### 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.

Original language | English |
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Title of host publication | EUROCAL 1985 - European Conference on Computer Algebra, Proceedings |

Editors | Bob F. Caviness |

Publisher | Springer-VDI-Verlag GmbH & Co. KG |

Pages | 246-261 |

Number of pages | 16 |

ISBN (Print) | 9783540159841 |

DOIs | |

Publication status | Published - 1 Jan 1985 |

Externally published | Yes |

Event | European Conference on Computer Algebra, EUROCAL 1985 - Linz, Austria Duration: 1 Apr 1985 → 3 Apr 1985 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 204 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | European Conference on Computer Algebra, EUROCAL 1985 |
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Country | Austria |

City | Linz |

Period | 1/04/85 → 3/04/85 |

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## Cite this

Arnon, D. S., Collins, G. E., & McCallum, S. (1985). An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space. In B. F. Caviness (Ed.),

*EUROCAL 1985 - European Conference on Computer Algebra, Proceedings*(pp. 246-261). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 204 LNCS). Springer-VDI-Verlag GmbH & Co. KG. https://doi.org/10.1007/3-540-15984-3_272