## Symmetric Drawings of Series Parallel Digraphs in Three Dimensions

 Seok-Hee Hong, Peter Eades and Jonathan Hillman, Linkless Symmetric Drawings of Series Parallel Digraphs,Computational Geometry: Theory and Applications, 29(3), pp. 191-222, 2004, Elsevier. In this paper,we present a linear time algorithmfor constructing linkless drawings of series parallel digraphswith maximum number of symmetries. Linkless drawing in three dimensions is a natural extension to planar drawing in two dimensions. Symmetry is one of the most important aesthetic criteria in graph drawing. More specifically, we present two algorithms: a symmetry finding algorithm which finds maximum number of three dimensional symmetries, and a drawing algorithm which constructs linkless symmetric drawings of series parallel digraphs in three dimensions. Seok-Hee Hong and Peter Eades,An Algorithm for Finding Three Dimensional Symmetry in Series Parallel Digraphs, Proceeding of ISAAC 2000, Lecture Notes in Computer Science 1969, Springer, pp. 266-277, 2000. Symmetry is one of the most important aesthetic criteria which clearly reveals the structure of the graph. However, previous work on symmetric graph drawing has focused on two dimensions. In this paper, we extend symmetric graph drawing into three dimensions. Symmetry in three dimensions is much richer than that of two dimensions. We present a linear time algorithm for finding maximum number of three dimensional symmetries in series parallel digraphs.

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 Vertical Rotation : Fig2 (a) Animated Gif AVI Horizontal Reflection : Fig2 (b) Animated Gif AVI Inversion : Fig2 (c) Animated Gif AVI Maximum 4k symmetry : Fig2 (d) Animated Gif AVI Maximum symmetry : Fig1 (b) Animated Gif AVI 3D Symmetric Drawing : Fig1 (d) Animated Gif AVI Maximum symmetry Animated Gif AVI Maximum symmetry : Fig1 (b) Animated Gif AVI 10 symmetries