{"_id":"3994","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."}],"year":"2003","title":"Area, perimeter and derivatives of a skin curve","date_published":"2003-10-01T00:00:00Z","month":"10","date_updated":"2021-01-12T07:53:43Z","doi":"10.1016/S0925-7721(02)00124-4","date_created":"2018-12-11T12:06:20Z","author":[{"full_name":"Cheng, Ho-Lun","first_name":"Ho","last_name":"Cheng"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Herbert Edelsbrunner","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"type":"journal_article","quality_controlled":0,"acknowledgement":"NSF under grant DMS-98-73945, ARO under grant DAAG55-98-1-0177 and by NSF under grants CCR- 97-12088, EIA-9972879, and CCR-00-86013.","publication":"Computational Geometry: Theory and Applications","status":"public","issue":"2","citation":{"ama":"Cheng H, Edelsbrunner H. Area, perimeter and derivatives of a skin curve. <i>Computational Geometry: Theory and Applications</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>","short":"H. Cheng, H. Edelsbrunner, Computational Geometry: Theory and Applications 26 (2003) 173–192.","mla":"Cheng, Ho, and Herbert Edelsbrunner. “Area, Perimeter and Derivatives of a Skin Curve.” <i>Computational Geometry: Theory and Applications</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>.","ieee":"H. Cheng and H. Edelsbrunner, “Area, perimeter and derivatives of a skin curve,” <i>Computational Geometry: Theory and Applications</i>, vol. 26, no. 2. Elsevier, pp. 173–192, 2003.","apa":"Cheng, H., &#38; Edelsbrunner, H. (2003). Area, perimeter and derivatives of a skin curve. <i>Computational Geometry: Theory and Applications</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>","ista":"Cheng H, Edelsbrunner H. 2003. Area, perimeter and derivatives of a skin curve. Computational Geometry: Theory and Applications. 26(2), 173–192.","chicago":"Cheng, Ho, and Herbert Edelsbrunner. “Area, Perimeter and Derivatives of a Skin Curve.” <i>Computational Geometry: Theory and Applications</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>."},"publication_status":"published","publist_id":"2135","publisher":"Elsevier","page":"173 - 192","day":"01","volume":26,"intvolume":"        26","extern":1}