Maximizing the overlap of two planar convex sets under rigid motions

Computational Geometry: Theory and Applications

Volumn 37, Issue 1 SPEC. ISS., 2007, Pages 3-15

  Ahn, Hee Kap ^a   Cheong, Otfried ^b   Park, Chong Dae ^b   Shin, Chan Su ^c   Vigneron, Antoine ^d  

^a Sejong University   (South Korea)

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

^c Hankuk University of Foreign Studies   (South Korea)

^d UR341 National Agronomical Research Institute (INRA)   (France)

Author keywords

Approximation algorithm; Convex shape; Geometric pattern matching; Sublinear algorithm

Indexed keywords

APPROXIMATION ALGORITHMS; PATTERN MATCHING;

BALANCED TREES; CONVEX POLYGON; CONVEX SHAPES; EXTREME POINTS; GEOMETRIC PATTERN MATCHING; RIGID MOTIONS; RUNNING TIME; SUBLINEAR ALGORITHM;

SET THEORY;

EID: 33847121346     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2006.01.005     Document Type: Conference Paper

References (12)

1. H.-K. Ahn, P. Brass, O. Cheong, H.-S. Na, C.-S. Shin, and A. Vigneron Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets Computational Geometry 33 2006 152 164 (Pubitemid 43167408)
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. H. Alt, U. Fuchs, G. Rote, and G. Weber Matching convex shapes with respect to the symmetric difference Algorithmica 21 1998 89 103 (Pubitemid 128664054)
5. M. de Berg, S. Cabello, P. Giannopoulos, C. Knauer, R. van Oostrum, and R.C. Veltkamp Maximizing the area of overlap of two unions of disks under rigid motion Scandinavian Workshop on Algorithm Theory Lecture Notes Comput. Sci. vol. 3111 2004 Springer Berlin 138 149
6. M. de Berg, O. Cheong, O. Devillers, M. van Kreveld, and M. Teillaud Computing the maximum overlap of two convex polygons under translations Theory of Computing Systems 31 1998 613 628 (Pubitemid 128342351)
7. O. Cheong, S. Har-Peled, A. Efrat, On finding a guard that sees most and a shop that sells most, in: Proc. 15th ACM-SIAM Symp. Discrete Algorithms, 2004, pp. 1098-1107; also in: Discrete & Computational Geometry, in press
8. M. Dickerson, and D. Scharstein Optimal placement of convex polygons to maximize point containment Computational Geometry 11 1998 1 16 (Pubitemid 128431777)
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. D.M. Mount, R. Silverman, and A.Y. Wu On the area of overlap of translated polygons Computer Vision and Image Understanding: CVIU 64 1 1996 53 61 (Pubitemid 126359970)
11. O. Schwarzkopf, U. Fuchs, G. Rote, and E. Welzl Approximation of convex figures by pairs of rectangles Computational Geometry 10 1998 77 87 also STACS 1990 Lecture Notes Comput. Sci. vol. 415 1990 Springer Berlin 240 249 (Pubitemid 128378550)
12. G. T. Toussaint, Solving geometric problems with the rotating calipers, in: Proc. IEEE MELECON, Athens, Greece, 1983, pp. 1-4