---
_id: '4029'
abstract:
- lang: eng
  text: A general and direct method for computing the Betti numbers of a finite simplicial
    complex in Bd is given. This method is complete for d less than or equal to 3,
    where versions of this method run in time O(n alpha(n)) and O(n), n the number
    of simplices. An implementation of the algorithm is applied to alpha shapes, which
    is a novel geometric modeling tool.
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 authors
  and do not necessarily reflect the view of the National Science Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Cecil
  full_name: Delfinado, Cecil
  last_name: Delfinado
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
citation:
  ama: Delfinado C, Edelsbrunner H. An incremental algorithm for Betti numbers of
    simplicial complexes on the 3-sphere. <i>Computer Aided Geometric Design</i>.
    1995;12(7):771-784. doi:<a href="https://doi.org/10.1016/0167-8396(95)00016-Y">10.1016/0167-8396(95)00016-Y</a>
  apa: Delfinado, C., &#38; Edelsbrunner, H. (1995). An incremental algorithm for
    Betti numbers of simplicial complexes on the 3-sphere. <i>Computer Aided Geometric
    Design</i>. Elsevier. <a href="https://doi.org/10.1016/0167-8396(95)00016-Y">https://doi.org/10.1016/0167-8396(95)00016-Y</a>
  chicago: Delfinado, Cecil, and Herbert Edelsbrunner. “An Incremental Algorithm for
    Betti Numbers of Simplicial Complexes on the 3-Sphere.” <i>Computer Aided Geometric
    Design</i>. Elsevier, 1995. <a href="https://doi.org/10.1016/0167-8396(95)00016-Y">https://doi.org/10.1016/0167-8396(95)00016-Y</a>.
  ieee: C. Delfinado and H. Edelsbrunner, “An incremental algorithm for Betti numbers
    of simplicial complexes on the 3-sphere,” <i>Computer Aided Geometric Design</i>,
    vol. 12, no. 7. Elsevier, pp. 771–784, 1995.
  ista: Delfinado C, Edelsbrunner H. 1995. An incremental algorithm for Betti numbers
    of simplicial complexes on the 3-sphere. Computer Aided Geometric Design. 12(7),
    771–784.
  mla: Delfinado, Cecil, and Herbert Edelsbrunner. “An Incremental Algorithm for Betti
    Numbers of Simplicial Complexes on the 3-Sphere.” <i>Computer Aided Geometric
    Design</i>, vol. 12, no. 7, Elsevier, 1995, pp. 771–84, doi:<a href="https://doi.org/10.1016/0167-8396(95)00016-Y">10.1016/0167-8396(95)00016-Y</a>.
  short: C. Delfinado, H. Edelsbrunner, Computer Aided Geometric Design 12 (1995)
    771–784.
date_created: 2018-12-11T12:06:32Z
date_published: 1995-11-01T00:00:00Z
date_updated: 2022-06-24T09:49:32Z
day: '01'
doi: 10.1016/0167-8396(95)00016-Y
extern: '1'
intvolume: '        12'
issue: '7'
language:
- iso: eng
main_file_link:
- url: https://www.sciencedirect.com/science/article/pii/016783969500016Y?via%3Dihub
month: '11'
oa_version: None
page: 771 - 784
publication: Computer Aided Geometric Design
publication_identifier:
  issn:
  - 0167-8396
publication_status: published
publisher: Elsevier
publist_id: '2096'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 12
year: '1995'
...