---
_id: '12431'
abstract:
- lang: eng
  text: This paper presents a new representation of curve dynamics, with applications
    to vortex filaments in fluid dynamics. Instead of representing these filaments
    with explicit curve geometry and Lagrangian equations of motion, we represent
    curves implicitly with a new co-dimensional 2 level set description. Our implicit
    representation admits several redundant mathematical degrees of freedom in both
    the configuration and the dynamics of the curves, which can be tailored specifically
    to improve numerical robustness, in contrast to naive approaches for implicit
    curve dynamics that suffer from overwhelming numerical stability problems. Furthermore,
    we note how these hidden degrees of freedom perfectly map to a Clebsch representation
    in fluid dynamics. Motivated by these observations, we introduce untwisted level
    set functions and non-swirling dynamics which successfully regularize sources
    of numerical instability, particularly in the twisting modes around curve filaments.
    A consequence is a novel simulation method which produces stable dynamics for
    large numbers of interacting vortex filaments and effortlessly handles topological
    changes and re-connection events.
acknowledgement: We thank the visual computing group at IST Austria for their valuable
  discussions and feedback. Houdini Education licenses were provided by SideFX software.
  This project was funded in part by the European Research Council (ERC Consolidator
  Grant 101045083 CoDiNA).
article_number: '241'
article_processing_charge: No
article_type: original
author:
- first_name: Sadashige
  full_name: Ishida, Sadashige
  id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
  last_name: Ishida
  orcid: 0000-0002-3121-3100
- first_name: Christopher J
  full_name: Wojtan, Christopher J
  id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
  last_name: Wojtan
  orcid: 0000-0001-6646-5546
- first_name: Albert
  full_name: Chern, Albert
  last_name: Chern
citation:
  ama: Ishida S, Wojtan C, Chern A. Hidden degrees of freedom in implicit vortex filaments.
    <i>ACM Transactions on Graphics</i>. 2022;41(6). doi:<a href="https://doi.org/10.1145/3550454.3555459">10.1145/3550454.3555459</a>
  apa: Ishida, S., Wojtan, C., &#38; Chern, A. (2022). Hidden degrees of freedom in
    implicit vortex filaments. <i>ACM Transactions on Graphics</i>. Association for
    Computing Machinery. <a href="https://doi.org/10.1145/3550454.3555459">https://doi.org/10.1145/3550454.3555459</a>
  chicago: Ishida, Sadashige, Chris Wojtan, and Albert Chern. “Hidden Degrees of Freedom
    in Implicit Vortex Filaments.” <i>ACM Transactions on Graphics</i>. Association
    for Computing Machinery, 2022. <a href="https://doi.org/10.1145/3550454.3555459">https://doi.org/10.1145/3550454.3555459</a>.
  ieee: S. Ishida, C. Wojtan, and A. Chern, “Hidden degrees of freedom in implicit
    vortex filaments,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 6. Association
    for Computing Machinery, 2022.
  ista: Ishida S, Wojtan C, Chern A. 2022. Hidden degrees of freedom in implicit vortex
    filaments. ACM Transactions on Graphics. 41(6), 241.
  mla: Ishida, Sadashige, et al. “Hidden Degrees of Freedom in Implicit Vortex Filaments.”
    <i>ACM Transactions on Graphics</i>, vol. 41, no. 6, 241, Association for Computing
    Machinery, 2022, doi:<a href="https://doi.org/10.1145/3550454.3555459">10.1145/3550454.3555459</a>.
  short: S. Ishida, C. Wojtan, A. Chern, ACM Transactions on Graphics 41 (2022).
date_created: 2023-01-29T23:00:59Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2026-04-07T12:02:23Z
day: '01'
ddc:
- '000'
department:
- _id: ChWo
doi: 10.1145/3550454.3555459
external_id:
  isi:
  - '000891651900061'
file:
- access_level: open_access
  checksum: a2fba257fdefe0e747182be6c0f7c70c
  content_type: application/pdf
  creator: dernst
  date_created: 2023-01-30T07:15:48Z
  date_updated: 2023-01-30T07:15:48Z
  file_id: '12433'
  file_name: 2022_ACM_Ishida.pdf
  file_size: 15551202
  relation: main_file
  success: 1
file_date_updated: 2023-01-30T07:15:48Z
has_accepted_license: '1'
intvolume: '        41'
isi: 1
issue: '6'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
  grant_number: '101045083'
  name: Computational Discovery of Numerical Algorithms for Animation and Simulation
    of Natural Phenomena
publication: ACM Transactions on Graphics
publication_identifier:
  eissn:
  - 1557-7368
  issn:
  - 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
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  - id: '20551'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Hidden degrees of freedom in implicit vortex filaments
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: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 41
year: '2022'
...