# Polygons with Prescribed Angles in 2D and 3D

We consider the construction of a polygon P with n vertices whose turning angles at the vertices are given by a sequence A=(α_0,…, α_n-1), α_i∈ (-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⊂ℝ^2 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⊂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 P⊂ℝ^3, and for every realizable sequence the algorithm finds a realization.

## Authors

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• 10 publications
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• 24 publications
• ### Quadrilateral meshes for PSLGs

We prove that every planar straight line graph with n vertices has a con...
07/20/2020 ∙ by Christopher J. Bishop, et al. ∙ 0

• ### Nonobtuse triangulations of PSLGs

We show that any planar straight line graph (PSLG) with n vertices has a...
07/20/2020 ∙ by Christopher J. Bishop, et al. ∙ 0

• ### Drawing Graphs with Circular Arcs and Right-Angle Crossings

In a RAC drawing of a graph, vertices are represented by points in the p...
03/10/2020 ∙ by Steven Chaplick, et al. ∙ 0

• ### Angles of Arc-Polygons and Lombardi Drawings of Cacti

We characterize the triples of interior angles that are possible in non-...
07/08/2021 ∙ by David Eppstein, et al. ∙ 0

• ### Efficient constructions of the Prefer-same and Prefer-opposite de Bruijn sequences

The greedy Prefer-same de Bruijn sequence construction was first present...
10/15/2020 ∙ by Evan Sala, et al. ∙ 0

• ### Neural Network Based Reconstruction of a 3D Object from a 2D Wireframe

We propose a new approach for constructing a 3D representation from a 2D...
07/14/2010 ∙ by Kyle Johnson, et al. ∙ 0