---
_id: '4028'
abstract:
- lang: eng
  text: Efficient algorithms are described for computing topological, combinatorial,
    and metric properties of the union of finitely many spherical balls in R(d) These
    algorithms are based on a simplicial complex dual to a decomposition of the union
    of balls using Voronoi cells, and on short inclusion-exclusion formulas derived
    from this complex. The algorithms are most relevant in R(3) where unions of finitely
    many balls are commonly used as models of molecules.
acknowledgement: This work is supported by the National Science Foundation, under
  Grant ASC-9200301, and the Alan T. Waterman award, Grant CCR-9118874. Any opinions,
  findings, conclusions, or recommendations expressed in this publication are those
  of the author and do not necessarily reflect the view of the National Science Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
citation:
  ama: Edelsbrunner H. The union of balls and its dual shape. <i>Discrete &#38; Computational
    Geometry</i>. 1995;13(1):415-440. doi:<a href="https://doi.org/10.1007/BF02574053">10.1007/BF02574053</a>
  apa: Edelsbrunner, H. (1995). The union of balls and its dual shape. <i>Discrete
    &#38; Computational Geometry</i>. Springer. <a href="https://doi.org/10.1007/BF02574053">https://doi.org/10.1007/BF02574053</a>
  chicago: Edelsbrunner, Herbert. “The Union of Balls and Its Dual Shape.” <i>Discrete
    &#38; Computational Geometry</i>. Springer, 1995. <a href="https://doi.org/10.1007/BF02574053">https://doi.org/10.1007/BF02574053</a>.
  ieee: H. Edelsbrunner, “The union of balls and its dual shape,” <i>Discrete &#38;
    Computational Geometry</i>, vol. 13, no. 1. Springer, pp. 415–440, 1995.
  ista: Edelsbrunner H. 1995. The union of balls and its dual shape. Discrete &#38;
    Computational Geometry. 13(1), 415–440.
  mla: Edelsbrunner, Herbert. “The Union of Balls and Its Dual Shape.” <i>Discrete
    &#38; Computational Geometry</i>, vol. 13, no. 1, Springer, 1995, pp. 415–40,
    doi:<a href="https://doi.org/10.1007/BF02574053">10.1007/BF02574053</a>.
  short: H. Edelsbrunner, Discrete &#38; Computational Geometry 13 (1995) 415–440.
date_created: 2018-12-11T12:06:31Z
date_published: 1995-12-01T00:00:00Z
date_updated: 2022-06-27T08:14:48Z
day: '01'
doi: 10.1007/BF02574053
extern: '1'
intvolume: '        13'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/article/10.1007/BF02574053
month: '12'
oa: 1
oa_version: Published Version
page: 415 - 440
publication: Discrete & Computational Geometry
publication_identifier:
  issn:
  - 0179-5376
publication_status: published
publisher: Springer
publist_id: '2095'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The union of balls and its dual shape
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 13
year: '1995'
...