Trade-Offs in Planar Polyline Drawings
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.
KeywordsPlanar Graph Angular Resolution Expansion Phase Grid Line Primary Vertex
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- 7.CircuitLogix, https://www.circuitlogix.com/ (accessed June 03, 2014)
- 8.ConceptDraw: http://www.conceptdraw.com/ (accessed June 03, 2014)
- 17.Schnyder, W.: Embedding planar graphs on the grid. In: Proceedings of ACM-SIAM SODA, January 22-24, pp. 138–148. ACM (1990)Google Scholar
- 18.SmartDraw Software, LLC, http://www.smartdraw.com/ (accessed June 03, 2014)