Polar Coordinate Drawing of Planar Graphs with Good Angular ResolutionDuncan, Christian A. and Kobourov, Stephen G. (2002) Polar Coordinate Drawing of Planar Graphs with Good Angular Resolution. In: Graph Drawing 9th International Symposium, GD 2001, September 2326, 2001 , pp. 407421(Official URL: http://dx.doi.org/10.1007/3540458484_32). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540458484_32
AbstractWe present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms which use polar representation. The main advantage of using a polar representation is that it allows us to exert independent control over grid size and bend positions. Polar coordinates allow us to specify different vertex resolution, bendpoint resolution and edge separation. We first describe a standard (Cartesian) representation algorithm (CRA) which we then modify to obtain a polar representation algorithm (PRA). In both algorithms we are concerned with the following drawing criteria: angular resolution, bends per edge, vertex resolution, bendpoint resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, $\sqrt{2}/2$ edge separation, $5n \times \frac{5n}{2}$ drawing area and $\frac{1}{2d(v)}$ angular resolution, where $d(v)$ is the degree of vertex $v$. The PRA algorithm has an improved angular resolution of $\frac{\pi}{4d(v)}$, 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bendpoint resolution and edge separation are parameters that can be modified to achieve different types of drawings and drawing areas. In particular, for the same parameters as the CRA algorithm (unit bendpoint resolution and $\sqrt{2}/2$ edge separation), the PRA algorithm creates a drawing of size $9n \times \frac{9n}{2}$.
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