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Japanese Conference on Discrete and Computational Geometry

JCDCG 2000: Discrete and Computational Geometry pp 156–159Cite as

Volume Queries in Polyhedra

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

Abstract

We present a simple and practical data structure for storing a (not necessarily convex) polyhedron P which can, given a query surface S cutting the polyhedron, determine the volume and the area of the portion of the polyhedron above S. The queries are answered in a time linear in the size (complexity) of S. The space and preprocessing time for this dara structure are linear in the size of P. We also present an intermediary data structure for planar graphs which is of use in other application domains.

Research supported by NSF grant CCR-9732689

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References

  1. R. Boland and J. Urrutia. Polygon Area Problems. Proc. of the 12th Canadian Conf. on Computational Geometry. Fredericton, NB, Canada, 2000.

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  2. F. Contreras-Alcalá. Cutting polygons and a problem on illumination of stages. Masters thesis, Dept. Comp. Sci. University of Ottawa, Ottawa, ON, Canada, 1998. http://www.csi.uottawa.ca/~fhca/thesis/

  3. J. Czyzowicz, F. Contreras-Alcalá and J. Urrutia. On measuring areas of polygons. Proc. of the 10th Canadian Conf. on Computational Geometry, Montráal, QC, Canada, 1998.

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  4. Julio C. Navas. Geometric Routing in a Datagram Network. Ph.D. Thesis. Rutgers University, 2001.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Rutgers University, New Brunswick, NJ, USA

    John Iacono & Stefan Langerman

Authors
  1. John Iacono
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  2. Stefan Langerman
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Editor information

Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Iacono, J., Langerman, S. (2001). Volume Queries in Polyhedra. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_13

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  • DOI: https://doi.org/10.1007/3-540-47738-1_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

  • eBook Packages: Springer Book Archive

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