@inproceedings{3594f0e994bf41efa57ca2e949c636bc,

title = "An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space",

abstract = "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.",

author = "Arnon, {Dennis S.} and Collins, {George E.} and Scott McCallum",

year = "1985",

month = jan,

day = "1",

doi = "10.1007/3-540-15984-3_272",

language = "English",

isbn = "9783540159841",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-VDI-Verlag GmbH & Co. KG",

pages = "246--261",

editor = "Caviness, {Bob F.}",

booktitle = "EUROCAL 1985 - European Conference on Computer Algebra, Proceedings",

address = "Germany",

note = "European Conference on Computer Algebra, EUROCAL 1985 ; Conference date: 01-04-1985 Through 03-04-1985",

}