My name is Mimi Tsuruga. I am an undergraduate student at Hunter College of the City University of New York. I am part of the National Science Foundation's (NSF) Research Experience for Undergraduates (REU) at the University of Illinois in Urbana-Champaign (UIUC) for the summer season in 2006. The program's title is "Geometric Visualizations".
Our goal was to create a portage between Syzygy and Mathematica. This portage translates code written in Mathematica to a working Syzygy application. We use a future version of Mathematica's Kernel in the distributed graphics system Syzygy. The new adaptive mesh feature is suitable for animating classic homotopies, like the Morin-Apery sphere eversions, and Dalbec's contraction of Zeeman's Duncehat, in cluster based virtual environments such as the CUBE, CAVE and CANVAS at UIUC.
We started by rendering the homotopies in Mathematica. The Apéry's RomBoy homotopy is quite famous. Some years ago, Donna Cox created an artistic variation on this homotopy creating the Etruscan Venus and Ida. Here we have the Venus to Boy Surface homotopy. A still image of Duncehat is available. Gastrula requires further tweaking and the animations for both are currently under construction.
A Mathematica-Python interface called PYML was developed some years ago which was formatted for Mathematica 3.0 and an old version of Python. Mathematica has changed significantly since the earlier version requiring us to make major modifications to the PYML code. Making these necessary changes requires significant expertise in the C language and Python language, and a thorough understanding of Mathlink. Moreover, our attempts to use the new Mathematica functions were unsuccessful. We tried to use Manipulate which allows the user to "manipulate" the parameters to render real-time images. The complicated surface rendering for complicated surfaces, such as those in our homotopies, causes tremendous lag on the beta version and is unsuitable for adaptation into Syzygy. Animate runs faster than Manipulate, but it will only animate the change to one parameter, which will not be a problem for Gastrula and Duncehat, but the surfaces the latter are more complicated, again creating lag. We have also experimented by storing a succession of single frames and running them on ListAnimate, however, the function is unable to render the images quickly enough to reach animation quality.
An endeavor to create this Mathematica portage for Python in such a short time is impossible and it seems that real-time calculations in the Mathematica kernel will take too much time. A more realistic goal for this project is to put animated VRMLs into the CUBE, which has never been done yet. Still VRML images have been in the CUBE and CAVE. The VRML files are created by Mathematica via an Export function which Syzygy reads to place those images into the CUBE. We will animate the homotopies using a prerendered succession of homotopies.
My associated mentor is Ulises Cervantes at Wolfram Research. This project is an extension of on-going projects by Professor George Francis at UIUC.
The above title is the Japanese word for Syzygy, which is a kind of unity, especially through coordination or alignment, most commonly used in the astronomical sense. Since we are working on a portage for Syzygy, and because I am Japanese-American, this name was chosen for the project.