---
_id: '3997'
abstract:
- lang: eng
  text: We combine topological and geometric methods to construct a multi-resolution
    data structure for functions over two-dimensional domains. Starting with the Morse-Smale
    complex, we construct a topological hierarchy by progressively canceling critical
    points in pairs. Concurrently, we create a geometric hierarchy by adapting the
    geometry to the changes in topology. The data structure supports mesh traversal
    operations similarly to traditional multi-resolution representations.
acknowledgement: This work was performed under the auspices of the U. S. Department
  of Energy by University of California Lawrence Livermore National Laboratory under
  contract No. W-7405-Eng-48. H. Edelsbrunner is partially supported by the National
  Science Foundation (NFS) under grants EIA-99-72879 and CCR-00-86013. B. Hamann is
  supported by the NSF under contract ACI 9624034, through the LSSDSV program under
  contract ACI 9982251, and through the NPACI; the National Institute of Mental Health
  and the NSF under contract NIMH 2 P20 MH60975-06A2; the Lawrence Livermore National
  Laboratory under ASCI ASAP Level-2 Memorandum Agreement B347878 and under Memorandum
  Agreement B503159.
article_processing_charge: No
author:
- first_name: Peer
  full_name: Bremer, Peer
  last_name: Bremer
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Bernd
  full_name: Hamann, Bernd
  last_name: Hamann
- first_name: Valerio
  full_name: Pascucci, Valerio
  last_name: Pascucci
citation:
  ama: 'Bremer P, Edelsbrunner H, Hamann B, Pascucci V. A multi-resolution data structure
    for two-dimensional Morse-Smale functions. In: <i>Proceedings of the 14th IEEE
    Conference on Visualization </i>. IEEE; 2003:139-146. doi:<a href="https://doi.org/10.1109/VISUAL.2003.1250365">10.1109/VISUAL.2003.1250365</a>'
  apa: 'Bremer, P., Edelsbrunner, H., Hamann, B., &#38; Pascucci, V. (2003). A multi-resolution
    data structure for two-dimensional Morse-Smale functions. In <i>Proceedings of
    the 14th IEEE Conference on Visualization </i> (pp. 139–146). Seattle, WA, USA
    : IEEE. <a href="https://doi.org/10.1109/VISUAL.2003.1250365">https://doi.org/10.1109/VISUAL.2003.1250365</a>'
  chicago: Bremer, Peer, Herbert Edelsbrunner, Bernd Hamann, and Valerio Pascucci.
    “A Multi-Resolution Data Structure for Two-Dimensional Morse-Smale Functions.”
    In <i>Proceedings of the 14th IEEE Conference on Visualization </i>, 139–46. IEEE,
    2003. <a href="https://doi.org/10.1109/VISUAL.2003.1250365">https://doi.org/10.1109/VISUAL.2003.1250365</a>.
  ieee: P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, “A multi-resolution
    data structure for two-dimensional Morse-Smale functions,” in <i>Proceedings of
    the 14th IEEE Conference on Visualization </i>, Seattle, WA, USA , 2003, pp. 139–146.
  ista: 'Bremer P, Edelsbrunner H, Hamann B, Pascucci V. 2003. A multi-resolution
    data structure for two-dimensional Morse-Smale functions. Proceedings of the 14th
    IEEE Conference on Visualization . VIS: IEEE Visualization, 139–146.'
  mla: Bremer, Peer, et al. “A Multi-Resolution Data Structure for Two-Dimensional
    Morse-Smale Functions.” <i>Proceedings of the 14th IEEE Conference on Visualization
    </i>, IEEE, 2003, pp. 139–46, doi:<a href="https://doi.org/10.1109/VISUAL.2003.1250365">10.1109/VISUAL.2003.1250365</a>.
  short: P. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci, in:, Proceedings of the
    14th IEEE Conference on Visualization , IEEE, 2003, pp. 139–146.
conference:
  end_date: 2003-10-24
  location: 'Seattle, WA, USA '
  name: 'VIS: IEEE Visualization'
  start_date: 2003-10-19
date_created: 2018-12-11T12:06:21Z
date_published: 2003-08-01T00:00:00Z
date_updated: 2024-02-27T11:12:50Z
day: '01'
doi: 10.1109/VISUAL.2003.1250365
extern: '1'
language:
- iso: eng
month: '08'
oa_version: None
page: 139 - 146
publication: 'Proceedings of the 14th IEEE Conference on Visualization '
publication_identifier:
  isbn:
  - '0780381203'
publication_status: published
publisher: IEEE
publist_id: '2131'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A multi-resolution data structure for two-dimensional Morse-Smale functions
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '2003'
...