TradeOffs in Planar Polyline DrawingsDurocher, Stephane and Mondal, Debajyoti (2014) TradeOffs in Planar Polyline Drawings. In: Graph Drawing 22nd International Symposium, GD 2014, September 2426, 2014 , pp. 306318(Official URL: http://dx.doi.org/10.1007/9783662458037_26). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783662458037_26
AbstractAngular resolution, area and the number of bends are some important aesthetic criteria of a polyline drawing. Although tradeoffs among these criteria have been examined over the past decades, many of these tradeoffs 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 tradeoff between the area and angular resolution for 2bend polyline drawings of any given planar graph. Specifically, for any given nvertex 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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