Folding and unfolding in computational geometry

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1763, Issue , 2000, Pages 258-266

  O’Rourke, Joseph ^a  

^a SMITH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

CONVEX POLYHEDRONS; FOLDING AND UNFOLDING; NONOVERLAPPING; POLYGONAL CHAINS;

COMPUTATIONAL GEOMETRY;

EID: 84947770218     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-46515-7_22     Document Type: Conference Paper

References (31)

1. P. K. Agarwal, B. Aronov, J. O’Rourke, and C. A. Schevon. Star unfolding of a polytope with applications. SIAM J. Comput., 26:1689-1713, 1997.
2. A. D. Alexandrov. Konvexe Polyeder. Akademie-Verlag, Berlin, West Germany, 1958.
3. B. Aronov and J. O’Rourke. Non-overlap of the star unfolding. Discrete Comput. Geom., 8:219-250, 1992.
4. T. Biedl, E. Demaine, M. Demaine, A. Lubiw, J. O’Rourke, M. Overmars, S. Robbins, I. Streinu, and S. Whitesides. On reconfiguring tree linkages: Trees can lock. In Proc. 10th Canad. Conf. Comput. Geom., pages 45, 1998. Fuller version in Electronic Proc. http://cgm.cs.mcgill.ca/cccg98/proceedings/.
5. T. Biedl, E. Demaine, M. Demaine, A. Lubiw, J. O’Rourke, M. Overmars, S. Robbins, and S. Whitesides. Unfolding some classes of orthogonal polyhedra. In Proc. 10th Canad. Conf. Comput. Geom., pages 7071, 1998. Fuller version in Electronic Proc. http://cgm.cs.mcgill.ca/cccg98/proceedings/.
6. T. Biedl, E. Demaine, M. Demaine, S. Lazard, A. Lubiw, J. O’Rourke, M. Overmars, S. Robbins, I. Streinu, G. Toussaint, and S. Whitesides. Locked and unlocked polygonal chains in 3D. In Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, pages 866-867, January 1999.
7. M. Bern, E. Demaine, D. Eppstein, and E. Kuo. Ununfoldable polyhedra. In Proc. 11th Canad. Conf. Comput. Geom., pages 13-16, 1999. Full version: LANL archive paper number cs. CG/9908003.
8. T. C. Biedl, E. Demaine, S. Lazard, S. Robbins, and M. Soss. Convexifying monotone polygons. Technical Report CS-99-03, Univ. Waterloo, Ontario, 1999.
9. J. Chen and Y. Han. Shortest paths on a polyhedron. Internat. J. Comput. Geom. Appl., 6:127-144, 1996.
10. J. Cantarella and H. Johnston. Nontrivial embeddings of polygonal intervals and unknots in 3-space. J. Knot Theory Ramifications, 7:1027-1039, 1998.
11. R. Cocan and J. O’Rourke. Polygonal chains cannot lock in 4D. Technical Report 063, Smith College, Northampton, MA, July 1999. Full version of proceedings abstract. LANL archive paper number cs. CG/9908005.
12. R. Cocan and J. O’Rourke. Polygonal chains cannot lock in 4D. In Proc. 11th Canad. Conf. Comput. Geom., pages 5-8, 1999.
13. P. Cromwell. Polyhedra. Cambridge University Press, 1997.
14. E. Demaine, M. Demaine, A. Lubiw, J. O’Rourke, and I. Pashchenko. Metamorphosis of the cube. In Proc. 15th. Annu. ACM Sympos. Comput. Geom., pages 409-410, 1999. Video and abstract.
15. E. Demaine, M. Demaine, A. Lubiw, and J. O’Rourke. Folding polygons: The decision question. Work in progress, 1999.
16. B. de, Sz. Nagy. Solution to problem 3763. Amer. Math. Monthly, 46:176-177, 1939.
17. A. Dürer. The painter’s manual: a manual of measurement of lines, areas, and solids by means of compass and ruler assembled by Albrecht Dürer for the use of all lovers of art with appropriate illustrations arranged to be printed in the year MDXXV. New York: Abaris Books, 1977, 1538. Translated and with a commentary by Walter L. Strauss.
18. H. Everett, S. Lazard, S. Robbins, H. Schröder, and S. Whitesides. Convex- ifying star-shaped polygons. In Proc. 10th Canad. Conf. Comput. Geom., pages 2-3, 1998.
19. R Erdôs. Problem 3763. Amer. Math. Monthly, 42:627, 1935.
20. S. K. Gupta, D. A. Bourne, K. H. Kim, and S. S. Krishnan. Automated process planning for sheet metal bending operations. J. Manufacturing Systems, 17(5):338-360, 1998.
21. Grünbaum. How to convexify a polygon. Geombinatorics, 5:24-30, July 1995.
22. A. Lubiw and J. O’Rourke. When can a polygon fold to a polytope? Technical Report 048, Dept. Comput. Sei., Smith College, June 1996. Presented at AMS Conf., 5 Oct. 1996.
23. W. J. Lenhart and S. H. Whitesides. Reconfiguring closed polygonal chains in Euclidean d-space. Discrete Comput. Geom., 13:123-140, 1995.
24. J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647-668, 1987.
25. M. Namiki and K. Fukuda. Unfolding 3-dimensional convex polytopes: A package for Mathematica 1.2 or 2.0. Mathematica Notebook, Univ. of Tokyo, 1993.
26. Schevon. Algorithms for geodesics on polytopes. PhD thesis, Johns Hopkins University, 1989.
27. G. C. Shephard. Convex polytopes with convex nets. Math. Proc. Camb. Phil. Soc., 78:389-403, 1975.
28. C. Schevon and J. O’Rourke. A conjecture on random unfoldings. Technical Report JHU-87/20, Johns Hopkins Univ., Baltimore, MD, July 1987.
29. M. Sharir and A. Schorr. On shortest paths in polyhedral spaces. SIAM J. Comput., 15:193-215, 1986.
30. G. T. Toussaint. The Erdös-Nagy theorem and its ramifications. In Proc. 11th Canad. Conf. Comput. Geom., pages 9-12, 1999. Puller version in Electronic Proc. http://www.cs.ubc.ca/conferences/CCCG/elecproc.html.
31. C.-H. Wang. Manufacturability-driven decomposition of sheet metal products. PhD thesis, Carnegie Mellon University, The Robotics Institute, 1997.