34
Views
1
CrossRef citations to date
0
Altmetric
Section A

An improved implementation and analysis of the Diaz and O'Rourke algorithm for finding the Simpson point of a convex polygon

&
Pages 244-259 | Received 29 Dec 2006, Accepted 23 Jan 2008, Published online: 04 Aug 2009

References

  • Brass , P. , Heinrich-Litan , L. and Morin , P. 2003 . Computing the center of area of a convex polygon . Internat. J. Comput. Geom. Appl. , 13 : 439 – 445 .
  • Carrizosa , E. , Conde , E. , Munoz-Marquez , M. and Puerto , J. 1997 . Simpson points in planar problems with locational constraints: the round-norm case . Math. Oper. Res. , 22 ( 2 ) : 276 – 290 .
  • Carrizosa , E. J. , Conde , E. , Munoz-Marquez , M. and Puerto , J. 1997 . Simpson points in planar problems with locational constraints: the polyhedral-gauge case . Math. Oper. Res. , 22 ( 2 ) : 291 – 300 .
  • Diaz , M. and O'Rourke , J. 1994 . Algorithms for computing the center of area of a convex polygon . Visual Comput. , 10 : 432 – 442 .
  • Drezner , Z. 1982 . Competitive location strategies for two facilities . Regional Sci. Urban Econ. , 12 : 485 – 493 .
  • Drezner , T. 1995 . Facility Location: A Survey of Applications and Methods , Edited by: Drezner , Z. New York, Inc : Springer-Verlag .
  • Drezner , Z. and Zemel , E. 1992 . Competitive location in the plane . Ann. Oper. Res. , 40 ( 1 ) : 173 – 190 .
  • Durier , R. 1989 . Continuous location theory under majority rule . Math. Oper. Res. , 14 ( 2 ) : 258 – 274 .
  • Eiselt , H. A. and Laporte , G. 1997 . Sequential location problems . Eur. J. Oper. Res. , 96 ( 2 ) : 217 – 231 .
  • Grünbaum , B. 1960 . Partitions of mass distributions and of convex bodies by hyperplanes . Pacific J. Math. , 10 : 1257 – 1261 .
  • Grünbaum , B. 1963 . “ Measures of symmetry for convex sets ” . In Pro. Symposia in Pure Math.: Convexity , Edited by: Klee , V. Vol. 7 , 223 – 270 . RI : American Mathematical Society, Providence .
  • Hakimi , S. L. 1990 . “ Locations with spatial interaction: competitive locations and games ” . In Discrete Location Theory , Edited by: Mirchandani , P. B. and Francis , R. L. New York : John Wiley & Sons .
  • Hammer , P. C. 1960 . Volumes cut form convex bodies by planes , unpublished, made available by T.J. Smith, Department of Mathematics, University of Michigan, Kalamazoo
  • Hansen , P. and Labbé , M. 1988 . Algorithms for voting and competitive location on a network . Transport. Sci. , 27 ( 4 ) : 278 – 288 .
  • Hogatt , V. E. Jr. 1962 . forbidden area . The American Monthly Journal , 62 ( 2 ) : 98 – 104 .
  • Hotelling , H. 1929 . Stability in competition . Econ. J. , 39 : 41 – 57 .
  • Langerman , S. and Steiger , W. Optimization in arrangements . Proceedings of the 20th International Symposium on Theoretical Aspects of Computer Science . Berlin, Germany.
  • Michelot , C. 1993 . The mathematics of continuous location . Stud. Locat. Anal. , (5) : 59 – 83 .
  • Plastria , F. 2001 . Static competitive facility location: an overview of optimisation approaches . Eur. J. Oper. Res. , 129 ( 3 ) : 461 – 470 .
  • Preparata , F. P. and Shamos , M. I. 1985 . Computational Geometry: An Introduction , New York, Inc : Springer Verlag .
  • Simpson , P. 1969 . On defining areas of voter choice: Professor Tullock on stable voting . Quart. J. Econ. , 83 : 478 – 487 .
  • Singmaster , D. S. and Singmaster , G. 1967 . Forbidden regions are convex . Am. Math. Monthly , 74 : 184 – 186 .
  • Tovey , C. A. 1993 . “ Some foundations for empirical study in the Euclidean spatial model of social choice, Ch. 7 ” . In Political Economy: Institutions, Competition, and Representation , Edited by: William , Barnett , Hinich , Melvin and Norman , Schofield . 175 – 194 . New York : Cambridge University Press .
  • Yaglom , I. M. and Boltyanskii , V. G. 1961 . Convex figures, Library of the Mathematical Circle , Vol. 4 , New York, NY : Holt Rinehart and Winston . (Translated by Paul Kelly and Lewis Walton)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.