# Discrete and Computational Geometry Projects

At Harvey Mudd, I'm taking a cool class called "Discrete and Computational Geometry", a special topics course taught by Professor Satyan Devadoss. It's a very interesting class. In lieu of normal problem sets, we instead do a bunch of group projects, each one very freeform. The basic instructions are "go make something related to this class". Here are a couple of the projects my group made:

### Interactive Art Gallery

This project was about the Art Gallery problem, which asks what is the fewest number of guards that can guard a polygonal art gallery. We built a visualization to allow you to construct a polygon and place guards. It also computes a lower bound solution, which is guaranteed to have floor(n/3) guards for a polygon with n vertices. You can see it here.

### Associahedron

This project is a visualization of an associahedron, a polyhedron that corresponds to the triangulations of a polygon. There's some crazy math about associahedrons, and one cool property is that computing "area vectors" of a triangulated hexagon creates a geometric 3d associahedron that deforms continuously. Check it out here. (Update: Or read the multimedia exposition paper here for more details on what it happening.)

### Fold and Cut

Finally, the Fold and Cut theorem states that any shape with straight sides can be cut out by folding a sheet of paper and then making a single cut. This was proved by Erik Demaine et al., and we implemented Demaine's construction to show how to fold and cut an arbitrary closed polygon. Try it out here.