--- res: bibo_abstract: - We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Therese foaf_name: Biedl, Therese foaf_surname: Biedl - foaf_Person: foaf_givenName: Martin foaf_name: Held, Martin foaf_surname: Held - foaf_Person: foaf_givenName: Stefan foaf_name: Huber, Stefan foaf_surname: Huber foaf_workInfoHomepage: http://www.librecat.org/personId=4700A070-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-8871-5814 - foaf_Person: foaf_givenName: Dominik foaf_name: Kaaser, Dominik foaf_surname: Kaaser - foaf_Person: foaf_givenName: Peter foaf_name: Palfrader, Peter foaf_surname: Palfrader bibo_doi: 10.1016/j.comgeo.2014.08.006 bibo_issue: '2' bibo_volume: 48 dct_date: 2015^xs_gYear dct_language: eng dct_publisher: Elsevier@ dct_title: Weighted straight skeletons in the plane@ ...