TY - GEN
T1 - Recent developments in the theory of arrangements of surfaces
AU - Sharir, Micha
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=15344344295&partnerID=8YFLogxK
U2 - 10.1007/3-540-46691-6_1
DO - 10.1007/3-540-46691-6_1
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AN - SCOPUS:15344344295
SN - 3540668365
SN - 9783540668367
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 1
EP - 21
BT - Foundations of Software Technology and Theoretical Computer Science - 19th Conference, Proceedings
A2 - Pandu Rangan, C.
A2 - Raman, V.
A2 - Ramanujam, R.
PB - Springer Verlag
T2 - 19th Conference on Foundations of Software Technology and Theoretical Computer Science, FSTandTCS 1999
Y2 - 13 December 1999 through 15 December 1999
ER -