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Computing the width of a three-dimensional point set: an experimental study

Authors:

R. JanardanAuthors Info & Claims

Journal of Experimental Algorithmics (JEA), Volume 4

Pages 8 - es

https://doi.org/10.1145/347792.347816

Published: 31 December 1999 Publication History

Abstract

We describe a robust, exact, and efficient implementation of an algorithm that computes the width of a three-dimensional point set. The algorithm is based on efficient solutions to problems that are at the heart of computational geometry: three-dimensional convex hulls, point location in planar graphs, and computing intersections between line segments. The latter two problems have to be solved for planar graphs and segments on the unit sphere, rather than in the two-dimensional plane. The implementation is based on LEDA, and the geometric objects are represented using exact rational arithmetic.

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References

[1]

AGARWAL, P. K. AND SHARIR, M. 1996. Efficient randomized algorithms for some geometric optimization problems. <i>Discrete Comput. Geom. 16</i>, 317-337.]]

[2]

BARTUSCHKA, U., MEHLHORN, K., AND NÄHER, S. 1997. A robust and efficient implementation of a sweep line algorithm for the straight line segment intersection problem. In <i>Proc. Workshop on Algorithm Engineering</i> (Venice, Italy, 1997), pp. 124-135.]]

[3]

BENTLEY, J. L. AND OTTMANN, T.A. 1979. Algorithms for reporting and counting geometric intersections. <i>IEEE Trans. Comput. C-28</i>, 643-647.]]

[4]

CHAZELLE, B., EDELSBRUNNER, H., GUIBAS, L. J., AND SHARIR, M. 1993. Diameter, width, closest line pair and parametric searching. <i>Discrete Comput. Geom. 10</i>, 183-196.]]

[5]

GRAHAM, R. L., KNUTH, D. E., AND PATASHNIK, O. 1989. <i>Concrete Mathematics.</i> Addison-Wesley, Reading, MA.]]

Digital Library

[6]

HOULE, M. E. AND TOUSSAINT, G. T., 1988. Computing the width of a set. <i>IEEE Trans. Pattern Anal. Mach. Intell. PAMI-10</i>, 761-765.]]

Digital Library

[7]

JACOBS, P.F. 1992. <i>Rapid Prototyping & Manufacturing: Fundamentals of StereoLithography. </i> McGraw-Hill, New York.]]

Digital Library

[8]

MAJHI, J., JANARDAN, R., SCHWERDT, J., SMID, M., AND GUPTA, P. 1999a. Minimizing support structures and trapped area in two-dimensional layered manufacturing. <i>Comput. Geom. Theory Appl. 12</i>, 241-267.]]

Digital Library

[9]

MAJHI, J., JANARDAN, R., SMID, M., AND GUPTA, P. 1999b. On some geometric optimization problems in layered manufacturing. <i>Comput. Geom. Theory Appl. 12</i>, 219-239.]]

Digital Library

[10]

MAJHI, J., JANARDAN, R., SMID, M., AND SCHWERDT, J. 1998. Multi-criteria geometric optimization problems in layered manufacturing. In <i>Proc. 14th Annu. ACM Sympos. Comput. Geom.</i> (1998), pp. 19-28.]]

Digital Library

[11]

MEHLHORN, K. AND NÄHER, S. 1999. LEDA: <i>A Platform for Combinatorial and Geometric Computing.</i> Cambridge University Press, Cambridge, U.K.]]

Digital Library

[12]

MEHLHORN, K., NÄHER, S., SEEL, M., SEIDEL, R., SCHILZ, T., SCHIRRA, S., AND UHRIG, C. 1999. Checking geometric programs or verification of geometric structures. <i>Comput. Geom. Theory Appl. 12</i>, 85-103.]]

[13]

MEHLHORN, K., NÄHER, S., SEEL, M., AND UHRIG, C. <i>The LEDA user manual.</i> http://www.mpi-sb.mpg.de/LEDA/MANUAL/MANUAL.html: Max-Planck-Institute for Computer Science.]]

[14]

PREPARATA, F. P. AND SHAMOS, M.I. 1988. <i>Computational Geometry: An Introduction.</i> Springer-Verlag, New York, NY.]]

Digital Library

[15]

RAMSEY, N. 1994. Literate programming simplified. <i>IEEE Software 11</i>, 97-105.]]

