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Term rewrite systems to derive set boolean operations on 2D objects

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FME '97: Industrial Applications and Strengthened Foundations of Formal Methods (FME 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1313))

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Abstract

Set boolean operations between 2-dimensional geometric objects are crucial in computational geometry and deserve rigorous treatments. We build up a simple and convergent system of rewrite rules modulo equations to cope with their design. This system is complete is the sense that it gives a detailed description for all particular cases. This specification leans on a new operation of labeling self-refinement of planar subdivisions. Starting from these abstract descriptions, we design concrete algorithms with a new method. The rewrite system is successively transformed in specialized ones from which we derive efficient treatments, like plane-sweep algorithms.

This research is supported by the GDR-PRC de Programmation and the GDR-PRC Algorithmes, modèles et infographie of the French CNRS and MENESR.

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Authors and Affiliations

  1. Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection (LSIIT, URA CNRS 1871), Université Louis Pasteur, Département d'Informatique, 7, rue René Descartes, 67084, Strasbourg Cedex

    David Cazier & Jean-François Dufourd

Authors
  1. David Cazier
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  2. Jean-François Dufourd
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John Fitzgerald Cliff B. Jones Peter Lucas

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© 1997 Springer-Verlag Berlin Heidelberg

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Cazier, D., Dufourd, JF. (1997). Term rewrite systems to derive set boolean operations on 2D objects. In: Fitzgerald, J., Jones, C.B., Lucas, P. (eds) FME '97: Industrial Applications and Strengthened Foundations of Formal Methods. FME 1997. Lecture Notes in Computer Science, vol 1313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63533-5_32

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  • DOI: https://doi.org/10.1007/3-540-63533-5_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63533-8

  • Online ISBN: 978-3-540-69593-6

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