---
_id: '65440'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n                  <jats:p>We present
    a novel algorithm for quantization and subsequent hexahedral mesh generation from
    seamless volumetric maps. Quantization is the process of choosing integers that
    represent the numbers of hexahedral elements to be placed in each region of the
    volume, and transforming the seamless map into an integer‐grid map matching that
    choice, inducing a hexahedral mesh. Previous work computes such quantizations
    under the restriction of a fixed predetermined singularity graph. Our novel approach
    allows for implicit modification and, in particular, simplification of the map's
    singularity structure wherever that benefits the chosen objective, such as matching
    target hexahedron sizes as closely as possible. It comes with two novel ingredients:
    A feature‐focused distortion measure guiding the quantization, and constraints
    ensuring map injectivity and structure preservation of geometric and topological
    features, both without relying on a fixed singularity structure. We demonstrate
    the benefit of the added flexibility offered by this approach: it allows for the
    generation of hexahedral meshes that more accurately match a desired resolution
    globally, as well as of meshes exhibiting a simpler block structure.</jats:p>"
article_number: e70349
author:
- first_name: Hendrik
  full_name: Brückler, Hendrik
  last_name: Brückler
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: Brückler H, Campen M. Volume Quantization with Flexible Singularities for Hexahedral
    Meshing. <i>Computer Graphics Forum</i>. Published online 2026. doi:<a href="https://doi.org/10.1111/cgf.70349">10.1111/cgf.70349</a>
  apa: Brückler, H., &#38; Campen, M. (2026). Volume Quantization with Flexible Singularities
    for Hexahedral Meshing. <i>Computer Graphics Forum</i>, Article e70349. <a href="https://doi.org/10.1111/cgf.70349">https://doi.org/10.1111/cgf.70349</a>
  bibtex: '@article{Brückler_Campen_2026, title={Volume Quantization with Flexible
    Singularities for Hexahedral Meshing}, DOI={<a href="https://doi.org/10.1111/cgf.70349">10.1111/cgf.70349</a>},
    number={e70349}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Brückler,
    Hendrik and Campen, Marcel}, year={2026} }'
  chicago: Brückler, Hendrik, and Marcel Campen. “Volume Quantization with Flexible
    Singularities for Hexahedral Meshing.” <i>Computer Graphics Forum</i>, 2026. <a
    href="https://doi.org/10.1111/cgf.70349">https://doi.org/10.1111/cgf.70349</a>.
  ieee: 'H. Brückler and M. Campen, “Volume Quantization with Flexible Singularities
    for Hexahedral Meshing,” <i>Computer Graphics Forum</i>, Art. no. e70349, 2026,
    doi: <a href="https://doi.org/10.1111/cgf.70349">10.1111/cgf.70349</a>.'
  mla: Brückler, Hendrik, and Marcel Campen. “Volume Quantization with Flexible Singularities
    for Hexahedral Meshing.” <i>Computer Graphics Forum</i>, e70349, Wiley, 2026,
    doi:<a href="https://doi.org/10.1111/cgf.70349">10.1111/cgf.70349</a>.
  short: H. Brückler, M. Campen, Computer Graphics Forum (2026).
date_created: 2026-04-15T07:32:52Z
date_updated: 2026-04-15T08:06:49Z
department:
- _id: '969'
doi: 10.1111/cgf.70349
language:
- iso: eng
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Volume Quantization with Flexible Singularities for Hexahedral Meshing
type: journal_article
user_id: '117512'
year: '2026'
...
