An example applet. Some possible topics:

- An applet showing the running of the "merge-sort" type of convex hull construction algorithm. (The applet should show every edge that is tested as the algorithm runs, including, for example, which edges are tested when finding the common lower tangent of two sub hulls).
- An applet showing Kirkpatrick's triangular decomposition data structure for point location (from lecture 13). (The applet should have a side by side picture. On the right, the "decomposition tree", whose root node represent the whole enclosing triangle, and on the left, the original set of points, and the set of triangles which the query point is being tested against).
- Algorithm showing randomized incremental construction of trapezoidal map, with, and the search structure that is built up along with it. Could include statistics of "if you inserted the segments in lots of random orders, what is the distribution of the longest search path in the search structure?".

Some possible topics:

- Can you find a point set where you can add a point and make the total weight of the min-weight triangulation (MWT) smaller? (answer, yes!). Can you find a point set where you can add 2 points and make the weight decrease each time? Can you find a point set of n-points where you can add n additional points, and with each point reduce the weight of the MWT? Can you find a point set where you can keep adding point and keep reducing the weight of the MWT every time? Alternatively, can you prove no such example exists? [Problem suggested by Joe Mitchell, from SUNY Stony Brook].
- Any unsolved problem from the Open Problems Project.

- Names of people in your group
- A specific description of the problem that you are trying to
solve,
**in two sentences or less**. This may be an answer to a question like: What does your applet do? What is your visualization trying to show? What open problem were you trying to address? - If you are doing a pedagogical applet
- Background information about the problem and approach. Does not need to be long (one or two paragraphs is ok), but state any assumptions that are necessary for your applet/approach to work (e.g. general position, no more than 10 points, etc.)
- describe the pseudo-code of the algorithm that you are creating,
- highlight what parts of that pseudocode you are animating.
- Discuss any interesting choices that you made in the implementation of the algorithm.

- If you are working on an open research problem.
- Background information about the problem. What is the current best known algorithm? What are the proven theoretical bounds on the problem?
- What approaches have you tried? Can you visualize the results? Show sketches of where proof attempts have failed, or example point sets where your (mostly good) algorithm has a bad case? [I understand that what is appropriate depends heavily on what you tried and what your problem is].

- If you have an application domain problem:
- Background information, what are your specific inputs and outputs (show a visualization, if possible). What are the needs for the problem domain -- is it important that you find the optimal solution? why or why not?
- What are the most related projects that others have built?
- Describe your algorithm and show example results. Give a complexity analysis of your algorithm, and also show measured running time for different sizes of inputs