Abstract
In this paper we study dynamic variants of conjugation trees and related structures that have recently been introduced for performing various types of queries on sets of points and line segments, like half-planar range searching, shooting, intersection queries, etc. For most of these types of queries dynamic structures are obtained with an amortized update time ofO(log2 n) (or less) with only minor increases in query times. As an application of the method we obtain an output-sensitive method for hidden surface removal in a set ofn triangles that runs in timeO(nlogn+n · k γ) whereγ=log2((1+√5)/2) ≈ 0.695 andk is the size of the visibility map obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agarwal, P. K.,A deterministic algorithm for partitioning arrangements of lines and its applications, Proc. 5th ACM Symp. on Computational Geometry, 1989, pp. 11–22.
Bentley, J. L.,Decomposable searching problems, Inform. Proc. Letters 8 (1979), 244–251.
Chazelle, B.,Polytope range searching and integral geometry, Proc. 28th Symp. on Foundations of Computer Science, 1987, pp. 1–10.
McCreight, E. M.,Priority search trees, SIAM J. Computing 14 (1985), 257–276.
Edelsbrunner, H.,Intersection problems in computational geometry, Forschungsberichte F93, Inst. f. Informationsverarbeitung, TU Graz, 1982.
Edelsbrunner, H.,Algorithms in Combinatorial Geometry, Springer-Verlag, Berlin, 1987.
Edelsbrunner, H. and E. Welzl,Halplanar range search in linear space and O(n 0.695) query time, Forschungsberichte F111, Inst. f. Informationsverarbeitung, TU Graz, 1983.
Edelsbrunner, H. and E. Welzl,Halfplanar range search in linear space and O(n 0.695)query time, Inform. Proc. Letters 23 (1986), 289–293.
Haussler, D. and E. Welzel,Epsilon nets and simplex range queries, Discrete Computational Geometry 2 (1987), 127–151.
Matoušek, J.,Construction of ɛ-nets, Proc. 5th ACM Symp. on Computational Geometry, 1989, pp. 1–10.
Megiddo, N.,Partitioning with two lines in the plane, J. Algorithms 6 (1985), 430–433.
Overmars, M. H.,The Design of Dynamic Data Structures, Springer-Verlag, Berlin, 1983.
Overmars, M. H.,Range searching in a set of line segments, Proc. 1st ACM Symp. on Computational Geometry, 1985, pp. 177–185.
Overmars, M. H., H. Schipper and M. Sharir,Storing line segments in partition trees, BIT 30 (1990), 385–403.
Overmars, M. H., and M. Sharir,Output-sensitive hidden surface removal, Proc. 30th IEEE Symp. on Foundations of Computer Science, 1989, pp. 598–603.
Preparata, F. P., and M. I. Shamos,Computational Geometry: An Introduction, Springer-Verlag, Berlin, 1985.
Preparata, F. P., and R. Tamassia,Dynamic techniques for point location and transitive closure in planar structures, Proc. 29th IEEE Symp. on Foundations of Computer Science, 1988, pp. 558–567.
Sharir, M., and M. H. Overmars,A simple output-sensitive algorithm for hidden surface removal, ACM Trans. on Graphics, to appear.
Sharir, M., and M. H. Overmars,An improved technique for output-sensitive hidden surface removal, Techn. Rep. RUU-CS-89-32, Dept. of Computer Science, Utrecht University, 1989.
Willard, D. E.,Polygon retrieval, SIAM J. Computing 11 (1982), 149–165.
Author information
Authors and Affiliations
Additional information
Research of the second author was partially supported by the ESPRIT II Basic Research Actions Program of the EC, under contract No. 3075 (project ALCOM).