This is an informal description of my current geometric research interests.

The aspect of the Venn triangle problem which I found most interesting was that of turning the abstract lines into actual straight lines in the plane. This is the problem of straightening of pseudolines.

When I created my system and when I wrote the technical reports on this topic I was unaware of the prior work. As far as I can tell, my approach is quite distinctive with its emphasis on polar and trilinear coordinates.

Currently I am reading up on pseudolines and oriented matroids, with the hope that I may be able to combine some of the already established ideas with my own work. Areas of interest include:

• Pseudoline stretching algorithms.
• Polar coordinates and oriented matroids.
• The convexity of Venn diagrams and stretchability.
(Why were all 126 pseudoline solutions of the 6-Venn triangle problem stretchable?)

References

Bjorner, Las Vergnas, Sturmfels, White, Zeigler, 1999

Oriented Matroids, second edition

Bokowski, Sturmfels, 1989

Computational Synthetic Geometry

Grunbaum, 1989

Arrangements and spreads