---
_id: '65554'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    An
    algorithm for cutting solid objects in a topology‐controlled manner is presented.
    Concretely, given a loop on the object boundary, a disk‐topology cut surface bounded
    by the loop is constructed in the interior. In contrast to various previous approaches,
    both disk topology and conformance to the prescribed loop are ensured by construction,
    while supporting not only contractible but also incontractible loops on the boundaries
    of manifold objects of higher genus and arbitrary non‐trivial topology. We describe
    an implementation of this algorithm in the discrete setting, with triangle mesh
    cut surfaces embedded in tetrahedral mesh objects. Making use of this novel cutting
    algorithm, we describe a method for the reliable construction of bijective volumetric
    maps between solid objects, demonstrating the algorithm's utility. This mapping
    method overcomes restrictions of the state of the art to topological balls, extending
    coverage to objects of arbitrary genus, specifically so‐called\r\n                    <jats:italic>1</jats:italic>\r\n
    \                   ‐handlebodies.\r\n                  </jats:p>"
article_number: e70379
author:
- first_name: Steffen
  full_name: Hinderink, Steffen
  id: '116615'
  last_name: Hinderink
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: 'Hinderink S, Campen M. DiskScissors: Cutting Arbitrary‐Topology Solids for
    Bijective Mapping. <i>Computer Graphics Forum</i>. Published online 2026. doi:<a
    href="https://doi.org/10.1111/cgf.70379">10.1111/cgf.70379</a>'
  apa: 'Hinderink, S., &#38; Campen, M. (2026). DiskScissors: Cutting Arbitrary‐Topology
    Solids for Bijective Mapping. <i>Computer Graphics Forum</i>, Article e70379.
    <a href="https://doi.org/10.1111/cgf.70379">https://doi.org/10.1111/cgf.70379</a>'
  bibtex: '@article{Hinderink_Campen_2026, title={DiskScissors: Cutting Arbitrary‐Topology
    Solids for Bijective Mapping}, DOI={<a href="https://doi.org/10.1111/cgf.70379">10.1111/cgf.70379</a>},
    number={e70379}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Hinderink,
    Steffen and Campen, Marcel}, year={2026} }'
  chicago: 'Hinderink, Steffen, and Marcel Campen. “DiskScissors: Cutting Arbitrary‐Topology
    Solids for Bijective Mapping.” <i>Computer Graphics Forum</i>, 2026. <a href="https://doi.org/10.1111/cgf.70379">https://doi.org/10.1111/cgf.70379</a>.'
  ieee: 'S. Hinderink and M. Campen, “DiskScissors: Cutting Arbitrary‐Topology Solids
    for Bijective Mapping,” <i>Computer Graphics Forum</i>, Art. no. e70379, 2026,
    doi: <a href="https://doi.org/10.1111/cgf.70379">10.1111/cgf.70379</a>.'
  mla: 'Hinderink, Steffen, and Marcel Campen. “DiskScissors: Cutting Arbitrary‐Topology
    Solids for Bijective Mapping.” <i>Computer Graphics Forum</i>, e70379, Wiley,
    2026, doi:<a href="https://doi.org/10.1111/cgf.70379">10.1111/cgf.70379</a>.'
  short: S. Hinderink, M. Campen, Computer Graphics Forum (2026).
date_created: 2026-05-05T08:15:52Z
date_updated: 2026-05-05T08:17:55Z
department:
- _id: '969'
doi: 10.1111/cgf.70379
language:
- iso: eng
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: 'DiskScissors: Cutting Arbitrary‐Topology Solids for Bijective Mapping'
type: journal_article
user_id: '117512'
year: '2026'
...
---
_id: '60314'
abstract:
- lang: eng
  text: <jats:p>A method for the construction of bijective volumetric maps between
    3D shapes is presented. Arbitrary shapes of ball-topology are supported, overcoming
    restrictions of previous methods to convex or star-shaped targets. In essence,
    the mapping problem is decomposed into a set of simpler mapping problems, each
    of which can be solved with previous methods for discrete star-shaped mapping
    problems. Addressing the key challenges in this endeavor, algorithms are described
    to reliably construct structurally compatible partitions of two shapes with constraints
    regarding star-shapedness and to compute a parsimonious common refinement of two
    triangulations.</jats:p>
author:
- first_name: Steffen
  full_name: Hinderink, Steffen
  id: '116615'
  last_name: Hinderink
- first_name: Hendrik
  full_name: Brückler, Hendrik
  id: '115694'
  last_name: Brückler
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: Hinderink S, Brückler H, Campen M. Bijective Volumetric Mapping via Star Decomposition.
