## Multi-dimensional Orthogonal Graph Drawing with Small Boxes(Extended Abstract)
Wood, David R.
(1999)
Full text not available from this repository. ## AbstractIn this paper we investigate the general position model for the drawing of arbitrary degree graphs in the D-dimensional (D \ge 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane. We show that for D \ge 3, given an arbitrary layout and initial edge routing a crossing-free orthogonal drawing can be determined. We distinguish two types of algorithms. Our layout-based algorithm, given an arbitrary fixed layout, determines a degree-restricted orthogonal drawing with each vertex having aspect ratio two. Using a balanced layout this algorithm establishes improved bounds on the size of vertices for 2-D and 3-D drawings. Our routing-based algorithm produces 2-degree-restricted 3-D orthogonal drawings. One advantage of our approach in 3-D is that edges are typically routed on each face of a vertex; hence the produced drawings are more truly three-dimensional than those produced by some existing algorithms.
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