Linear time approximation of 3D convex polytopes

Computational Geometry: Theory and Applications

Volumn 23, Issue 3, 2002, Pages 291-301

  Lopez, Mario A ^a   Reisner, Shlomo ^b  

^a UNIVERSITY OF DENVER   (United States)

^b UNIVERSITY OF HAIFA   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750695724     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(02)00100-1     Document Type: Article

References (17)

1. H. Brönnimann, M. Goodrich, Almost optimal set covers in finite VC-dimensions, Discrète Comput. Geom. 14 (1995) 463-179.
2. T.M. Chan, Optimal output-sensitive convex hull algorithms in two and three dimensions, Discrete Comput. Geom. 16 (1996) 361-368.
3. B. Chazelle, J. Matousek, Derandomizing an output-sensitive convex hull algorithm in three dimensions, Computational Geometry 5 (1995) 27-32.
4. K.L. Clarkson, Algorithms for polytope covering and approximation, in: Proc. 3rd Workshop on Algorithms and Data Structures, in: Lecture Notes in Computer Science, Vol. 709, Springer-Verlag, 1993, pp. 246-252.
5. O.P. Dobkin, D.G. Kirkpatrick, Determining the separation of preprocessed polyhedra - a unified approach, in: Proc. 17th Internat. Colloq. Automata Lang. Program, in: Lecture Notes in Computer Science, Vol. 443, Springer-Verlag, 1990, pp. 400-413.
6. Y. Gordon, M. Meyer, S. Reisner, Constructing a polytope to approximate a convex body, Geom. Dedicata 57 (1995) 217-222.
7. P.M. Gruber, Aspects of approximation of convex bodies, in: P.M. Gruber, J.M. Wills (Eds.), Handbook of Convex Geometry, North-Holland, Amsterdam, 1993, pp. 319-345.
8. P.M. Gruber, Approximation by convex polytopes, in: T. Bistriczky, et al. (Eds.), Polytopes: Abstract, Convex and Computational, Kluwer Academic, Dordrecht, 1994, pp. 173-203.
9. W. Habicht, B .L. van der Waerden, Lagerung von Punkten auf der Kugel, Math. Ann. 123 ( 1951 ) 223-234.
10. P.S. Heckbert, M. Garland, Survey of polygonal surface simplification algorithms, Technical Report, Carnegie-Mellon University, 1997.
11. P.S. Heckbert, M. Garland, Optimal triangulation and quadric-based surface simplification, Computational Geometry 14 (1999)49-65.
12. D.G. Kirkpatrick, Optimal search in planar subdivisions, SLAM J. Comp. 12 (1983) 28-35.
13. M.A. Lopez, S. Reisner, Algorithms for polyhedral approximation of multidimensional ellipsoids, J. Algorithms 33 (1999) 140-165.
14. M.A. Lopez, S. Reisner, Efficient approximation of convex polygons, International J. Comput. Geom. Appl. 10 (2000) 445-52.
15. J. O'Rourke, Computational Geometry in C, 2nd Edition, Cambridge University Press, 1998.
16. P.P. Preparata, S.J. Hong, Convex hulls of finite sets of points in two and three dimensions, Comm. ACM 20 (1977) 87-93.
17. S. Reisner, C. Schutt, E. Werner, Dropping a vertex or a facet from a convex polytope, Forum Math. 13 (2001) 359-378.