Geometry of planar graphs with angles
SCG '86 Proceedings of the second annual symposium on Computational geometry
On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Angles of Planar Triangular Graphs
SIAM Journal on Discrete Mathematics
The techniques of Komolgorov and Bardzin for three-dimensional orthogonal graph drawings
Information Processing Letters
New results on drawing angle graphs
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Two Algorithms for Three Dimensional Orthogonal Graph Drawing
GD '96 Proceedings of the Symposium on Graph Drawing
Incremental Orthogonal Graph Drawing in Three Dimensions
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
An Algorithm for Three-Dimensional Orthogonal Graph Drawing
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Orthogonal 3D Shapes of Theta Graphs
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Orthogonal Drawings of Cycles in 3D Space (Extended Abstract)
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
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We determine the reachability properties of the embeddings in R3 of a directed path, in the graph theoretic sense, whose edges have each been assigned a desired direction (East, West, North, South, Up, or Down) but no length. We ask which points of R3 can be reached by the terminus of an embedding of such a path, by choosing appropriate positive lengths for the edges, if the embedded path starts at the origin, does not intersect itself, and respects the directions assigned to its edges. This problem arises in the context of extending planar graph embedding techniques and VLSI rectilinear layout techniques from 2D to 3D. We give combinatorial characterizations of reachability that yield linear time recognition and layout algorithms.