Visibility Graph: A Simple Proof of Staircase Equivalence of Polygons
نویسنده
چکیده
In this paper we present a very simple proof of the following result due to Abello et al [5], concerning the visibility graphs of simple polygons. The result says that the visibility graph of any simple nondegenerate polygon is isomorphic to the visibility graph of some simple staircase polygon. As a result of the above proof we also give an O(n log n) time algorithm for the following problem: Given an n-sided simple polygon P find a simple staircase polygon P ′ whose visibility map is isomorphic to that of P .
منابع مشابه
Visibility Graphs of Staircase Polygons and the Weak Bruhat Order, I: from Visibility Graphs to Maximal Chains
The recognition problem for visibility graphs of simple polygons is not known to be in NP, nor is it known to be NP-hard. It is, however, known to be in PSPACE. Further, every such visibility graph can be dismantled as a sequence of visibility graphs of convex fans. Any nondegenerate configuration of n points can be associated with a maximal chain in the weak Bruhat order of the symmetric group...
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