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
Three-dimensional orthogonal graph drawing algorithms
Discrete Applied Mathematics
Embedding Problems for Paths with Direction Constrained Edges
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
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
Complexity results for three-dimensional orthogonal graph drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
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Let C be a directed cycle, whose edges have each been assigned a desired direction in 3D (East, West, North, South, Up, or Down) but no length. We say that C is a shape cycle. We consider the following problem. Does there exist an orthogonal drawing Γ of C in 3D such that each edge of Γ respects the direction assigned to it and such that Γ does not intersect itself? If the answer is positive, we say that C is simple. This problem arises in the context of extending orthogonal graph drawing techniques and VLSI rectilinear layout techniques from 2D to 3D. We give a combinatorial characterization of simple shape cycles that yields linear time recognition and drawing algorithms.