Thursday, September 18, 2008

Movie of a Groebner fan

This summer I spent some time thinking about animation and visualizing algebraic and geometric information. I have a longer to-do list than accomplishments but I have made some progress.

One of pilot project ideas was to take a 5-variable polynomial ideal and:
1) compute the Groebner fan using Sage and Gfan,
2) intersect it with a hyperplane (so now we're down to 4 dimensions)
3) slowly rotate the resulting polyhedral complex in 4 dimensions, rendering it using Tachyon/Sage
4) animate the resulting set of frames.

For step 4, I initially wanted to use Blender, but that was really overkill for what I needed and I didn't want to figure out how to get Sage and Blender using the same copy of Python (although someone should). In the end I used ffmpeg to get my movie.

Check out my current best effort.

My next goal in this direction is to do something with Sage's @interact command and JMol to highlight pieces of the fan, since the movie isn't really informative (more art than math I think).

1 comment:

Anonymous said...

Sweet, brometheus! Now go and make a Wikipedia page for the proles to appreciate this snazziness.