Digital Library

[16]

SCHWERDT, J. AND SMID, M. 1999. Computing the width of a three-dimensional point set: documentation. Report 4, Department of Computer Science, University of Magdeburg, Magdeburg, Germany. http://isgwww.cs.uni-magdeburg.de/~schwerdt/Cwidth.ps.]]

[17]

SCHWERDT, J., SMID, M., JANARDAN, R., AND JOHNSON, E. 2000. Protecting critical facets in layered manufacturing: implementation and experimental results. In <i>Proc. 2nd Workshop on Algorithm Engineering and Experiments</i> (2000), pp. 43-57.]]

[18]

SCHWERDT, J., SMID, M., JANARDAN, R., JOHNSON, E., AND MAJHI, J. 1999. Protecting facets in layered manufacturing. In <i>Proc. 19th Conf. Found. Softw. Tech. Theoret. Comput. Sci., Volume 1738 of Lecture Notes Comput. Sci.</i> (1999), pp. 281-292. Springer-Verlag.]]

Digital Library

[19]

STOLFI, J. 1991. <i>Oriented Projective Geometry: A Framework for Geometric Computations. </i> Academic Press, New York, NY.]]

Digital Library

Cited By

Zhou MZheng G(2012)The Optimized Iterative Projection Method to Determine the Width of an Arbitrary 3D ObjectAdvanced Materials Research10.4028/www.scientific.net/AMR.591-593.688591-593(688-691)Online publication date: Nov-2012
https://doi.org/10.4028/www.scientific.net/AMR.591-593.688
Larsson TAkenine‐Möller T(2009)Bounding Volume Hierarchies of Slab Cut BallsComputer Graphics Forum10.1111/j.1467-8659.2009.01548.x28:8(2379-2395)Online publication date: 9-Dec-2009
https://doi.org/10.1111/j.1467-8659.2009.01548.x
Kim YLin MManocha D(2004)Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space ExpansionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2004.126076710:2(152-163)Online publication date: 1-Mar-2004
https://dl.acm.org/doi/10.1109/TVCG.2004.1260767
Show More Cited By

Index Terms

Computing the width of a three-dimensional point set: an experimental study
1. Applied computing
  1. Operations research
    1. Computer-aided manufacturing
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Journal of Experimental Algorithmics

ACM Journal of Experimental Algorithmics Volume 4, Issue

1999

165 pages

ISSN:1084-6654

EISSN:1084-6654

DOI:10.1145/347792

Editor:
Bernard M. E. Moret
Univ. of New Mexico

Issue’s Table of Contents

Copyright © 1999 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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 December 1999

Published in JEA Volume 4

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Cited By

Zhou MZheng G(2012)The Optimized Iterative Projection Method to Determine the Width of an Arbitrary 3D ObjectAdvanced Materials Research10.4028/www.scientific.net/AMR.591-593.688591-593(688-691)Online publication date: Nov-2012
https://doi.org/10.4028/www.scientific.net/AMR.591-593.688
Larsson TAkenine‐Möller T(2009)Bounding Volume Hierarchies of Slab Cut BallsComputer Graphics Forum10.1111/j.1467-8659.2009.01548.x28:8(2379-2395)Online publication date: 9-Dec-2009
https://doi.org/10.1111/j.1467-8659.2009.01548.x
Kim YLin MManocha D(2004)Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space ExpansionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2004.126076710:2(152-163)Online publication date: 1-Mar-2004
https://dl.acm.org/doi/10.1109/TVCG.2004.1260767
Schwerdt JSmid MJanardan RJohnson E(2003)Protecting critical facets in layered manufacturing: implementation and experimental resultsComputer-Aided Design10.1016/S0010-4485(02)00090-835:7(647-657)Online publication date: Jun-2003
https://doi.org/10.1016/S0010-4485(02)00090-8
Schwerdt JSmid MHon MJanardan R(2002)Computing An Optimal Hatching Direction In Layered ManufacturingInternational Journal of Computer Mathematics10.1080/0020716021270579:10(1067-1081)Online publication date: Jan-2002
https://doi.org/10.1080/00207160212705
Ilinkin IJanardan RMajhi JSchwerdt JSmid MSriram R(2002)A decomposition-based approach to layered manufacturingComputational Geometry: Theory and Applications10.1016/S0925-7721(01)00059-123:2(117-151)Online publication date: 1-Sep-2002
https://dl.acm.org/doi/10.1016/S0925-7721%2801%2900059-1

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