Abstract
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.
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Durocher, S., Mondal, D. (2014). Trade-Offs in Planar Polyline Drawings. In: Duncan, C., Symvonis, A. (eds) Graph Drawing. GD 2014. Lecture Notes in Computer Science, vol 8871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45803-7_26
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DOI: https://doi.org/10.1007/978-3-662-45803-7_26
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