Local polyhedra and geometric graphs

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2003, Pages 171-180

  Erickson, Jeff ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Binary space partition; Bounding volume hierarchies; Collision detection; Realistic input models

Indexed keywords

COMPUTATIONAL GEOMETRY; HIERARCHICAL SYSTEMS; POLYNOMIALS; TREES (MATHEMATICS);

GEOMETRIC GRAPHS;

GRAPH THEORY;

EID: 0038376540     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/777792.777820     Document Type: Conference Paper

References (44)

1. G. Barequet, B. Chazelle, L. Guibas, J. Mitchell, and A. Tal. BOXTREE: A hierarchical representation for surfaces in 3D. Comput. Graph. Forum 15(3):C387-C396, C484, 1996. Proc. Eurographics'96.
2. M. de Berg. Linear size binary space partitions for uncluttered scenes. Algorithmica 28:353-366, 2000.
3. M. de Berg, M. Katz, M. Overmars, A. F. van der Stappen, and J. Vleugels. Models and motion planning. Proc. 6th Scand. Workshop Algorithm Theory, 83-94, 1998. Lecture Notes Comput. Sci. 1432, Springer-Verlag.
4. M. de Berg, M. J. Katz, A. F. van der Stappen, and J. Vleugels. Realistic input models for geometric algorithms. Proc. 13th Annu. ACM Sympos. Comput. Geom., 294-303, 1997.
5. T. Brinkhoff, H.-P. Kriegel, and B. Seeger. Efficient processing of spatial joins using R-trees. Proc. ACM SIGMOD Conf. on Management of Data, 237-246, 1993.
6. B. Chazelle. Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm. SIAM J. Comput. 13:488-507, 1984.
7. B. Chazelle, H. Edelsbrunner, L. J. Guibas, and M. Sharir. Algorithms for bichromatic line segment problems and polyhedral terrains. Algorithmica 11:116-132, 1994.
8. N. Chin and S. Feiner. Near real-time shadow generation using BSP trees. Comput. Graph. 23:99-106, 1989. Proc. SIGGRAPH '89.
9. N. Chin and S. Feiner. Fast object-precision shadow generation for areal light sources using BSP trees. Comput. Graph. 25:21-30, Mar. 1992. Proc. 1992 Sympos. Interactive 3D Graphics.
10. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom. 4:387-421, 1989.
11. J. Erickson. On the relative complexities of some geometric problems. Proc. 7th Canad. Conf. Comput. Geom., 85-90, 1995. 〈http://www.uiuc.edu/̃jeffe/pubs/relative.html〉.
12. J. Erickson. New lower bounds for Hopcroft's problem. Discrete Comput. Geom. 16:389-418, 1996.
13. J. Erickson. Nice point sets can have nasty Delaunay triangulations. Proc. 17th Annu. ACM Sympos. Comput, Geom., 96-105, 2001. Full version to appear in Discrete Comput. Geom., 2003.
14. H. Fuchs, Z. M. Kedem, and B. Naylor. On visible surface generation by a priori tree structures. Comput. Graph. 14:124-133, 1980. Proc. SIGGRAPH '80.
15. S. Gottschalk, M. C. Lin, and D. Manocha. OBB-tree: A hierarchical structure for rapid interference detection. Comput. Graph. ??:171-180, 1996. Proc. SIGGRAPH '96.
16. L. Guibas, A. Nguyen, D. Russel, and L. Zhang. Collision detection for deforming necklaces. Proc. 18th Annu. ACM Sympos. Comput. Geom., 33-42, 2002.
17. A. Guttmann. R-trees: A dynamic index structure for spatial searching. Proc. ACM SIGMOD Conf. on Management Data, 47-57, 1984.
18. H. H. Haverkort, M. de Berg, and J. Gudmundsson. Boxtrees for collision checking in industrial applications. Proc. 18th Annu. ACM Sympos. Comput. Geom., 53-62, 2002.
19. P. M. Hubbard. Approximating polyhedra with spheres for time-critical collision detection. ACM Trans. Graph. 15(3):179-210, 1996.
20. J. Klosowski, M. Held, J. S. B. Mitchell, K. Zikan, and H. Sowizral. Efficient collision detection using bounding volume hierarchies of κ-DOPs. IEEE Trans. Visualizat. Comput. Graph. 4(1):21-36, 1998.
