Drawing Trees with Perfect Angular Resolution and Polynomial Area

Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G. Kobourov, Martin Nöllenburg

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We study methods for drawing trees with perfect angular resolution, i. e., with angles at each node v equal to 2π /d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.

Original languageEnglish (US)
Pages (from-to)157-182
Number of pages26
JournalDiscrete and Computational Geometry
Volume49
Issue number2
DOIs
StatePublished - Jan 1 2013

Keywords

  • Circular-arc drawings
  • Lombardi drawings
  • Perfect angular resolution
  • Polynomial area
  • Straight-line drawings
  • Tree drawings

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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