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Orthogonal Polyhedra: Representation and Computation

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Hybrid Systems: Computation and Control (HSCC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1569))

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Abstract

In this paper we investigate orthogonal polyhedra, i.e. polyhedra which are finite unions of full-dimensional hyper-rectangles. We define representation schemes for these polyhedra based on their vertices, and show that these compact representation schemes are canonical for all (convex and non-convex) polyhedra in any dimension. We then develop efficient algorithms for membership, face-detection and Boolean operations for these representations.

This work was partially supported by the European Community Esprit-LTR Project 26270 VHS (Verification of Hybrid systems) and the French-Israeli collaboration project 970MAEFUT5 (Hybrid Models of Industrial Plants).

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Author information

Authors and Affiliations

  1. Verimag, Centre Equation, 2, av. de Vignate, 38610, Gières, France

    Olivier Bournez & Oded Maler

  2. Dept. of Computer Science, Weizmann Inst., Rehovot, 76100, Israel, Grenoble

    Amir Pnueli

Authors
  1. Olivier Bournez
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  2. Oded Maler
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  3. Amir Pnueli
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Editor information

Editors and Affiliations

  1. Computing Science Institute, University of Nijmegen, P.O. Box 9010, 6500, GL, Nijmegen, The Netherlands

    Frits W. Vaandrager

  2. CWI, P.O. Box 94079, 1090, GB, Amsterdam, The Netherlands

    Jan H. van Schuppen

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© 1999 Springer-Verlag Berlin Heidelberg

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Bournez, O., Maler, O., Pnueli, A. (1999). Orthogonal Polyhedra: Representation and Computation. In: Vaandrager, F.W., van Schuppen, J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48983-5_8

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  • DOI: https://doi.org/10.1007/3-540-48983-5_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65734-7

  • Online ISBN: 978-3-540-48983-2

  • eBook Packages: Springer Book Archive

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