Polar coordinate drawing of planar graphs with good angular resolution

Christian A. Duncan, Stephen G. Kobourov

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms for constructing it. The main advantage of the polar representation is that it allows independent control over grid size and bend positions. We first describe a standard (Cartesian) representation algorithm, CRA, which we then modify to obtain a polar representation algorithm, PRA. In both algorithms we are concerned with the following drawing criteria: angular resolution, bends per edge, vertex resolution, bend-point resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, √2/2 edge separation, 5n x 5n/2 drawing area and 1/2d(v) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of π/4d(v), 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point resolution and edge separation are parameters that can be modi.ed to achieve di.erent types of drawings and drawing areas. In particular, for the same parameters as the CRA algorithm (unit bend-point resolution and √2/2 edge separation), the PRA algorithm creates a drawing of size 9n x 9n/2.

Original languageEnglish (US)
Pages (from-to)311-333
Number of pages23
JournalJournal of Graph Algorithms and Applications
Issue number4
StatePublished - 2003

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Computer Science Applications
  • Geometry and Topology
  • Computational Theory and Mathematics


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