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Skewed projections with an application to line stabbing in R3

Authors:

J. W. Jaromczyk,

M. KowalukAuthors Info & Claims

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

Pages 362 - 370

https://doi.org/10.1145/73393.73430

Published: 06 January 1988 Publication History

Abstract

A new geometrical transform, skewed-projection, is introduced. This transform is applied to design a new algorithm for a common transversal problem for families of polyhedra in R³. The time and space analysis, using Davenport-Schinzel sequences, is given.

References

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Jaromczyk, J. W. and M. Kowaluk, in preparation.

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Cited By

Pettie S(2015)Sharp Bounds on Davenport-Schinzel Sequences of Every OrderJournal of the ACM10.1145/279407562:5(1-40)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2794075
Goaoc X(2009)Some Discrete Properties of the Space of Line Transversals to Disjoint BallsNonlinear Computational Geometry10.1007/978-1-4419-0999-2_3(51-83)Online publication date: 9-Oct-2009
https://doi.org/10.1007/978-1-4419-0999-2_3
Coll NFort MMadern NSellarès J(2006)Computing terrain multi-visibility maps for a set of view segments using graphics hardwareProceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I10.1007/11751540_10(81-90)Online publication date: 8-May-2006
https://dl.acm.org/doi/10.1007/11751540_10
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No Helly Theorem for Stabbing Translates by Lines in R3

For each $n>2$ we construct a convex body $K\subset {\Bbb R}^3$ and a finite family ${\cal F}$ of disjoint translates of $K$ such that any $n-1$ members ${\cal F}$ admit a line transversal, but ${\cal F}$ has no line transversal.

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cover image ACM Conferences

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

January 1988

403 pages

ISBN:0897912705

DOI:10.1145/73393

Chairman:
H. Edelsbrunner
Univ. of Illinois, Urbana-Champaign

Copyright © 1988 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 January 1988

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CG88: Symposium on Computational Geometery

June 6 - 8, 1988

Illinois, Urbana-Champaign, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Pettie S(2015)Sharp Bounds on Davenport-Schinzel Sequences of Every OrderJournal of the ACM10.1145/279407562:5(1-40)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2794075
Goaoc X(2009)Some Discrete Properties of the Space of Line Transversals to Disjoint BallsNonlinear Computational Geometry10.1007/978-1-4419-0999-2_3(51-83)Online publication date: 9-Oct-2009
https://doi.org/10.1007/978-1-4419-0999-2_3
Coll NFort MMadern NSellarès J(2006)Computing terrain multi-visibility maps for a set of view segments using graphics hardwareProceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I10.1007/11751540_10(81-90)Online publication date: 8-May-2006
https://dl.acm.org/doi/10.1007/11751540_10
Jaromczyk JKowaluk M(2003)Sets of lines and cutting out polyhedral objectsComputational Geometry: Theory and Applications10.1016/S0925-7721(02)00131-125:1-2(67-95)Online publication date: 1-May-2003
https://dl.acm.org/doi/10.1016/S0925-7721%2802%2900131-1
Bern MDobkin DEppstein DGrossman R(1994)Visibility with a moving point of viewAlgorithmica10.1007/BF0118701911:4(360-378)Online publication date: 1-Apr-1994
https://dl.acm.org/doi/10.1007/BF01187019
Pellegrini M(1993)Lower bounds on stabbing lines in 3-spaceComputational Geometry10.1016/0925-7721(93)90030-A3:1(53-58)Online publication date: Jun-1993
https://doi.org/10.1016/0925-7721(93)90030-A
Pellegrini MShor P(1992)Finding stabbing lines in 3-spaceDiscrete & Computational Geometry10.1007/BF022930438:2(191-208)Online publication date: 1-Dec-1992
https://dl.acm.org/doi/10.1007/BF02293043
Pellegrini MShor PAggarwal A(1991)Finding stabbing lines in 3-dimensional spaceProceedings of the second annual ACM-SIAM symposium on Discrete algorithms10.5555/127787.126018(24-31)Online publication date: 1-Mar-1991
https://dl.acm.org/doi/10.5555/127787.126018
Bern MDobkin DEppstein DGrossman RJohnson D(1990)Visibility with a moving point of viewProceedings of the first annual ACM-SIAM symposium on Discrete algorithms10.5555/320176.320188(107-117)Online publication date: 1-Jan-1990
https://dl.acm.org/doi/10.5555/320176.320188
Pellegrini MSeidel R(1990)Stabbing and ray shooting in 3 dimensional spaceProceedings of the sixth annual symposium on Computational geometry10.1145/98524.98563(177-186)Online publication date: 1-May-1990
https://dl.acm.org/doi/10.1145/98524.98563
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