Representing Directed Trees as Straight Skeletons

Aichholzer, Oswin and Biedl, Therese and Hackl, Thomas and Held, Martin and Huber, Stefan and Palfrader, Peter and Vogtenhuber, Birgit (2015) Representing Directed Trees as Straight Skeletons. In: Graph Drawing and Network Visualization: 23rd International Symposium, GD 2015, September 24-26, 2015, Los Angeles, CA, USA , pp. 335-347 (Official URL: http://dx.doi.org/10.1007/978-3-319-27261-0_28).

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Abstract

The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.

Item Type:Conference Paper
Classifications:G Algorithms and Complexity > G.560 Geometry
Z Theory > Z.250 Geometry
ID Code:1500

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References

Aichholzer, O., Aurenhammer, F.: Straight skeletons for general polygonal figures in the plane. In: Samoilenko, A. (ed.) Voronoi’s Impact on Modern Sciences II, vol. 21, pp. 7–21. Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, Ukraine (1998)

Aichholzer, O., Aurenhammer, F., Alberts, D., Gärtner, B.: A novel type of skeleton for polygons. J. Univ. Comput. Sci. 1(12), 752–761 (1995)

Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., Vogtenhuber, B.: Representing directed trees as straight skeletons [cs.CG] (2015). http://​arxiv.​org/​abs/​1508.​01076

Aichholzer, O., Cheng, H., Devadoss, S.L., Hackl, T., Huber, S., Li, B., Risteski, A.: What makes a tree a straight skeleton? In: Proceedings of the 24th Canadian Conference on Computational Geometry, (CCCG 2012), pp. 253–258. Charlottetown, PE, Canada (2012)

Biedl, T., Held, M., Huber, S.: Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: Gavrilova, M., Vyatkina, K. (eds.) Proceedings of the 10th International Symposium on Voronoi Diagrams in Science & Engineering (ISVD 2013), pp. 37–46. IEEE Computer Society, Saint Petersburg, Russia (2013)

Chalopin, J., Gonçalves, D.: Every planar graph is the intersection graph of segments in the plane (Extended Abstract). In: Proceedings of 41st Annual ACM Symposium Theory Computing (STOC 2009), pp. 631–638. ACM, Bethesda, MD, USA (2009)

Di Battista, G., Lenhart, W., Liotta, G.: Proximity drawability: a survey. In: Tamassia, R., Tollis, I.G. (eds.) GD ’94. LNCS, vol. 894, pp. 328–339. Springer, Princeton, NJ, USA (1995)

Dillencourt, M.B., Smith, W.D.: Graph-theoretical conditions for inscribability and delaunay realizability. Discrete Math. 161(1–3), 63–77 (1996)

Eppstein, D., Erickson, J.: Raising roofs, crashing cycles, and playing pool: applications of a data structure for finding pairwise interactions. Discrete Comput. Geom. 22(4), 569–592 (1999)

Huber, S., Held, M.: A fast straight-skeleton algorithm based on generalized motorcycle graphs. Int. J. Comput. Geom. Appl. 22(5), 471–498 (2012)

Liotta, G., Lubiw, A., Meijer, H., Whitesides, S.: The rectangle of influence drawability problem. Comput. Geom. 10(1), 1–22 (1998)

Liotta, G., Meijer, H.: Voronoi drawings of trees. Comput. Geom. 24(3), 147–178 (2003)