Trade-Offs in Planar Polyline Drawings

  • Stephane Durocher
  • Debajyoti Mondal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)


Angular resolution, area and the number of bends are some important aesthetic criteria of a polyline drawing. Although trade-offs among these criteria have been examined over the past decades, many of these trade-offs are still not known to be optimal. In this paper we give a new technique to compute polyline drawings for planar triangulations. Our algorithm is simple and intuitive, yet implies significant improvement over the known results. We present the first smooth trade-off between the area and angular resolution for 2-bend polyline drawings of any given planar graph. Specifically, for any given n-vertex triangulation, our algorithm computes a drawing with angular resolution r/d(v) at each vertex v, and area f(n,r), for any r ∈ (0,1], where d(v) denotes the degree at v. For r < 0.389 or r > 0.5, f(n,r) is less than the drawing area required by previous algorithms; f(n,r) ranges from 7.12n 2 when r ≤ 0.3 to 32.12n 2 when r = 1.


Planar Graph Angular Resolution Expansion Phase Grid Line Primary Vertex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Stephane Durocher
    • 1
  • Debajyoti Mondal
    • 1
  1. 1.Department of Computer ScienceUniversity of ManitobaCanada

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