{"date_published":"2013-12-01T00:00:00Z","publication_status":"published","month":"12","citation":{"ama":"Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:<a href=\"https://doi.org/10.1109/ISVD.2013.11\">10.1109/ISVD.2013.11</a>","ieee":"T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. <a href=\"https://doi.org/10.1109/ISVD.2013.11\">https://doi.org/10.1109/ISVD.2013.11</a>.","ista":"Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) , , 37–46.","mla":"Biedl, Therese, et al. <i>Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input</i>. IEEE, 2013, pp. 37–46, doi:<a href=\"https://doi.org/10.1109/ISVD.2013.11\">10.1109/ISVD.2013.11</a>.","short":"T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.","apa":"Biedl, T., Held, M., &#38; Huber, S. (2013). Recognizing straight skeletons and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia: IEEE. <a href=\"https://doi.org/10.1109/ISVD.2013.11\">https://doi.org/10.1109/ISVD.2013.11</a>"},"doi":"10.1109/ISVD.2013.11","alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "],"publist_id":"4763","scopus_import":1,"quality_controlled":"1","oa_version":"None","publication_identifier":{"eisbn":["978-0-7695-5037-4 "]},"year":"2013","title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input","language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:56:00Z","conference":{"name":"ISVD: Voronoi Diagrams in Science and Engineering","end_date":"2013-07-10","location":"St. Petersburg, Russia","start_date":"2013-07-08"},"date_created":"2018-12-11T11:56:20Z","publisher":"IEEE","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Martin","full_name":"Held, Martin","last_name":"Held"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","full_name":"Huber, Stefan","first_name":"Stefan"}],"type":"conference","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"37 - 46","day":"01","_id":"2209","status":"public","abstract":[{"lang":"eng","text":"A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skeleton? We show how to reduce this problem to the problem of finding a line that intersects a set of convex polygons. We can find these convex polygons and all such lines in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number of edges of the input graph. We also explain how our approach can be used for recognizing Voronoi diagrams of points, thereby completing a partial solution provided by Ash and Bolker in 1985.\r\n"}]}