21. X.-Y. Li and S.-H. Teng. Generating well-shaped Delaunay meshes in 3D. Proc. 12th Annu. ACM-SIAM Sympos. Discrete Algorithms, 28-37, 2001.
22. I. Lotan, F. Schwarzer, D. Halperin, and J.-C. Latombe. Efficient maintenance and self-collision testing for kinematic chains. Proc. 18th Annu. ACM Sympos. Comput. Geom., 43-52, 2002.
23. G. L. Miller, D. Talmor, S.-H. Teng, and N. Walkington. A Delaunay based numerical method for three dimensions: generation, formulation, and partition. Proc. 27th Annu. ACM Sympos. Theory Comput., 683-692, 1995.
24. B. Mirtich and J. Canny. Impulse-based dynamic simulation. The Algorithmic Foundations of Robotics, 1995. A. K. Peters.
25. T. M. Murali and T. A. Funkhouser. Consistent solid and boundary representations from arbitrary polygonal data. Proc. 1997 Sympos. Interactive 3D Graphics, 1997.
26. B. Naylor, J. A. Amanatides, and W. Thibault. Merging BSP trees yields polyhedral set operations. Comput. Graph. 24:115-124, Aug. 1990. Proc. SIGGRAPH'90.
27. P. van Oosterom. An R-tree based map-overlay algorithm. Proc. EGIS '94, 318-327, 1994.
28. M. H. Overmars and A. F. van der Stappen. Range searching and point location among fat objects. J. Algorithms 21:629-656, 1996.
29. M. S. Paterson and F. F. Yao. Efficient binary space partitions for hidden-surface removal and solid modeling. Discrete Comput. Geom. 5:485-503, 1990.
30. M. S. Paterson and F. F. Yao. Optimal binary space partitions for orthogonal objects. J. Algorithms 13:99-113, 1992.
31. M. Pellegrini. Ray shooting on triangles in 3-space. Algorithmica 9:471-494, 1993.
32. O. Schwarzkopf and J. Vleugels. Range searching in low-density environments. Inform. Process. Lett. 60:121-127, 1996.
33. J. R. Shewchuk. Tetrahedral mesh generation by Delaunay refinement. Proc. 14th Annu. ACM Sympos. Comput. Geom., 86-95, 1998.
34. A. F. van der Stappen. Motion Planning amidst Fat Obstacles. Ph.D. dissertation, Dept. Comput. Sci., Utrecht Univ., Utrecht, Netherlands, 1994.
35. S. Suri, P. M. Hubbard, and J. F. Hughes. Collision detection in aspect and scale bounded polyhedra. Proc. 9th ACM-SIAM Sympos. Discrete Algorithms, 127-136, 1998.
36. E. Schömer and C. Thiel. Efficient collision detection for moving polyhedra. Proc. 11th Annu. ACM Sympos. Comput. Geom., 51-60, 1995.
37. R. A. Schumacker, R. Brand, M. Gilliland, and W. Sharp. Study for applying computer-generated images to visual simulation. Tech. Rep. AFHRL-TR-69-14, U.S. Air Force Human Resources Laboratory, 1969.
38. D. Talmor. Well-Spaced Points and Numerical Methods. Ph.D. thesis, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, August 1997. 〈http://reports-archive.adm.cs.cmu.edu/anon/1997/abstracts/97-164.html 〉. Technical report CMU-CS-97-164.
39. S. J. Teller and C. H. Séquin. Visibility preprocessing for interactive walkthroughs Comput. Graph. 25(4): 61-69, 1991. Proc. SIGGRAPH '91.
40. S.-H. Teng. Points, Spheres, and Separators: A Unified Geometric Approach to Graph Partitioning. Ph.D. thesis, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1992. Technical report CMU-CS-91-184.
41. W. C. Thibault and B. F. Naylor. Set operations on polyhedra using binary space partitioning trees. Comput. Graph. 21:153-162, 1987. Proc. SIGGRAPH '87.
42. J. Vleugels. On Fatness and Fitness - Realistic Input Models for Geometric Algorithms. Ph.D. thesis, Dept. Comput. Sci., Univ. Utrecht, Utrecht, The Netherlands, 1997.
43. Y. Zhou and S. Suri. Analysis of a bounding box heuristic for object intersection. Proc. 10th Annu. ACM-SIAM Sympos. Discrete Algorithms, 830-839, 1999.
44. A. Zomorodian and H. Edelsbrunner. Fast software for box intersection. Proc. 16th Annu. ACM Sympos. Comput. Geom., 129-138, 2000.