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Projects in Computational Mathematics

UIMATH.grafiXlab, Summer 1997

Watch this site for abstracts and reports. In the meantime, have a look at what we proposed to do last summer. Some of it even got done. Here is an index of projects that are getting underway this summer. They are listed, last born first, by nickname and developer(s).

illiMBone ... Ulises Cervantes, John Estabrook, Matthew Stiak

In this first, exploratory phase of a larger project we have enabled the grafiXlab to multicast over 3 systems: the SGI Impact, the Pentium Linux box, and a WindowsNT box. We are developing the ability to originate broadcasts over Vosaic and multicasts over the MBone. We will soon join the MSRI MBone project to promote real-time electronic communication in mathematics.

CAVEgladiator... Kevin Vlack, UIUC; Alex Francis, U.Chicago; Umesh Thakkar, NCSA

This is an illiShell94 derived CAVE action game with physics based ballistics, collisions and wave motions. Action is controlled by intuitively obvious wand gestures. We shall use it for controlled experiments to determine the relative importance of head-tracking and stere-opsis in immersive virtual enviroments. In a multifactorial block design we will test naive subjects in each of the four modes and record their scores in this fast paced, highly entertaining but difficult CAVE game developed for Math 198 by Kevin Vlack. Cognitive scientist, Alex Francis at the University of Chicago will consult on the statistical design and evaluation.

graviLens ... Birgit Bluemer, John Estabrook; Bob Patterson, Bill Sherman, NCSA

This real-time, interactive CAVE animation simulates the relativistic distortion of space in the presence of a gravitational lens of variable mass. Each vertex of the displayed scene is processed depending on the position of the head and an object with variable mass. Thus the load on the display resources is proportional to the complexity of the scene displayed, but not, for instance, on the speed of navigation. We are currently installing this project in the Marcus Thiebaux's Virtual Director and illiConnecting it to the mutliprocessor Onyxes.

illiConnect ... John Estabrook; Alex Bourd, Qualcomm.

The goal of this project is to develop the prototype of a distributed interactive VR application that takes advantage of SGI parallel hardware. We are primarily interested in real-time, interactive simulations of scientific processes which require substantial computation and are displayed in immersive virtual environments (IVEs) such as the CAVE, Immersadesk, and the Infinity Wall. Currently, most such simulations run as batch jobs and dump results into files, from which VR-viewers then read to create virtual scenes. One is unable to see the simulation in progress---consequently, time is wasted waiting to view calculations that may, in fact, have continued in an undesirable direction. With illiConnect, research and development teams will greatly benefit from not only observing the progress of the process in real-time, but also from the abilty to steer the simulation in the desired direction.

illiVert ... Chris Hartman, John Sullivan

Continuation of the Minimax Sphere Eversion project. It will be adapted to produce a high quality videotape for the International Congress of Mathematics, Berlin 1998. It will also be prepared to go real-time over StarTap from NCSA to Potsdam, Germany, August 1998.

philEver ... Matthew Stiak, Chris Hartman

We have created an OpenGL/Xlib GUI which is compatible with the original (1993) RTICA, illiLevel. This tool uses interpolating piece-wise cubic splines to sew a two-way collection of level lines of a surface homotopy along the levels (smoothing a polygon), across levels (rendering a smoothed surface), and through time (homotopy.) The goal of this effort is a real-time interactive computer animation of Tony Phillips' handrawn sphere eversion in a Scientific American cover story in the 60's. This article inspired the physicist Bryce DeWitt to design an alternative, arguably simpler homotopy, which could be an eversion too. We expect to use the CAVE wholly immersive virtual environment to decide the validity of this 30 year old conjecture.

churfStory ... Chris Hartman

The locus along which an surface, immersed in 3-space, intersects itself is called its double locus. Typically, this is a set of double curves passing through the triple points. A regular homotopy of the surface produces a homotopy of the double locus. Generically, this succession of curves may be considered the level sets of a 2-D surface in 4-space as a 3-D hyperplane slices through it. In this project we visualize this surface. The details are accumulating here.

walkAbout ... Ulrike Axen

The Post-Euclidean Walkabout is a real-time interactive CAVE application which takes you on a visit to the post-Euclidean geometry of Gauss, Riemann, Klein, Poincare, and Thurston. Ever since its premiere in the Virtual Reality Room at SIGGRAPH94 this has been the perennial favorite to hundreds of CAVE visitors at VROOM, NCSA, EVL and elsewhere. We have rewritten the code in OpenGL and restored the extensive audification to recompile and run with the Virtual Sound Server 2.3 in the current environment (12 R10000 CPU, 2 IR SGI Onyx CAVE.)

illiWeb .. illiGallery .. illiMuseum ... illiStaff

In this shared effort, all three involve taking an electronic image from a third party rtica and displaying it inside a collection, on the Web, in an advanced CAVEshell, and in print medium (cibachrome print mounted in model case or on wall.) Since in each case there will be some documentation, the web form is them most extensible, the museum the most static and the gallery the most abbreviated.