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We prove that this factor is the same <jats:italic>on average<\/jats:italic> (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as <jats:italic>Voronoi path<\/jats:italic>), and extend the results to all dimensions, generalizing Voronoi paths to <jats:italic>Voronoi scapes<\/jats:italic>.<\/jats:p>","DOI":"10.1007\/s00454-024-00660-y","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T15:04:46Z","timestamp":1717513486000},"page":"490-499","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Average and Expected Distortion of Voronoi Paths and Scapes"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9823-6833","authenticated-orcid":false,"given":"Herbert","family":"Edelsbrunner","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0659-3201","authenticated-orcid":false,"given":"Anton","family":"Nikitenko","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"key":"660_CR1","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1137\/0216006","volume":"16","author":"F Aurenhammer","year":"1987","unstructured":"Aurenhammer, F.: Power diagrams: properties, algorithms and applications. 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