TY - CHAP

T1 - Polar coordinate drawing of planar graphs with good angular resolution

AU - Duncan, Christian A.

AU - Kobourov, Stephen G.

N1 - Publisher Copyright:
© 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2006/1/1

Y1 - 2006/1/1

N2 - We present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms for constructing it. The main advantage of the polar representation is that it allows independent control over grid size and bend positions. 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, bend-point resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, (formula presented) edge separation, (formula presented) drawing area and (formula presented) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of (formula presented), 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point 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 bend-point resolution and (formula presented) edge separation), the PRA algorithm creates a drawing of size (formula presented).

AB - We present a novel way to draw planar graphs with good angular resolution. We introduce the polar coordinate representation and describe a family of algorithms for constructing it. The main advantage of the polar representation is that it allows independent control over grid size and bend positions. 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, bend-point resolution, edge separation, and drawing area. The CRA algorithm achieves 1 bend per edge, unit vertex and bend resolution, (formula presented) edge separation, (formula presented) drawing area and (formula presented) angular resolution, where d(v) is the degree of vertex v. The PRA algorithm has an improved angular resolution of (formula presented), 1 bend per edge, and unit vertex resolution. For the PRA algorithm, the bend-point 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 bend-point resolution and (formula presented) edge separation), the PRA algorithm creates a drawing of size (formula presented).

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U2 - 10.1142/9789812773296_0015

DO - 10.1142/9789812773296_0015

M3 - Chapter

AN - SCOPUS:84969667984

SN - 9812568441

SN - 9789812568441

SP - 311

EP - 334

BT - Graph Algorithms and Applications 4

PB - World Scientific Publishing Co.

ER -