---
_id: '7952'
abstract:
- lang: eng
  text: "Isomanifolds are the generalization of isosurfaces to arbitrary dimension
    and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued
    smooth function f: ℝ^d → ℝ^(d-n). A natural (and efficient) way to approximate
    an isomanifold is to consider its Piecewise-Linear (PL) approximation based on
    a triangulation \U0001D4AF of the ambient space ℝ^d. In this paper, we give conditions
    under which the PL-approximation of an isomanifold is topologically equivalent
    to the isomanifold. The conditions are easy to satisfy in the sense that they
    can always be met by taking a sufficiently fine triangulation \U0001D4AF. This
    contrasts with previous results on the triangulation of manifolds where, in arbitrary
    dimensions, delicate perturbations are needed to guarantee topological correctness,
    which leads to strong limitations in practice. We further give a bound on the
    Fréchet distance between the original isomanifold and its PL-approximation. Finally
    we show analogous results for the PL-approximation of an isomanifold with boundary. "
alternative_title:
- LIPIcs
article_number: 20:1-20:18
article_processing_charge: No
author:
- first_name: Jean-Daniel
  full_name: Boissonnat, Jean-Daniel
  last_name: Boissonnat
- first_name: Mathijs
  full_name: Wintraecken, Mathijs
  id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
  last_name: Wintraecken
  orcid: 0000-0002-7472-2220
citation:
  ama: 'Boissonnat J-D, Wintraecken M. The topological correctness of PL-approximations
    of isomanifolds. In: <i>36th International Symposium on Computational Geometry</i>.
    Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2020.20">10.4230/LIPIcs.SoCG.2020.20</a>'
  apa: 'Boissonnat, J.-D., &#38; Wintraecken, M. (2020). The topological correctness
    of PL-approximations of isomanifolds. In <i>36th International Symposium on Computational
    Geometry</i> (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2020.20">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>'
  chicago: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
    of PL-Approximations of Isomanifolds.” In <i>36th International Symposium on Computational
    Geometry</i>, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
    <a href="https://doi.org/10.4230/LIPIcs.SoCG.2020.20">https://doi.org/10.4230/LIPIcs.SoCG.2020.20</a>.
  ieee: J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL-approximations
    of isomanifolds,” in <i>36th International Symposium on Computational Geometry</i>,
    Zürich, Switzerland, 2020, vol. 164.
  ista: 'Boissonnat J-D, Wintraecken M. 2020. The topological correctness of PL-approximations
    of isomanifolds. 36th International Symposium on Computational Geometry. SoCG:
    Symposium on Computational Geometry, LIPIcs, vol. 164, 20:1-20:18.'
  mla: Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness
    of PL-Approximations of Isomanifolds.” <i>36th International Symposium on Computational
    Geometry</i>, vol. 164, 20:1-20:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
    2020, doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2020.20">10.4230/LIPIcs.SoCG.2020.20</a>.
  short: J.-D. Boissonnat, M. Wintraecken, in:, 36th International Symposium on Computational
    Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
conference:
  end_date: 2020-06-26
  location: Zürich, Switzerland
  name: 'SoCG: Symposium on Computational Geometry'
  start_date: 2020-06-22
date_created: 2020-06-09T07:24:11Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-02T06:49:16Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2020.20
ec_funded: 1
file:
- access_level: open_access
  checksum: 38cbfa4f5d484d267a35d44d210df044
  content_type: application/pdf
  creator: dernst
  date_created: 2020-06-17T10:13:34Z
  date_updated: 2020-07-14T12:48:06Z
  file_id: '7969'
  file_name: 2020_LIPIcsSoCG_Boissonnat.pdf
  file_size: 1009739
  relation: main_file
file_date_updated: 2020-07-14T12:48:06Z
has_accepted_license: '1'
intvolume: '       164'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: 36th International Symposium on Computational Geometry
publication_identifier:
  isbn:
  - 978-3-95977-143-6
  issn:
  - 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
  record:
  - id: '9649'
    relation: later_version
    status: public
scopus_import: '1'
status: public
title: The topological correctness of PL-approximations of isomanifolds
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 164
year: '2020'
...