A Framework for Drawing Planar Graphs with Curves and PolylinesGoodrich, Michael T. and Wagner, Cristopher G. (1998) A Framework for Drawing Planar Graphs with Curves and Polylines. In: Graph Drawing 6th International Symposium, GD’ 98, August 1315, 1998 , pp. 153166(Official URL: http://dx.doi.org/10.1007/3540376232_12). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540376232_12
AbstractWe describe a unified framework of aesthetic criteria and complexity measures for drawing planar graphs with polylines and curves. This framework includes several visual properties of such drawings, including aspect ratio, vertex resolution, edge length, edge separation, and edge curvature, as well as complexity measures such as vertex and edge representational complexity and the area of the drawing. In addition to this general framework, we present algorithms that operate within this framework. Specifically, we describe an algorithm for drawing any nvertex planar graph in an O(n) \times O(n) grid using polylines that have at most two bends per edge and asymptoticallyoptimal worstcase angular resolution.More significantly, we show how to adapt this algorithm to draw any nvertex planar graph using cubic Bézier curves, with all vertices and control points placed within an O(n) \times O(n) integer grid so that the curved edges achieve a curvilinear analogue of good angular resolution. All of our algorithms run in O(n) time.
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