Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane
In Part I of the present paper we defined cylindrical algebraic decompositions (cad’s), and described an algorithm for cad construction. In Part II we give an algorithm that provides information about the topological structure of a cad of the plane. Informally, two disjoint cells in E r , r ≥ 1, are adjacent if they touch each other; formally, they are adjacent if their union is connected. In a picture of a cad, eg Fig. 2 of Part I, it is obvious to the eye which pairs of cells are adjacent. However, the cad algorithm of Part I does not actually produce this information, nor did the original version of that algorithm in (Collins 1975).
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