For almost as long as there have been computers, people have tried out ways of creating origami—or at least, folded paper shapes—using computational techniques. Once they began developing computational tools for folding, there arose the supporting field of computational origami: the study of mathematical laws and data structures that apply to the intersection of computing and folding.
Computational origami is a subset of the branch of computer science known as computational geometry; many of the algorithms of the former have broader applicability in the latter. We see, for example, the straight skeleton appearing in problems as diverse as the design of origami insects and the design of pitched roofs on buildings!
The practical realization of computational origami theory and algorithms are tools—computer programs—that carry out origami design and computations. In this section I present several computational investigations of my own.
- Origami Simulation
An early attempt to create an interactive folding simulator, I wrote this in Object Pascal for the early Macintosh computer.
TreeMaker was, I believe, the first practical tool for origami design that could outperform a human (albeit within a very narrow class of structures). While I have only used it for a handful of origami designs, writing it and exercising its capabilities led me to most of the current theory of uniaxial bases.
ReferenceFinder is a very simple tool for a single purpose: finding good, short, accurate approximations (or exact sequences) to fold a given point or line. ReferenceFinder solves a problem that didn't exist before algorithmic design techniques, and is a real-life, practical application of the Huzita-Justin Axioms.
This article describes an investigation into a particular class of modular origami polyhedra. Along the way, I found the first complete enumeration of the class of uniform-edge "orderly tangles," or, as I called them, polypolyhedra.
This article provides a download link for a Mathematica notebook that is a very large package of functions and routines for the creation, analysis, and visualization of origami tessellations (and mathematical origami in general). You'll need to own Mathematica in order to use it.
Since the turn of the millenium, the field of computational origami has exploded, and there are many more computational tools and theoretical explorations in the field. Check out my of scientific/mathematical links for many of the latest developments.