    <i>ACM Transactions on Graphics</i>. 2024;43(6):1-11. doi:<a href="https://doi.org/10.1145/3687950">10.1145/3687950</a>
  apa: Hinderink, S., Brückler, H., &#38; Campen, M. (2024). Bijective Volumetric
    Mapping via Star Decomposition. <i>ACM Transactions on Graphics</i>, <i>43</i>(6),
    1–11. <a href="https://doi.org/10.1145/3687950">https://doi.org/10.1145/3687950</a>
  bibtex: '@article{Hinderink_Brückler_Campen_2024, title={Bijective Volumetric Mapping
    via Star Decomposition}, volume={43}, DOI={<a href="https://doi.org/10.1145/3687950">10.1145/3687950</a>},
    number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Hinderink, Steffen and Brückler, Hendrik and
    Campen, Marcel}, year={2024}, pages={1–11} }'
  chicago: 'Hinderink, Steffen, Hendrik Brückler, and Marcel Campen. “Bijective Volumetric
    Mapping via Star Decomposition.” <i>ACM Transactions on Graphics</i> 43, no. 6
    (2024): 1–11. <a href="https://doi.org/10.1145/3687950">https://doi.org/10.1145/3687950</a>.'
  ieee: 'S. Hinderink, H. Brückler, and M. Campen, “Bijective Volumetric Mapping via
    Star Decomposition,” <i>ACM Transactions on Graphics</i>, vol. 43, no. 6, pp.
    1–11, 2024, doi: <a href="https://doi.org/10.1145/3687950">10.1145/3687950</a>.'
  mla: Hinderink, Steffen, et al. “Bijective Volumetric Mapping via Star Decomposition.”
    <i>ACM Transactions on Graphics</i>, vol. 43, no. 6, Association for Computing
    Machinery (ACM), 2024, pp. 1–11, doi:<a href="https://doi.org/10.1145/3687950">10.1145/3687950</a>.
  short: S. Hinderink, H. Brückler, M. Campen, ACM Transactions on Graphics 43 (2024)
    1–11.
date_created: 2025-06-23T09:09:51Z
date_updated: 2025-07-14T12:33:54Z
department:
- _id: '969'
doi: 10.1145/3687950
extern: '1'
intvolume: '        43'
issue: '6'
language:
- iso: eng
page: 1-11
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
  - 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Bijective Volumetric Mapping via Star Decomposition
type: journal_article
user_id: '117512'
volume: 43
year: '2024'
...
---
_id: '60335'
abstract:
- lang: eng
  text: <jats:p>A method is presented to compute volumetric maps and parametrizations
    of objects over 3D domains. As a key feature, continuity and bijectivity are ensured
    by construction. Arbitrary objects of ball topology, represented as tetrahedral
    meshes, are supported. Arbitrary convex as well as star-shaped domains are supported.
    Full control over the boundary mapping is provided. The method is based on the
    technique of simplicial foliations, generalized to a broader class of domain shapes
    and applied adaptively in a novel localized manner. This increases flexibility
    as well as efficiency over the state of the art, while maintaining reliability
    in guaranteeing map bijectivity.</jats:p>
author:
- first_name: Steffen
  full_name: Hinderink, Steffen
  id: '116615'
  last_name: Hinderink
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: 'Hinderink S, Campen M. Galaxy Maps: Localized Foliations for Bijective Volumetric
    Mapping. <i>ACM Transactions on Graphics</i>. 2023;42(4):1-16. doi:<a href="https://doi.org/10.1145/3592410">10.1145/3592410</a>'
  apa: 'Hinderink, S., &#38; Campen, M. (2023). Galaxy Maps: Localized Foliations
    for Bijective Volumetric Mapping. <i>ACM Transactions on Graphics</i>, <i>42</i>(4),
    1–16. <a href="https://doi.org/10.1145/3592410">https://doi.org/10.1145/3592410</a>'
  bibtex: '@article{Hinderink_Campen_2023, title={Galaxy Maps: Localized Foliations
    for Bijective Volumetric Mapping}, volume={42}, DOI={<a href="https://doi.org/10.1145/3592410">10.1145/3592410</a>},
    number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Hinderink, Steffen and Campen, Marcel}, year={2023},
    pages={1–16} }'
  chicago: 'Hinderink, Steffen, and Marcel Campen. “Galaxy Maps: Localized Foliations
    for Bijective Volumetric Mapping.” <i>ACM Transactions on Graphics</i> 42, no.
