A note on 3D orthogonal drawings with direction constrained edges

摘要

The recent interest in three-dimensional graph drawing has been motivating studies on how to extend two-dimensional techniques to higher dimensions. A common 2D approach for computing an orthogonal drawing separates the task of defining the shape of the drawing from the task of computing its coordinates. First results towards finding a three-dimensional counterpart of this approach are presented by G. Di Battista, et al. [Graph Drawing (Proc. GD'OO), Lecture Notes in Comput. Sci., vol. 1984, Springer, Berlin, 2001; Theoret. Comput. Sci. 289 (2002) 897], where characterizations of orthogonal representations of paths and cycles are studied. In this paper we show that the characterization for cycles given by G. Di Battista, et al. [Theoret. Comput. Sci. 289 (2002) 897] does not immediately extend to even seemingly simple graphs.