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

  • Dennis S. Arnon
  • George E. Collins
  • Scott McCallum
Algebraic Algorithms III
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


Given a set of r-variate integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space Er is a certain partition of Er 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.


Boundary Point Limit Point Primitive Element Boundary Property Positive Degree 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Dennis S. Arnon
    • 1
  • George E. Collins
    • 2
  • Scott McCallum
    • 3
  1. 1.Xerox PARCPalo Alto
  2. 2.Department of Computer ScienceUniversity of Wisconsin — MadisonMadison
  3. 3.Department of Computer ScienceUniversity of TorontoTorontoCanada

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