Global rigidity: The effect of coning

Discrete and Computational Geometry

Volumn 43, Issue 4, 2010, Pages 717-735

  Connelly, R ^a   Whiteley, W J ^b  

^a Department of Obstetrics Gynecology   (United States)

^b YORK UNIVERSITY   (Canada)

Author keywords

Coning; Global rigidity; Infinitesimal rigidity; Projective geometry; Self stress; Spherical geometry

Indexed keywords

EID: 77952010383     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-009-9220-0     Document Type: Article

References (23)

1. Anderson, B. D. O., Belhumeur, P., Eren, T., Goldenberg, D., Morse, A. S., Whiteley, W., Yang, Y.: Graphical properties of easily localizable sensor networks. Wirel. Netw. 15(2), 177-191 (2009).
2. Bolker, E. D., Roth, B.: When is a bipartite graph a rigid framework? Pac. J. Math. 90(1), 27-44 (1980).
3. Berg, A., Jordán, T.: A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid. J. Comb. Theory, Ser. B 88, 77-97 (2003).
4. Cheung, M., Whiteley, W.: Transfer of global rigidity results among dimensions: graph powers and coning. Preprint, York University, Revised 2008.
5. Connelly, R.: Rigidity and energy. Invent. Math. 66(1), 11-33 (1982).
6. Connelly, R.: On generic global rigidity. In: Applied Geometry and Discrete Mathematics. DIMACS Ser. Discrete Math, Theoret. Comput. Sci., vol. 4, pp. 147-155. AMS, Providence (1991).
7. Connelly, R.: Generic global rigidity. Discrete Comput. Geometry 33, 549-563 (2005).
8. Connelly, R., Jordán, T., Whiteley, W.: Generic global rigidity of body bar frameworks. Preprint (2009).
9. Eren, T., Goldenberg, D., Whiteley, W., Morse, A., Anderson, B. D. O., Belhumeur, P.: Rigidity, computation, and randomization in network localization. In: Proceedings of the International Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), Hong Kong, March 2004, pp. 2673-2684.
10. Gortler, S., Healy, A., Thurston, D.: Characterizing generic global rigidity. arXiv: 0710. 0907v1 (2007).
11. Graver, J.: Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures. Dolciani Mathematical Expositions, vol. 25. The Mathematical Association of America, Washington (2001).
12. Hendrickson, B.: Conditions for unique graph realizations. SIAM J. Comput. 21, 65-84 (1992).
13. Jackson, B., Jordán, T.: Connected rigidity matroids and unique realization graphs. J. Comb. Theory B 94, 1-29 (2005).
14. Jackson, B., Jordán, T., Szabadka, Z.: Globally linked pairs of vertices in equivalent realizations of graphs. Discrete Comput. Geom. 35(3), 493-512 (2006).
15. Jordán, T., Szabadka, Z.: Operations preserving the global rigidity of graphs and frameworks in the plane. Comput. Geom. 42(6-7), 511-521 (2009).
16. Pogorelov, A. V.: A Study of Surfaces in an Elliptic Space, (English Translation of the Russian Title "Nekotorye Voprosy Teorii Poverkhnostei") Hindustan Publishing Corporation (India) 6-U. B., Jawahar Nagar, DELHI-6 (1964).
17. Saliola, F., Whiteley, W.: Some notes on the equivalence of first-order rigidity in various geometries. Preprint Department of Mathematics, York University (2002).
18. Saliola, F., Whiteley, W.: Averaging and equivalent frameworks: transfer among various geometries. Draft, Department of Mathematics, York University (2005).
19. Tay, T.-S., Whiteley, W.: Generating isostatic frameworks. Structural Topology 11, 20-69 (1985).
20. Whiteley, W.: Cones, infinity and one-story buildings. Struct. Topol. 8, 53-70 (1983).
21. Whiteley, W.: Vertex splitting in isostatic frameworks. Struct. Topol. 16, 23-30 (1991).
22. Whiteley, W.: Matroids from discrete geometry, In: Bonin, J. E., Oxley, J. G., Servatius, B. (eds.) Matroid Theory. American Mathematical Society, Contemporary Mathematics, vol. 197, pp. 171-313 (1996).
23. Whiteley, W.: Rigidity and Scene Analysis, In: Goodman, J., O'Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, 2nd edn., pp. 1327-1354 (2004).