---
OA_type: free access
_id: '3984'
abstract:
- lang: eng
  text: We combine topological and geometric methods to construct a multiresolution
    representation for a function over a two-dimensional domain. In a preprocessing
    stage, we create the Morse-Smale complex of the function and progressively simplify
    its topology by cancelling pairs of critical points. Based on a simple notion
    of dependency among these cancellations, we construct a hierarchical data structure
    supporting traversal and reconstruction operations similarly to traditional geometry-based
    representations. We use this data structure to extract topologically valid approximations
    that satisfy error bounds provided at runtime.
article_processing_charge: No
article_type: original
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 topological hierarchy for
    functions on triangulated surfaces. <i>IEEE Transactions on Visualization and
    Computer Graphics</i>. 2004;10(4):385-396. doi:<a href="https://doi.org/10.1109/TVCG.2004.3">10.1109/TVCG.2004.3</a>
  apa: Bremer, P., Edelsbrunner, H., Hamann, B., &#38; Pascucci, V. (2004). A topological
    hierarchy for functions on triangulated surfaces. <i>IEEE Transactions on Visualization
    and Computer Graphics</i>. IEEE. <a href="https://doi.org/10.1109/TVCG.2004.3">https://doi.org/10.1109/TVCG.2004.3</a>
  chicago: Bremer, Peer, Herbert Edelsbrunner, Bernd Hamann, and Valerio Pascucci.
    “A Topological Hierarchy for Functions on Triangulated Surfaces.” <i>IEEE Transactions
    on Visualization and Computer Graphics</i>. IEEE, 2004. <a href="https://doi.org/10.1109/TVCG.2004.3">https://doi.org/10.1109/TVCG.2004.3</a>.
  ieee: P. Bremer, H. Edelsbrunner, B. Hamann, and V. Pascucci, “A topological hierarchy
    for functions on triangulated surfaces,” <i>IEEE Transactions on Visualization
    and Computer Graphics</i>, vol. 10, no. 4. IEEE, pp. 385–396, 2004.
  ista: Bremer P, Edelsbrunner H, Hamann B, Pascucci V. 2004. A topological hierarchy
    for functions on triangulated surfaces. IEEE Transactions on Visualization and
    Computer Graphics. 10(4), 385–396.
  mla: Bremer, Peer, et al. “A Topological Hierarchy for Functions on Triangulated
    Surfaces.” <i>IEEE Transactions on Visualization and Computer Graphics</i>, vol.
    10, no. 4, IEEE, 2004, pp. 385–96, doi:<a href="https://doi.org/10.1109/TVCG.2004.3">10.1109/TVCG.2004.3</a>.
  short: P. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci, IEEE Transactions on
    Visualization and Computer Graphics 10 (2004) 385–396.
das_tickbox: '1'
date_created: 2018-12-11T12:06:16Z
date_published: 2004-07-01T00:00:00Z
date_updated: 2026-07-01T11:01:44Z
day: '01'
doi: 10.1109/TVCG.2004.3
extern: '1'
external_id:
  pmid:
  - '18579967'
intvolume: '        10'
issue: '4'
language:
- iso: eng
month: '07'
oa_version: None
page: 385 - 396
pmid: 1
publication: IEEE Transactions on Visualization and Computer Graphics
publication_identifier:
  eissn:
  - 1941-0506
  issn:
  - 1077-2626
publication_status: published
publisher: IEEE
publist_id: '2139'
status: public
title: A topological hierarchy for functions on triangulated surfaces
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 10
year: '2004'
...