Author(s):

Cheng, HoLun; 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:

09257721

Publisher:

Elsevier

Date Published:

20031001

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 DMS9873945, ARO under grant DAAG559810177 and by NSF under grants CCR 9712088, EIA9972879, and CCR0086013.

DOI: 
10.1016/S09257721(02)001244

Open access: 
no 