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• W3124720285 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 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.
• W3124720285 created "2021-02-01" @default.
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• W3124720285 date "2020-01-01" @default.
• W3124720285 modified "2023-09-23" @default.
• W3124720285 title "Polygons with Prescribed Angles in 2D and 3D" @default.
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• W3124720285 doi "https://doi.org/10.1007/978-3-030-68766-3_11" @default.
• W3124720285 hasPublicationYear "2020" @default.
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