TY - GEN

T1 - Triangles in space or Building (and analyzing) castles in the air

AU - Aronov, Boris

AU - Sharir, Micha

N1 - Funding Information:
Work on this paper by the first author has been supported by an AT&T Bell Laboratories PhD Scholarship. Work on this paper by the second author has been supported by Office of Naval Research Grant N00014-82-K-0381. by National Science Foundation Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, the IBM Corporation. and by a research grant from the NCRD-the Israeli National Council for Research and Development.
Publisher Copyright:
© 1988 ACM.

PY - 1988/1/6

Y1 - 1988/1/6

N2 - We show that the combinatorial complexity of all non-convex cells in an arrangement of n (possibly intersecting) triangles in 3-space is O(n7/3+δ), for any δ>0, and that this bound is almost tight in the worst case. Our bound significantly improves a previous nearly cubic bound of Pach and Sharir. We also present a (nearly) worst-case optimal randomized algorithm for calculating a single cell of the arrangement, analyze some special cases of the problem where improved bounds (and better algorithms) can be obtained, and describe applications of our results to translational motion planning for polyhedra in 3-space.

AB - We show that the combinatorial complexity of all non-convex cells in an arrangement of n (possibly intersecting) triangles in 3-space is O(n7/3+δ), for any δ>0, and that this bound is almost tight in the worst case. Our bound significantly improves a previous nearly cubic bound of Pach and Sharir. We also present a (nearly) worst-case optimal randomized algorithm for calculating a single cell of the arrangement, analyze some special cases of the problem where improved bounds (and better algorithms) can be obtained, and describe applications of our results to translational motion planning for polyhedra in 3-space.

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U2 - 10.1145/73393.73432

DO - 10.1145/73393.73432

M3 - Conference contribution

AN - SCOPUS:38049018141

T3 - Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988

SP - 381

EP - 391

BT - Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988

PB - Association for Computing Machinery, Inc

T2 - 4th Annual Symposium on Computational Geometry, SCG 1988

Y2 - 6 June 1988 through 8 June 1988

ER -