Abstract
We 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 n- vertex planar graph in an O(n) × O(n) grid using polylines that have at most two bends per edge and asymptotically-optimal worst-case angular resolution. More significantly, we show how to adapt this algorithm to draw any n-vertex planar graph using cubic Bézier curves, with all vertices and control points placed within an O(n) × 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.
Work by this author is supported in part by the U.S. Army Research Office under Grant DAAH04-96-1-0013 and by NSF under Grant CCR-96-25289.
Work by this author is supported in part by ONR grant N00014-96-1-0829.
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© 1998 Springer-Verlag Berlin Heidelberg
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Goodrich, M.T., Wagner, C.G. (1998). A Framework for Drawing Planar Graphs with Curves and Polylines. In: Whitesides, S.H. (eds) Graph Drawing. GD 1998. Lecture Notes in Computer Science, vol 1547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37623-2_12
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DOI: https://doi.org/10.1007/3-540-37623-2_12
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