Efficiently Approximating the Minimum-Volume Bounding Box of a Point Set in Three Dimensions

Journal of Algorithms

Volumn 38, Issue 1, 2001, Pages 91-109

  Barequet, Gill ^a,c   Har Peled, Sariel ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

^c Johns Hopkins University   (United States)

Author keywords

Approximation; Bounding box

Indexed keywords

EID: 0002755657     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.2000.1127     Document Type: Article

References (21)

1. P. K. Agarwal, S. Har-Peled, M. Sharir, and K. R. Varadarajan, Approximate shortest paths on a convex polytope in three dimensions, J. Assoc. Comput. Mach. 44 (1997), 567-584.
2. G. E. Andrews, A lower bound for the volume of strictly convex bodies with many boundary lattice points, Trans. Amer. Math. Soc. 106 (1963), 270-279.
3. G. Barequet, B. Chazelle, L. J. Guibas, J. S. B. Mitchell, and A. Tal, BOXTREE: A hierarchical representation for surfaces in 3D, Comput. Graphics Forum 15, No. 3 (August 1996), C387-C396, C484.
4. N. Beckmann, H.-P. Kriegel, R. Schneider, and B. Seeger, The r*-tree: An efficient and robust access method for points and rectangles, in "ACM SIGMOID International Conference on Management of Data, 1990," pp. 322-331.
5. S. Bespamyatnikh and M. Segal, Covering a set of points by two axis-parallel boxes, in "Proceedings, 9th Canadian Conference on Computational Geometry, 1997," 33-38.
6. T. M. Chan, Output-sensitive results on convex hulls, extreme points, and related problems, Discrete Comput. Geom. 16 (1996), 369-387.
7. K. L. Clarkson and P. W. Shor, Applications of random sampling in computational geometry, II, Discrete Comput. Geom. 4 (1989), 387-421.
8. R. M. Dudley, Metric entropy of some classes of sets with differentiable boundaries, J. Approx. Theory 10, No. 3 (1974), 227-236.
9. O. Egecioglu and B. Kalantari, Approximating the diameter of a set of points in the Euclidean space, Inform. Process. Lett. 32 (1989), 205-211.
10. C. Faloutsos and K.-I. Lin, FastMap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets, ACM SIGMOD Record 24, No. 2 (1995), 163-174.
11. O. D. Faugeras and J. Ponce, An object-centered hierarchical representation for 3-d objects: The prism-tree, Comput. Vision, Graphics, Image Process. 38 (1987), 1-28.
12. P. Gritzmann and V. Klee, Inner and outer j-radii of convex bodies in finite-dimensional normed spaces, Discrete Comput. Geom. 7 (1992), 255-280.
13. S. Gottschalk, M. C. Lin, and D. Manocha, OBB-tree: A hierarchical structure for rapid interference detection, in "Proceedings, SIGGRAPH '96, 1992," pp. 171-180.
14. S. Har-Peled, Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions, Discrete Comput. Geom. 21 (1999), 216-231.
15. P. M. Hubbard, Collision detection for interactive graphics applications, IEEE Trans. Visual. Compu. Graphics 1, No. 3 (1995), 218-230.
16. J. Klosowski, M. Held, J. S. B. Mitchell, K. Zikan, and H. Sowizral, Efficient collision detection using bounding volume hierarchies of k-DOPs, IEEE Trans. Visual. Comput. Graphics 4, No. 1 (1998), 21-36.
17. J. O'Rourke, Finding minimal enclosing boxes, Int. J. Comput. Inform. Sci. 14 (1985), 183-199.
18. N. Roussopoulos and D. Leifker, Direct spatial search on pictorial databases using packed r-trees, in "Proceedings, ACM SIGACT-SIGMOD Conference on Principles of Database Systems, 1985," pp. 17-31.
19. H. Samet, "Spatial Data Structures: Quadtrees, Octrees, and Other Hierarchical Methods," Addison-Wesley, Reading, MA, 1989.
20. +-tree: A dynamic index for multi-dimensional objects, in "Proceedings, 13th Conference on Very Large Databases, 1987," pp. 507-517.
21. G. T. Toussaint, Solving geometric problems with the rotating calipers, in "Proceedings IEEE MELECON, 1983," pp. 1-4.