## REU on Geometric Visualization in Virtual Environments

The 2010 REU in Mathematics directed by Dr. George K. Francis at the University of Illinois Urbana/Champaign involves visualization of interesting topics, mathematical and otherwise, with the end result of their display in three-dimensional virtual environments such as the Cube at the Illinois Simulator Laboratory.

CubeMathematica, originally caveMathematica, is an effort to use the visualization capabilities of Wolfram Mathematica to make a simple front end for users to display geometrical objects in the Cube (and CAVE). My work this summer in this capacity involved simplifying and documenting some of the aspects of this process so as to make it more readily understandable by users familiar with Mathematica but not necessarily the workings of the Cube.

Wolfram Mathematica is publicly in its 7th edition but version 8 is coming to completion. The other students in the REU and I were given prerelease copies of Mathematica 8 Beta and told to play with the new aspects of the program, most notably the integration of parallel processing via NVIDIA graphics processing units. Due to the massive expansion of the GPU in comparison to the CPU and the logical ease of parallelizing repetitive aspects of programs, it is evident the future involves extensive use of massively parallel processing. Mathematica 8 allows the user to input a program written in CUDA C (the language used by NVIDIA GPUs) and have it execute CUDA kernals on the GPU. Much of my time this summer was spent learning how to use this functionality and in preparation of examples illustrating its many applications.

To see more about these topics and their varying successes, visit the links at left. Also present is a general idea of who I am.