Geometric Folding Algorithms

Erik D. Demaine is the Esther and Harold E. Edgerton Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, where he joined the faculty in 2001. He is the recipient of several awards, including the MacArthur Fellowship, the Harold E. Edgerton Faculty Achievement Award, the Ruth and Joel Spira Award for Distinguished Teaching, and the NSERC Doctoral Prize. His research interests range throughout algorithms from data structures for improving web searches to the geometry of understanding how proteins relate to the computational difficulty of playing games. He has published more than 150 papers with more than 150 collaborators and coedited the book Tribute to a Mathemagician in honor of the influential recreational mathematician Martin Gardner. Joseph O'Rourke is the Olin Professor of Computer Science at Smith College and the Chair of the Computer Science Department. He recently completed a one-year appointment as Interim Director of Engineering. He has received several grants and awards, including a Presidential Young Investigator Award, a Guggenheim Fellowship, and the NSF Director's Award for Distinguished Teaching Scholars. His research is in the field of computational geometry, where he has published a monograph and a textbook, and he coedited the 1500-page Handbook of Discrete and Computational Geometry. Thirty-one of his more than one hundred papers published in journals and conference proceedings are coauthored with undergraduates.

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. Foundations; 12. Simple crease patterns; 13. General crease patterns; 14. Map folding; 15. Silhouettes and gift wrapping; 16. The tree method; 17. One complete straight cut; 18. Flattening polyhedra; 19. Geometric constructibility; 20. Rigid origami and curved creases; Part III. Polyhedra: 21. Introduction and overview; 22. Edge unfolding of polyhedra; 23. Reconstruction of polyhedra; 24. Shortest paths and geodesics; 25. Folding polygons to polyhedra; 26. Higher dimensions.