A Framework for Drawing Planar Graphs with Curves and Polylines
✍ Scribed by Michael T. Goodrich; Christopher G. Wagner
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 204 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0196-6774
No coin nor oath required. For personal study only.
✦ Synopsis
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 Ž . Ž . 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 Bezier curves, with all vertices and control points placed within an Ž .
Ž . O n = O n integer grid so that the curved edges achieve a curvilinear analogue Ž . of good angular resolution. All of our algorithms run in O n time. ᮊ 2000