Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets

Computational Geometry: Theory and Applications

Volumn 33, Issue 3, 2006, Pages 152-164

  Ahn, Hee Kap ^a   Brass, Peter ^b   Cheong, Otfried ^a   Na, Hyeon Suk ^c   Shin, Chan Su ^d   Vigneron, Antoine ^e  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b City College of the City University of New York   (United States)

^c Soongsil University   (South Korea)

^d Hankuk University of Foreign Studies   (South Korea)

^e NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Approximation; Axial symmetry; Shape matching

Indexed keywords

EID: 84867925351     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2005.06.001     Document Type: Article

References (23)

1. P.K. Agarwal, S. Har-Peled, and K.R. Varadarajan Approximating extent measures of points J. ACM 51 2004 606 635
2. H. Alt, J. Blömer, M. Godau, and H. Wagener Approximation of convex polygons Proc. 17th Internat. Colloq. Automata Lang. Program. Lecture Notes Comput. Sci. vol. 443 1990 Springer Berlin 703 716
3. D. Avis, P. Bose, G. Toussaint, T. Shermer, B. Zhu, J. Snoeyink, On the sectional area of convex polytopes, in: Proc. 12th ACM Symp. Comput. Geometry, 1996, pp. 411-412
4. G. Barequet, V. Rogol, Maximizing the area of an axially-symmetric polygon inscribed by a simple polygon, in: Proc. 16th Canadian Conf. on Computational Geometry, Montréal, Québec, Canada, 2004, pp. 128-131
5. M. de Berg, O. Devillers, M. van Kreveld, O. Schwarzkopf, and M. Teillaud Computing the maximum overlap of two convex polygons under translations Theory Comput. Syst. 31 1998 613 628
6. M.P. do Carmo Differential Geometry of Curves and Surfaces 1976 Prentice-Hall Englewood Cliffs, NJ
7. T. Chan, Faster core-set constructions and data stream algorithms in fixed dimensions, in: Proc. 20th ACM Symp. Comput. Geometry, 2004, pp. 152-159
8. B. Chazelle, D. Liu, A. Magen, Sublinear geometric algorithms, in: Proc. 35th ACM Symp. Theory Comp., 2003, pp. 531-540
9. R.M. Dudley Metric entropy of some classes of sets with differentiable boundaries J. Approx. Theory 10 1974 227 236 Erratum in J. Approx. Theory 26 1979 192 193
10. H. Edelsbrunner Computing the extreme distances between two convex polygons J. Algorithms 6 1985 213 224
11. B. Grünbaum Measures of symmetry of convex sets V. Klee, Convexity Proc. Symp. Pure Math. vol. 7 1963 Amer. Math. Soc. Providence, RI 233 270
12. H. Hotelling Tubes and spheres in n-spaces, and a class of statistical problems Amer. J. Math. 61 1939 440 460
13. F. John, Extremum problems with inequalities as subsidiary conditions, in: Courant Anniversary Volume, 1948, pp. 187-204
14. D. Kirkpatrick, and J. Snoeyink Tentative prune-and-search for computing fixed-points with applications to geometric computation Fundamenta Informaticae 22 1995 353 370
15. M. Lassak Approximation of convex bodies by axially symmetric bodies Proc. Amer. Math. Soc. 130 2002 3075 3084 Erratum in Proc. Amer. Math. Soc. 131 2003 2301
16. M. Lassak Approximation of convex bodies by rectangles Geom. Dedicata 47 1993 111 117
17. M.A. Lopez, and S. Reisner Efficient approximation of convex polygons Internat. J. Comput. Geom. Appl. 10 2000 445 452
18. R3 and related problems SIAM J. Comput. 12 1983 759 776
19. O. Schwarzkopf, U. Fuchs, G. Rote, and E. Welzl Approximation of convex figures by pairs of rectangles Computational Geometry 10 1998 77 87 also in STACS 1990 Lecture Notes Comput. Sci. vol. 415 1990 Springer Berlin 240 249
20. G.T. Toussaint, Solving geometric problems with the rotating calipers, in: Proc. IEEE MELECON, Athens 1983, pp. 1-4
21. B.A. de Valcourt Axially symmetric polygons inscribed in and circumscribed about convex polygons Elemente Math. 22 1967 121 133
22. I.M. Yaglom, and V.G. Boltyanskii Convex Figures 1961 Holt, Rinehart and Winston New York
23. H. Weyl On the volume of tubes Amer. J. Math. 61 1939 461 472