Abstract
It will become apparent in Chapters 7 through 15 of this book that many computational problems in geometry can be solved by constructing arrangements of hyperplanes. Unfortunately, the rather large number of faces of arrangements entails the use of large amounts of storage. It is thus advantageous to construct only part of an arrangement whenever the problem at hand admits it. Examples of useful structures in arrangements are single cells or faces (see Chapter 8), zones (see Chapters 5 and 7), stabbing regions (see Chapter 15), and levels (see Chapters 3, 9, and 13).
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© 1987 Springer-Verlag Berlin Heidelberg
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Edelsbrunner, H. (1987). The Complexity of Families of Cells. In: Algorithms in Combinatorial Geometry. EATCS Monographs in Theoretical Computer Science, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61568-9_6
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DOI: https://doi.org/10.1007/978-3-642-61568-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64873-1
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