering of both multidimensional and multivariate data, to allow extraction of data subject to constraints on their position or value within an n -dimensional window, and on choice of dimensions for display. A simple example of understanding the trajectory of solutions from an optimization algorithm is given—this involves a combination of multidimensional and multivariate data.

Visualization of surface data to preserve positivity and other simple constraints

Abstract The presentation of 2-D data in the form of a contour map or surface view is a common operation in scientific visualization. It involves building some empirical model from the data (by means of interpolation), and then “picturing” that model. If there are inherent constraints, such as positivity for example, it is vital that these are incorporated into the model. This paper therefore addresses the problem of interpolation subject to simple linear constraints. Specifically, it looks at the problem of constructing a piecewise bicubic function u(x, y) from data on a rectangular mesh, such that u(x, y) is nonnegative (positive). Sufficient conditions for positivity are derived in terms of the first partial derivatives and mixed partial derivatives at the grid points. These conditions form the basis of a positive interpolation algorithm. The problem of positivity is generalized to the case of linearly constrained interpolation, where it is required that u(x, y) lie between bounds which are linear functions of x and y.