Abstract
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.
Research partially supported by operating grants from the Natural Sciences and Engineering Research Council (NSERC) of Canada, by the project “Algorithms for Large Data Sets: Science and Engineering” of the Italian Ministry of University and Scientific and Technological Research (MURST 40%), and by the project “Geometria Computazionale Robusta con Applicazioni alla Grafica ed a CAD” of the Italian National Research Council (CNR).
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Di Battista, G., Liotta, G., Lubiw, A., Whitesides, S. (2001). Orthogonal Drawings of Cycles in 3D Space. In: Marks, J. (eds) Graph Drawing. GD 2000. Lecture Notes in Computer Science, vol 1984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44541-2_26
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DOI: https://doi.org/10.1007/3-540-44541-2_26
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