[{"extern":"1","publication":"Computational Geometry","title":"Area, perimeter and derivatives of a skin curve","article_processing_charge":"No","publication_status":"published","volume":26,"year":"2003","day":"01","date_created":"2018-12-11T12:06:20Z","language":[{"iso":"eng"}],"OA_type":"closed access","publisher":"Elsevier","abstract":[{"lang":"eng","text":"The body defined by a finite collection of disks is a subset of the plane bounded by a tangent continuous curve, which we call the skin. We give analytic formulas for the area, the perimeter, the area derivative, and the perimeter derivative of the body. Given the filtrations of the Delaunay triangulation and the Voronoi diagram of the disks, all formulas can be evaluated in time proportional to the number of disks."}],"page":"173 - 192","oa_version":"None","_id":"3994","quality_controlled":"1","keyword":["Computational geometry","Differential geometry","Skin curves","Voronoi diagrams","Delaunay triangulations","Filtrations","Disks","Hyperbolas","Area","Perimeter","Derivatives"],"doi":"10.1016/S0925-7721(02)00124-4","issue":"2","citation":{"chicago":"Cheng, Ho, and Herbert Edelsbrunner. “Area, Perimeter and Derivatives of a Skin Curve.” <i>Computational Geometry</i>. Elsevier, 2003. <a href=\"https://doi.org/10.1016/S0925-7721(02)00124-4\">https://doi.org/10.1016/S0925-7721(02)00124-4</a>.","mla":"Cheng, Ho, and Herbert Edelsbrunner. “Area, Perimeter and Derivatives of a Skin Curve.” <i>Computational Geometry</i>, vol. 26, no. 2, Elsevier, 2003, pp. 173–92, doi:<a href=\"https://doi.org/10.1016/S0925-7721(02)00124-4\">10.1016/S0925-7721(02)00124-4</a>.","ama":"Cheng H, Edelsbrunner H. Area, perimeter and derivatives of a skin curve. <i>Computational Geometry</i>. 2003;26(2):173-192. doi:<a href=\"https://doi.org/10.1016/S0925-7721(02)00124-4\">10.1016/S0925-7721(02)00124-4</a>","ieee":"H. Cheng and H. Edelsbrunner, “Area, perimeter and derivatives of a skin curve,” <i>Computational Geometry</i>, vol. 26, no. 2. Elsevier, pp. 173–192, 2003.","ista":"Cheng H, Edelsbrunner H. 2003. Area, perimeter and derivatives of a skin curve. Computational Geometry. 26(2), 173–192.","short":"H. Cheng, H. Edelsbrunner, Computational Geometry 26 (2003) 173–192.","apa":"Cheng, H., &#38; Edelsbrunner, H. (2003). Area, perimeter and derivatives of a skin curve. <i>Computational Geometry</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0925-7721(02)00124-4\">https://doi.org/10.1016/S0925-7721(02)00124-4</a>"},"date_published":"2003-10-01T00:00:00Z","month":"10","author":[{"full_name":"Cheng, Ho","first_name":"Ho","last_name":"Cheng"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publist_id":"2135","type":"journal_article","status":"public","article_type":"original","intvolume":"        26","date_updated":"2026-05-06T08:12:09Z"}]