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European Conference on Computer Algebra

EUROCAL 1985: EUROCAL '85 pp 246–261Cite as

An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space

  • Algebraic Algorithms III
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 204))

Abstract

Given a set of r-variate integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space E r is a certain partition of E r into connected subsets compatible with the zeros of the polynomials. Each subset is a cell. Two cells of a cad are adjacent if their union is connected. In applications of cad's, one often wishes to know the pairs of adjacent cells. In a previous paper we gave an algorithm which determines the adjacent cells as it constructs a cad of the plane. We give such an algorithm here for three-dimensional space.

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References

  1. D. S. Arnon, G. E. Collins, S. McCallum ”Cylindrical algebraic decomposition I: the basic algorithm”, SIAM J. Comp, 13, (1984), pp. 865–877.

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Author information

Authors and Affiliations

  1. Xerox PARC, 333 Coyote Hill Road, 94304, Palo Alto, California

    Dennis S. Arnon

  2. Department of Computer Science, University of Wisconsin — Madison, 53706, Madison, Wisconsin

    George E. Collins

  3. Department of Computer Science, University of Toronto, M5S 1A4, Toronto, Canada

    Scott McCallum

Authors
  1. Dennis S. Arnon
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  2. George E. Collins
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  3. Scott McCallum
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Editor information

Bob F. Caviness

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© 1985 Springer-Verlag Berlin Heidelberg

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Arnon, D.S., Collins, G.E., McCallum, S. (1985). An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space. In: Caviness, B.F. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15984-3_272

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  • DOI: https://doi.org/10.1007/3-540-15984-3_272

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15984-1

  • Online ISBN: 978-3-540-39685-7

  • eBook Packages: Springer Book Archive

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