Publisher
Brown UniversityCitation
Efrat, A., Fulek, R., Kobourov, S., & Tóth, C. D. (2022). Polygons with Prescribed Angles in 2D and 3D. Journal of Graph Algorithms and Applications, 26(3), 363–380.Rights
Copyright © The Author(s). This work is licensed under the terms of the CC-BY license.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We consider the construction of a polygon P with n vertices whose turning angles at the vertices are given by a sequence A = (α0, …, αn−1), αi ∈ (−π, π), for i ∈ {0, …, 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 P ⊂ R2 realizing A has at least c crossings, for every c ∈ N, and describe an efficient algorithm that constructs, for a given sequence A, a generic polygon P ⊂ R2 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 P ⊂ R3, and for every realizable sequence the algorithm finds a realization. © 2022, Brown University. All rights reserved.Note
Open access journalISSN
1526-1719Version
Final published versionae974a485f413a2113503eed53cd6c53
10.7155/jgaa.00599
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Except where otherwise noted, this item's license is described as Copyright © The Author(s). This work is licensed under the terms of the CC-BY license.

