Area, perimeter and derivatives of a skin curve Journal Article


Author(s): Cheng, Ho-Lun; Edelsbrunner, Herbert
Article Title: Area, perimeter and derivatives of a skin curve
Affiliation
Abstract: 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.
Journal Title: Computational Geometry: Theory and Applications
Volume: 26
Issue 2
ISSN: 0925-7721
Publisher: Elsevier  
Date Published: 2003-10-01
Start Page: 173
End Page: 192
Copyright Statement: Computational geometry; Differential geometry; Skin curves; Voronoi diagrams; Delaunay triangulations; Filtrations; Disks; Hyperbolas; Area; Perimeter; Derivatives
Sponsor: 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.
DOI: 10.1016/S0925-7721(02)00124-4
Open access: no
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