Multi-dimensional Orthogonal Graph Drawing with Small Boxes(Extended Abstract)
Wood, David R. (1999) Multi-dimensional Orthogonal Graph Drawing with Small Boxes(Extended Abstract). In: Graph Drawing 7th International Symposium, GD’99, September 15-19, 1999, Štirín Castle, Czech Republic , pp. 311-322 (Official URL: http://dx.doi.org/10.1007/3-540-46648-7_32).
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In 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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