Topological Art in Simple Galleries
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Date
2024-04
Publication Type
Journal Article
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yes
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Abstract
Let P be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in P. We say two points a, b ∈ P can see each other if the line segment seg(a, b) is contained in P. We denote by V(P) the family of all minimum guard placements. The Hausdorff distance makes V(P) a metric space and thus a topological space. We show homotopy-universality, that is, for every semi-algebraic set S there is a polygon P such that V(P) is homotopy equivalent to S. Furthermore, for various concrete topological spaces T, we describe instances I of the art gallery problem such that V(I) is homeomorphic to T.
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published
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Journal / series
Volume
71 (3)
Pages / Article No.
1092 - 1130
Publisher
Springer
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Software
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Subject
Computational geometry; Art gallery problem; Topological universality
Organisational unit
03457 - Welzl, Emo (emeritus) / Welzl, Emo (emeritus)
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