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 , pp. 335-347(Official URL:

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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

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