Recent developments in the theory of arrangements of surfaces

Micha Sharir

doi:10.1007/3-540-46691-6_1

Recent developments in the theory of arrangements of surfaces

Micha Sharir^*

^*Corresponding author for this work

School of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to a variety of problems in computational geometry and its applications, including motion planning, Voronoi diagrams, union of geometric objects, visibility, and geometric optimization.

Original language	English
Title of host publication	Foundations of Software Technology and Theoretical Computer Science - 19th Conference, Proceedings
Editors	C. Pandu Rangan, V. Raman, R. Ramanujam
Publisher	Springer Verlag
Pages	1-21
Number of pages	21
ISBN (Print)	3540668365, 9783540668367
DOIs	https://doi.org/10.1007/3-540-46691-6_1
State	Published - 1999
Event	19th Conference on Foundations of Software Technology and Theoretical Computer Science, FSTandTCS 1999 - Chennai, India Duration: 13 Dec 1999 → 15 Dec 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1738
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th Conference on Foundations of Software Technology and Theoretical Computer Science, FSTandTCS 1999
Country/Territory	India
City	Chennai
Period	13/12/99 → 15/12/99

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10.1007/3-540-46691-6_1

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Sharir, M. (1999). Recent developments in the theory of arrangements of surfaces. In C. Pandu Rangan, V. Raman, & R. Ramanujam (Eds.), Foundations of Software Technology and Theoretical Computer Science - 19th Conference, Proceedings (pp. 1-21). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1738). Springer Verlag. https://doi.org/10.1007/3-540-46691-6_1

Sharir, Micha. / Recent developments in the theory of arrangements of surfaces. Foundations of Software Technology and Theoretical Computer Science - 19th Conference, Proceedings. editor / C. Pandu Rangan ; V. Raman ; R. Ramanujam. Springer Verlag, 1999. pp. 1-21 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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author = "Micha Sharir",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1999.; 19th Conference on Foundations of Software Technology and Theoretical Computer Science, FSTandTCS 1999 ; Conference date: 13-12-1999 Through 15-12-1999",

year = "1999",

doi = "10.1007/3-540-46691-6_1",

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Sharir, M 1999, Recent developments in the theory of arrangements of surfaces. in C Pandu Rangan, V Raman & R Ramanujam (eds), Foundations of Software Technology and Theoretical Computer Science - 19th Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1738, Springer Verlag, pp. 1-21, 19th Conference on Foundations of Software Technology and Theoretical Computer Science, FSTandTCS 1999, Chennai, India, 13/12/99. https://doi.org/10.1007/3-540-46691-6_1

Recent developments in the theory of arrangements of surfaces. / Sharir, Micha.
Foundations of Software Technology and Theoretical Computer Science - 19th Conference, Proceedings. ed. / C. Pandu Rangan; V. Raman; R. Ramanujam. Springer Verlag, 1999. p. 1-21 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1738).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Sharir M. Recent developments in the theory of arrangements of surfaces. In Pandu Rangan C, Raman V, Ramanujam R, editors, Foundations of Software Technology and Theoretical Computer Science - 19th Conference, Proceedings. Springer Verlag. 1999. p. 1-21. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-46691-6_1

Recent developments in the theory of arrangements of surfaces

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