Polar coordinate drawing of planar graphs with good angular resolution

Christian A. Duncan, Stephen G Kobourov

Research output: Chapter in Book/Report/Conference proceedingChapter


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, (formula presented) edge separation, (formula presented) drawing area and (formula presented) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of (formula presented), 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point resolution and edge separation are parameters that can be modified to achieve different types of drawings and drawing areas. In particular, for the same parameters as the CRA algorithm (unit bend-point resolution and (formula presented) edge separation), the PRA algorithm creates a drawing of size (formula presented).

Original languageEnglish (US)
Title of host publicationGraph Algorithms and Applications 4
PublisherWorld Scientific Publishing Co.
Number of pages24
ISBN (Print)9789812773296, 9812568441, 9789812568441
StatePublished - Jan 1 2006

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Duncan, C. A., & Kobourov, S. G. (2006). Polar coordinate drawing of planar graphs with good angular resolution. In Graph Algorithms and Applications 4 (pp. 311-334). World Scientific Publishing Co.. https://doi.org/10.1142/9789812773296_0015