On Rigid Origami I: Piecewise-planar Paper with Straight-line Creases

TL;DR

This paper develops a theoretical framework for rigid origami with piecewise-planar paper and straight-line creases, connecting it to rigidity theory, graph theory, and computational methods to analyze configuration spaces.

Contribution

It introduces formal definitions and analytical tools to describe the configuration space of rigid origami, bridging it with established mathematical theories.

Findings

Configuration space shape and connectedness analyzed

Algebraic, geometric, and numeric methods reviewed

Framework connects rigid origami with rigidity and graph theories

Abstract

We develop a theoretical framework for rigid origami, and show how this framework can be used to connect rigid origami and results from cognate areas, such as the rigidity theory, graph theory, linkage folding and computer science. First, we give definitions on important concepts in rigid origami, then focus on how to describe the configuration space of a creased paper. The shape and 0-connectedness of the configuration space are analyzed using algebraic, geometric and numeric methods, where the key results from each method are gathered and reviewed.