Recognizing Weakly Simple Polygons

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چکیده

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Recognizing Weakly Simple Polygons

We present an O(n log n)-time algorithm that determines whether a given planar n-gon is weakly simple. This improves upon an O(n log n)-time algorithm by Chang, Erickson, and Xu [5]. Weakly simple polygons are required as input for several geometric algorithms. As such, how to recognize simple or weakly simple polygons is a fundamental question.

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Reconstruction of Weakly Simple Polygons from their Edges

Given n line segments in the plane, do they form the edge set of a weakly simple polygon; that is, can the segment endpoints be perturbed by at most ε, for any ε > 0, to obtain a simple polygon? While the analogous question for simple polygons can easily be answered in O(n logn) time, we show that it is NP-complete for weakly simple polygons. We give O(n)-time algorithms in two special cases: w...

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ژورنال

عنوان ژورنال: Discrete & Computational Geometry

سال: 2017

ISSN: 0179-5376,1432-0444

DOI: 10.1007/s00454-017-9918-3