Force-Directed Lombardi-Style Graph Drawing

  • Roman Chernobelskiy
  • Kathryn I. Cunningham
  • Michael T. Goodrich
  • Stephen G. Kobourov
  • Lowell Trott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)

Abstract

A Lombardi drawing of a graph is one in which vertices are represented as points, edges are represented as circular arcs between their endpoints, and every vertex has perfect angular resolution (equal angles between consecutive edges, as measured by the tangents to the circular arcs at the vertex). We describe two algorithms that create “Lombardi-style” drawings (which we also call near-Lombardi drawings), in which all edges are still circular arcs, but some vertices may not have perfect angular resolution. Both of these algorithms take a force-directed, spring-embedding approach, with one using forces at edge tangents to produce curved edges and the other using dummy vertices on edges for this purpose. As we show, these approaches produce near-Lombardi drawings, with one being slightly better at achieving near-perfect angular resolution and the other being slightly better at balancing edge placements.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Roman Chernobelskiy
    • 1
  • Kathryn I. Cunningham
    • 1
  • Michael T. Goodrich
    • 2
  • Stephen G. Kobourov
    • 1
  • Lowell Trott
    • 2
  1. 1.Department of Computer ScienceUniversity of ArizonaTucsonUSA
  2. 2.Department of Computer ScienceUniversity of CaliforniaIrvineUSA

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