Drawing Trees with Perfect Angular Resolution and Polynomial Area

Abstract

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, v, equal to 2p=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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2010
Accession Number
ADA530802

Entities

People

  • Christian A. Duncan
  • David Eppstein
  • Martin Nollenburg
  • Michael T. Goodrich
  • Stephen G. Kobourov

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Artificial Intelligence
  • Computer Science
  • Computers
  • Construction
  • Containers
  • Crossings
  • Decomposition
  • Diameters
  • Embedding
  • Geometry
  • Lepidoptera
  • Polynomials
  • Software Development
  • Trees (Data Structures)
  • Universities

Readers

  • Graph Algorithms and Convex Optimization.
  • Image Processing and Computer Vision.