6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2010)

Prof. Erik Demaine

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Project

2010 Projects

Here is a selection of the 20 projects, and resulting publications, from 6.849 in 2010:

“2 × n Map Folding” by Eric Liu and Tom Morgan
A polynomial-time algorithm for the 2 × n special case of the venerable map-folding problem. Became Tom Morgan's MEng thesis.
“Filling a Hole in a Crease Pattern: Isometric Mapping of a Polygon given a Folding of its Boundary” by Jason Ku, published at 6OSME
Introduces and solves the “hole filling” problem: given a folding of a piece of paper's boundary, when can the interior be filled in with a valid folding?
“An Interactive Fold-and-Cut Editor” by David Benjamin and Anthony Lee
A Java implementation of the straight-skeleton method of fold-and-cut. The software and source code are available.

Requirements

The main requirement for this class, other than problem sets, is the project. The project consists of at least two components:

A paper describing what you did.
This should be a well-written document describing the problem you tackled (be it an implementation, mathematical, or artistic challenge), what approaches you took, what difficulties you encountered, and what results you found, in addition to citing the relevant literature.
Aim for on the order of 10 pages, say in the range 5–20 pages.
A presentation describing what you did (or how far you've gotten at the time of presentation).
For slides, I will assume that you will be using a data projector (showing PDF, PostScript, PowerPoint, or your own programs). You should ideally send me the files ahead of time for use on my laptop (and send a draft early for testing), but you can use your own laptop if necessary. If you need other technology, let me know. Pure blackboard presentations are discouraged except for the experienced.
The exact length is to be determined, but the presentations will be during normal lecture time.
If your project involves writing software, then you should submit the source code. If your project involves a physical object, you should show it during your presentation.

Projects can take many different forms. Here are the five main general categories:

Implement an algorithm, an illustration of a result, or a tool for experimenting with a problem.
Typically, a good format for such an implementation is a web applet (written in JavaScript, AJAX, Java, or Jython) but other environments are fine too.
Design and create a sculpture that uses ideas from this class.
Such a sculpture should be both artistically compelling and technically grounded (though the latter need not be explicitly visible). The sculpture can be physical or virtual, though in the latter case the standards will be higher because of the reduced challenge. (One way to compensate is to make several virtual sculptures, e.g., connected in a theme.) Sculpture is to be loosely interpreted, e.g., you could make several aesthetic models illustrating a particular algorithm like folding and one straight cut.
Pose an open problem (or collection of related open problems).
You might pose open problems related to another field of research with which you are familiar, or pose something that comes to you out of the lectures. Ideally you should think about solving the problem, or how it relates to other problems.
Survey a collection of 2 or 3 or more related papers.
Ideally you should avoid overlap with the textbook, Geometric Folding Algorithms: Linkages, Origami, Polyhedra.
Try to solve an open problem.
This is the most ambitious kind of project, so the expectations in terms of results are correspondingly lower. What is important is to describe a clear problem, take (at least) one good approach to that problem, and describe to what extent it worked or did not work. You should not feel pressure in terms of grades to produce results, but you should spend time thinking and trying to solve the problem. (In particular, if you succeed, you/we can write a research paper and try to publish it.) Collaboration is particularly encouraged for projects of this type, as is participation in the open-problem solving session.

No matter what you choose, project proposals must be approved by Erik. You should do this as soon as possible, and no later than Wednesday, October 27, 2010.

Deadlines

Project proposals are due Wednesday, October 27, 2010, via email to Erik.

By MIT policy, the paper is due on the last regularly scheduled lecture of this class, Wednesday, December 8, 2010. The presentation is due somewhat earlier depending on when it gets scheduled into a lecture slot; if your presentation is earlier, you are expected to have made less progress, but you should still give a clear description of the problem you are tackling and what you plan to do.

Collaboration

Collaboration is strongly encouraged, especially for research projects—this is often the key to successful research in theoretical computer science. You can work in a small group of students in the class if you find common interests. (Keep in mind that students listening to the class will have less time to devote, but they are welcome to participate in a project too.) You are also welcome to collaborate with anyone outside the class, including your research supervisor (if you have one) and including me. The only constraint for the class is that your own contribution should be substantial enough, both in terms of solving problems and writing it up. To evaluate "substantial enough", you should talk to me.

In any case, you should tell me who you are working with as the collaborations arise (i.e., before you turn in your project paper). Collaborations should also be clearly marked on the paper and presentation slides.