This paper proposes a modification of the Marching Cubes algorithm for isosurfacing, with the intent of improving the representation of the surface in the interior of each grid cell. Our objective is to create a representation which correctly models the topology of the trilinear interpolant within the cell and which is robust under perturbations of the data and threshold value. To achieve this, we identify a small number of key points in the cell interior that are critical to the surface definition. This allows us to efficiently represent the different topologies that can occur, including the possibility of "tunnels." The representation is robust in the sense that the surface is visually continuous as the data and threshold change in value. Each interior point lies on the isosurface. Finally, a major feature of our new approach is the systematic method of triangulating the polygon in the cell interior.

Universities of Leeds, Sheffield and York http://eprints.whiterose.ac.uk/ This is an author produced version of a book chapter published in Expanding the Frontiers of Visual Analytics and Visualization.

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Visualization has proved an e ective 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.

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.