    4 (2023): 1–16. <a href="https://doi.org/10.1145/3592410">https://doi.org/10.1145/3592410</a>.'
  ieee: 'S. Hinderink and M. Campen, “Galaxy Maps: Localized Foliations for Bijective
    Volumetric Mapping,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, pp.
    1–16, 2023, doi: <a href="https://doi.org/10.1145/3592410">10.1145/3592410</a>.'
  mla: 'Hinderink, Steffen, and Marcel Campen. “Galaxy Maps: Localized Foliations
    for Bijective Volumetric Mapping.” <i>ACM Transactions on Graphics</i>, vol. 42,
    no. 4, Association for Computing Machinery (ACM), 2023, pp. 1–16, doi:<a href="https://doi.org/10.1145/3592410">10.1145/3592410</a>.'
  short: S. Hinderink, M. Campen, ACM Transactions on Graphics 42 (2023) 1–16.
date_created: 2025-06-23T10:38:02Z
date_updated: 2025-07-14T12:48:12Z
department:
- _id: '969'
doi: 10.1145/3592410
extern: '1'
intvolume: '        42'
issue: '4'
language:
- iso: eng
page: 1-16
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
  - 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: 'Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping'
type: journal_article
user_id: '117512'
volume: 42
year: '2023'
...
---
_id: '60365'
article_number: '102085'
author:
- first_name: Steffen
  full_name: Hinderink, Steffen
  id: '116615'
  last_name: Hinderink
- first_name: Manish
  full_name: Mandad, Manish
  last_name: Mandad
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: Hinderink S, Mandad M, Campen M. Angle-bounded 2D mesh simplification. <i>Computer
    Aided Geometric Design</i>. 2022;95. doi:<a href="https://doi.org/10.1016/j.cagd.2022.102085">10.1016/j.cagd.2022.102085</a>
  apa: Hinderink, S., Mandad, M., &#38; Campen, M. (2022). Angle-bounded 2D mesh simplification.
    <i>Computer Aided Geometric Design</i>, <i>95</i>, Article 102085. <a href="https://doi.org/10.1016/j.cagd.2022.102085">https://doi.org/10.1016/j.cagd.2022.102085</a>
  bibtex: '@article{Hinderink_Mandad_Campen_2022, title={Angle-bounded 2D mesh simplification},
    volume={95}, DOI={<a href="https://doi.org/10.1016/j.cagd.2022.102085">10.1016/j.cagd.2022.102085</a>},
    number={102085}, journal={Computer Aided Geometric Design}, publisher={Elsevier
    BV}, author={Hinderink, Steffen and Mandad, Manish and Campen, Marcel}, year={2022}
    }'
  chicago: Hinderink, Steffen, Manish Mandad, and Marcel Campen. “Angle-Bounded 2D
    Mesh Simplification.” <i>Computer Aided Geometric Design</i> 95 (2022). <a href="https://doi.org/10.1016/j.cagd.2022.102085">https://doi.org/10.1016/j.cagd.2022.102085</a>.
  ieee: 'S. Hinderink, M. Mandad, and M. Campen, “Angle-bounded 2D mesh simplification,”
    <i>Computer Aided Geometric Design</i>, vol. 95, Art. no. 102085, 2022, doi: <a
    href="https://doi.org/10.1016/j.cagd.2022.102085">10.1016/j.cagd.2022.102085</a>.'
  mla: Hinderink, Steffen, et al. “Angle-Bounded 2D Mesh Simplification.” <i>Computer
    Aided Geometric Design</i>, vol. 95, 102085, Elsevier BV, 2022, doi:<a href="https://doi.org/10.1016/j.cagd.2022.102085">10.1016/j.cagd.2022.102085</a>.
  short: S. Hinderink, M. Mandad, M. Campen, Computer Aided Geometric Design 95 (2022).
date_created: 2025-06-25T08:50:14Z
date_updated: 2025-07-14T12:47:05Z
department:
- _id: '969'
doi: 10.1016/j.cagd.2022.102085
extern: '1'
intvolume: '        95'
language:
- iso: eng
publication: Computer Aided Geometric Design
publication_identifier:
  issn:
  - 0167-8396
publication_status: published
publisher: Elsevier BV
status: public
title: Angle-bounded 2D mesh simplification
type: journal_article
user_id: '117512'
volume: 95
year: '2022'
...