---
OA_type: closed access
_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.
article_processing_charge: No
article_type: original
author:
- first_name: Ho
  full_name: Cheng, Ho
  last_name: Cheng
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
citation:
  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>
  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>
  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>.
  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.
  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>.
  short: H. Cheng, H. Edelsbrunner, Computational Geometry 26 (2003) 173–192.
date_created: 2018-12-11T12:06:20Z
date_published: 2003-10-01T00:00:00Z
date_updated: 2026-05-06T08:12:09Z
day: '01'
doi: 10.1016/S0925-7721(02)00124-4
extern: '1'
intvolume: '        26'
issue: '2'
keyword:
- Computational geometry
- Differential geometry
- Skin curves
- Voronoi diagrams
- Delaunay triangulations
- Filtrations
- Disks
- Hyperbolas
- Area
- Perimeter
- Derivatives
language:
- iso: eng
month: '10'
oa_version: None
page: 173 - 192
publication: Computational Geometry
publication_status: published
publisher: Elsevier
publist_id: '2135'
quality_controlled: '1'
status: public
title: Area, perimeter and derivatives of a skin curve
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 26
year: '2003'
...