Circle packing for origami design is hard

Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education

Volumn , Issue , 2016, Pages 609-626

  Demaine, Erik D ^a   Fekete, Sándor P ^b   Lang, Robert J ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^c NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85011398932     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (15)

1. Marshall Bern and Barry Hayes. "On the Complexity of Flat Origami." In Proceedings of the 7th ACM-SIAM Symposium on Discrete Algorithms, pp. 175-183. New York: ACM Press, 1996.
2. Erik Demaine and Sándor P. Fekete. "Worst-Case Bounds for Dense Packings." Manuscript, 2011.
3. 4: Fourth International Meeting of Origami Science, Mathematics, and Education, edited by Robert J. Lang, pp. 259-272. Wellesley, MA: A K Peters, 2009.
4. Erik D. Demaine, Joseph S.B. Mitchell, and Joseph O'Rourke. "The Open Problems Project." Availalbe at http://cs.smith. edu/~orourke/TOPP/Welcome.html, 2004.
5. Jon H. Folkman and Ronald L. Graham. "A Packing Inequality for Compact Convex Subsets of the Plane." Canadian Mathematics Bulletin 12 (1969), 745-752.
6. Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W. H. Freeman, 1979.
7. Robert J. Lang. "Mathematical Algorithms for Origami Design." Symmetry: Culture and Science 5:2 (1994), 115-152.
8. Robert J. Lang. "A Computational Algorithm for Origami Design." In Proceedings of the Twelfth Annual Symposium on Computational Geometry, pp. 98-105. New York: ACM Press, 1996.
9. Robert J. Lang. "The Tree Method of Origami Design." In Origami Science and Art: Proceedings of the Second International Meeting of Origami Science and Scientific Origami, edited by Koryo Miura, pp. 73-82. Shiga, Japan: Seian University of Art and Design, 1997.
10. Robert J. Lang. Origami Design Secrets: Mathematical Methods for an Ancient Art. Natick, MA: A K Peters, 2003.
11. Joseph Y.-T. Leung, Tommy W. Tam, C. S. Wing, Gilbert H. Young, and Francis Y.L. Chin. "Packing Squares into a Square." J. Parallel Distrib. Comput. 10:3 (1990), 271-275.
12. Toshiyuki Meguro. "Jitsuyou Origami Sekkeihou (Practical Methods of Origami Designs)." Origami Tanteidan Shinbun 2 (1991-1992), 7-14.
13. Toshiyuki Meguro. "Tobu Kuwagatamushi-to Ryoikienbunshiho (Flying Stag Beetle and the Circular Area Molecule Method)." In Oru, pp. 92-95. Tokyo: Sojusha, 1994.
14. Eckard Specht. "The Best Known Packings of Equal Circles in a Square." Available at http://hydra.nat.uni-magdeburg.de/packing/csq/csq. html, 2010.
15. 4: Fourth International Meeting of Origami Science, Mathematics, and Education, edited by Robert J. Lang, pp. 259-272. Wellesley, MA: A K Peters, 2009.