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Arrangements. (English) Zbl 1116.65025

Boissonnat, Jean-Daniel (ed.) et al., Effective computational geometry for curves and surfaces. Berlin: Springer (ISBN 978-3-540-33258-9/hbk). Mathematics and Visualization, 1-66 (2007).
From the introduction: Arrangements of geometric objects have been intensively studied in combinatorial and computational geometry for several decades. Given a finite collection \(S\) of geometric objects (such as lines, planes, or spheres) the arrangement \({\mathcal A}(S)\) is the subdivision of the space where these objects reside into cells as induced by the objects in \(S\).
Arrangements are defined and have been investigated for general families of geometric objects. One of the best studied type of arrangements is that of lines in the plane. This means that arrangements may have unbounded edges and faces. Furthermore, arrangements are defined in any dimension. There are, for example, naturally defined and useful arrangements of hypersurfaces in six-dimensional space, arising in the study of rigid motion of bodies in three-dimensional space.
For the entire collection see [Zbl 1165.65318].

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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