A Framework for Drawing Planar Graphs with Curves and Polylines

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...

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Bibliographic Details
Published in:Journal of algorithms Vol. 37; no. 2; pp. 399 - 421
Main Authors: Goodrich, Michael T., Wagner, Christopher G.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.11.2000
Elsevier
Subjects:
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Graph construction
Planar graph
Worst case method
Asymptotic behavior
Curve
Asymptotic optimality
Graph theory
Aspect ratio
Algorithm
Complexity
Bézier curve
Optimal solution
Aesthetics
ISSN:0196-6774, 1090-2678
Online Access:Get full text
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Description
Summary: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.
ISSN:0196-6774
1090-2678
DOI:10.1006/jagm.2000.1115