Geometric Folding Algorithms: Linkages, Origami, Polyhedra

Description

Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this intriguing treatment of the geometry of folding and unfolding presents hundreds of results and over 60 unsolved ‘open problems’ to spur further research. The authors cover one-dimensional objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from students to researchers.

• Fascinating, tangible, cutting-edge research with applications throughout science and engineering

• Full color throughout

• Erik Demaine won a MacArthur fellowship in 2003 for his work on the mathematics of origami

Table of Contents

Introduction;

Part I. Linkages:

1. Problem classification and examples;

2. Upper and lower bounds;

3. Planar linkage mechanisms;

4. Rigid frameworks;

5. Reconfiguration of chains;

6. Locked chains;

7. Interlocked chains;

8. Joint-constrained motion;

9. Protein folding;

Part II. Paper:

10. Introduction;

11. One-dimensional paper;

12. Two-dimensional paper and continuous foldability;

13. Single-vertex foldability;

14. Multi-vertex flat foldability;

15. 2D Map folding;

16. Silhouettes and gift wrapping;

17. Tree method;

18. One complete straight cut;

19. Flattening polyhedra;

20. Geometric constructibility;

21. Curved and curved-fold origami;

Part III. Polyhedra:

22. Introduction and overview;

23. Edge unfolding of polyhedra;

24. Reconstruction of polyhedra;

25. Shortest paths and geodesics;

26. Folding polygons to polyhedra;

27. Higher dimensions.