The union of congruent cubes in three dimensions

Discrete and Computational Geometry

Volumn 30, Issue 1, 2003, Pages 133-160

  Pach, János ^a,b,c   Safruti, Ido ^d   Sharir, Micha ^b,d  

^a City University of New York   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^d TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038648110     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-003-2928-3     Document Type: Conference Paper

References (17)

1. P. Agarwal and M. Sharir, Pipes, cigars, and kreplach: the union of Minkowski sums in three dimensions, Discrete Comput. Geom. 24 (2000), 645-685.
2. H. Alt, R. Fleischer, M. Kaufmann, K. Mehlhorn, S. Näher, S. Schirra, and C. Uhrig, Approximate motion planning and the complexity of the boundary of the union of simple geometric figures, Algorithmica 8 (1992), 391-406.
3. B. Aronov and M. Sharir, On translational motion planning of a convex polyhedron in 3-space, SIAM J. Comput. 26 (1997), 1785-1803.
4. B. Aronov, M. Sharir, and B. Tagansky, The union of convex polyhedra in three dimensions, SIAM J. Comput. 26 (1997), 1670-1688.
5. J. D. Boissonnat, M. Sharir, B. Tagansky, and M. Yvinec, Voronoi diagrams in higher dimensions under certain polyhedral distance functions, Discrete Comput. Geom. 19 (1998), 485-519.
6. K. Clarkson and P. Shor, Applications of random sampling in computational geometry, II, Discrete Comput. Geom. 4 (1989), 387-421.
7. A. Efrat, The complexity of the union of (α, β)-covered objects, Proc. 15th ACM Symp. on Computational Geometry, 1999, pp. 134-142.
8. A. Efrat and M. Katz, On the union of α-curved objects, Proc. 14th ACM Symp. on Computational Geometry, 1998, pp. 206-213.
9. A. Efrat, G. Rote, and M. Sharir, On the union of fat wedges and separating a collection of segments by a line, Comput. Geom. Theory Appl. 3 (1993), 277-288.
10. A. Efrat and M. Sharir, The complexity of the union of fat objects in the plane, Discrete Comput. Geom. 23 (2000), 171-189.
11. D. Halperin and C.-K. Yap, Combinatorial complexity of translating a box in polyhedral 3-space, Comput. Geom. Theory Appl. 9 (1998), 181-196.
12. K. Kedem, R. Livne, J. Pach, and M. Sharir, On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles, Discrete Comput. Geom. 1 (1986), 59-71.
13. D. Leven and M. Sharir, On the number of critical free contacts of a convex polygonal object moving in two-dimensional polygonal space, Discrete Comput. Geom. 2 (1987), 255-270.
14. J. Matoušek, J. Pach, M. Sharir, S. Sifrony, and E. Welzl, Fat triangles determine linearly many holes, SIAM J. Comput. 23 (1994), 154-169.
15. J. Pach and G. Tardos, On the boundary complexity of the union of fat triangles, Proc. 41st Annual Symp. Foundations of Computer Science, 2000, pp. 423-431. Also to appear in SIAM J. Comput.
16. J. Pach and G. Tardos, On the boundary complexity of the union of fat triangles, Proc. 41st Annual Symp. Foundations of Computer Science, 2000, pp. 423-431. Also to appear in SIAM J. Comput.
17. M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, Cambridge, 1995.