Polygons with Prescribed Angles in 2D and 3D

Alon Efrat, Radoslav Fulek, Stephen Kobourov, Csaba D. Tóth

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationGraph Drawing and Network Visualization - 28th International Symposium, GD 2020, Revised Selected Papers
EditorsDavid Auber, Pavel Valtr
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783030687656
StatePublished - 2020
Event28th International Symposium on Graph Drawing and Network Visualization, GD 2020 - Virtual, Online
Duration: Sep 16 2020Sep 18 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12590 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Symposium on Graph Drawing and Network Visualization, GD 2020
CityVirtual, Online


  • Angle graph
  • Crossing number
  • Polygon
  • Spherical polygon

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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