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- W4287686009 abstract "We consider the construction of a polygon $P$ with $n$ vertices whose turning angles at the vertices are given by a sequence $A=(alpha_0,ldots, alpha_{n-1})$, $alpha_iin (-pi,pi)$, for $iin{0,ldots, n-1}$. The problem of realizing $A$ by a polygon can be seen as that of constructing a straight-line drawing of a graph with prescribed angles at vertices, and hence, it is a special case of the well studied problem of constructing an emph{angle graph}. In 2D, we characterize sequences $A$ for which every generic polygon $Psubset mathbb{R}^2$ realizing $A$ has at least $c$ crossings, for every $cin mathbb{N}$, and describe an efficient algorithm that constructs, for a given sequence $A$, a generic polygon $Psubset mathbb{R}^2$ that realizes $A$ with the minimum number of crossings. In 3D, we describe an efficient algorithm that tests whether a given sequence $A$ can be realized by a (not necessarily generic) polygon $Psubset mathbb{R}^3$, and for every realizable sequence the algorithm finds a realization." @default.
- W4287686009 created "2022-07-26" @default.
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- W4287686009 date "2020-08-24" @default.
- W4287686009 modified "2023-09-24" @default.
- W4287686009 title "Polygons with Prescribed Angles in 2D and 3D" @default.
- W4287686009 doi "https://doi.org/10.48550/arxiv.2008.10192" @default.
- W4287686009 hasPublicationYear "2020" @default.
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