First and foremost, this webpage is an assignment I did as an undergraduate at McGill University. It was presented to Stefan Langerman on December 2^nd, 2002, for the COMP 507 course.

It also is intended to be a resource to internet surfers, and an anchor in time where I can come to see what was on my mind back in the old days.

That is a long story, most of which I do not remember myself. I became interested in origami for the sake of paperfolding sometime around my acceptance at McGill University. When I took the Computational Geometry course, an occasion presented itself to me: Explore origami with a perspective I had never thought of before, mathematics and computer science.

So I decided to use the, unfortunately small, corpus of knowledge in Mathematical Origami to build an Origami Computational Model of my own.

But this explanation belittles the Origami Computational Model to a freak historical accident, and does not give good reasons for you, my reader, to explore origami beyond the art of paperfolding that it is. In order to convince you there is a point, here are some reasons that have been used to explore mathematical origami, which will serve as a basis for Computational Origami:

Teaching purposes, for the visually impaired

Humiaki Huzita, the man who first published the 6 axioms as I describe them here, was attempting to teach geometry to blind people. Origami, because of its more manual approach, does not depend on visual skills as much as Euclid's Edge & Compass constructions on a sheet of paper. A blind person can feel the features of sheet, instead of having to read them.

Exploration of Computational Models

While I am still tooting my own horn here, the study of computational models is a fundamental study of computer science. A great many questions have not yet been resolved about the RAM model (the one that best fits commercially available computers), like the P = NP question. A study of many computational models might provide the clues required to solve those questions.

Map, solar sails, and parachute folding

Most of us fold maps on a trip, and Mathematical and Computational Origami provides the framework required to understand why the dang thing never folds right. But even more important to some people is the folding of solar sails for satellites and parachutes for parachutists. In the latter case, someone's life is on the line. Origami is the framework that studies good and bad foldings, and understands how to prevent bad ones.

The axioms of Origami

Those are described at maths.html. The page goes thru each and gives the equations for most (in std form) resulting folds, and figures of their meanings.

Computational Model

This part, at computational.html describes the model proper, and describes in high-level terms the whole idea behind the model.

History of Origami

I've put a smallish history available at history.html. It links to much better history webpages online.

Links & files & bibliography

I placed all files I could muster at files.html and all links I could find at links.html for you to browse. Finally, a list of papers I read for the project is available at bibliography.html.