---
_id: '60189'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Several state‐of‐the‐art algorithms
    for semi‐structured hexahedral meshing involve a so called <jats:italic>quantization</jats:italic>
    step to decide on the integer DoFs of the meshing problem, corresponding to the
    number of hexahedral elements to embed into certain regions of the domain. Existing
    reliable methods for quantization are based on solving a sequence of <jats:italic>integer
    quadratic programs</jats:italic> (IQP). Solving these in a timely and predictable
    manner with general‐purpose solvers is a challenge, even more so in the open‐source
    field. We present here an alternative robust and efficient quantization scheme
    that is instead based on solving a series of continuous <jats:italic>linear programs</jats:italic>
    (LP), for which solver availability and efficiency are not an issue. In our formulation,
    such LPs are used to determine where inflation or deflation of virtual hexahedral
    sheets are favorable. We compare our method to two implementations of the former
    IQP formulation (using a commercial and an open‐source MIP solver, respectively),
    finding that (a) the solutions found by our method are near‐optimal or optimal
    in most cases, (b) these solutions are found within a much more predictable time
    frame, and (c) the state of the art run time is outperformed, in the case of using
    the open‐source solver by orders of magnitude.</jats:p>
author:
- first_name: Hendrik
  full_name: Brückler, Hendrik
  id: '115694'
  last_name: Brückler
- first_name: David
  full_name: Bommes, David
  last_name: Bommes
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: Brückler H, Bommes D, Campen M. Integer‐Sheet‐Pump Quantization for Hexahedral
    Meshing. <i>Comput Graph Forum</i>. 2024;43(5). doi:<a href="https://doi.org/10.1111/cgf.15131">10.1111/cgf.15131</a>
  apa: Brückler, H., Bommes, D., &#38; Campen, M. (2024). Integer‐Sheet‐Pump Quantization
    for Hexahedral Meshing. <i>Comput. Graph. Forum</i>, <i>43</i>(5). <a href="https://doi.org/10.1111/cgf.15131">https://doi.org/10.1111/cgf.15131</a>
  bibtex: '@article{Brückler_Bommes_Campen_2024, title={Integer‐Sheet‐Pump Quantization
    for Hexahedral Meshing}, volume={43}, DOI={<a href="https://doi.org/10.1111/cgf.15131">10.1111/cgf.15131</a>},
    number={5}, journal={Comput. Graph. Forum}, publisher={Wiley}, author={Brückler,
    Hendrik and Bommes, David and Campen, Marcel}, year={2024} }'
  chicago: Brückler, Hendrik, David Bommes, and Marcel Campen. “Integer‐Sheet‐Pump
    Quantization for Hexahedral Meshing.” <i>Comput. Graph. Forum</i> 43, no. 5 (2024).
    <a href="https://doi.org/10.1111/cgf.15131">https://doi.org/10.1111/cgf.15131</a>.
  ieee: 'H. Brückler, D. Bommes, and M. Campen, “Integer‐Sheet‐Pump Quantization for
    Hexahedral Meshing,” <i>Comput. Graph. Forum</i>, vol. 43, no. 5, 2024, doi: <a
    href="https://doi.org/10.1111/cgf.15131">10.1111/cgf.15131</a>.'
  mla: Brückler, Hendrik, et al. “Integer‐Sheet‐Pump Quantization for Hexahedral Meshing.”
    <i>Comput. Graph. Forum</i>, vol. 43, no. 5, Wiley, 2024, doi:<a href="https://doi.org/10.1111/cgf.15131">10.1111/cgf.15131</a>.
  short: H. Brückler, D. Bommes, M. Campen, Comput. Graph. Forum 43 (2024).
date_created: 2025-06-11T13:47:29Z
date_updated: 2025-06-23T09:01:46Z
department:
- _id: '969'
doi: 10.1111/cgf.15131
extern: '1'
intvolume: '        43'
issue: '5'
language:
- iso: eng
publication: Comput. Graph. Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Integer‐Sheet‐Pump Quantization for Hexahedral Meshing
type: journal_article
user_id: '114904'
volume: 43
year: '2024'
...
---
_id: '60333'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We describe HalfedgeCNN, a collection
    of modules to build neural networks that operate on triangle meshes. Taking inspiration
    from the (edge‐based) MeshCNN, convolution, pooling, and unpooling layers are
    consistently defined on the basis of halfedges of the mesh, pairs of oppositely
    oriented virtual instances of each edge. This provides benefits over alternative
    definitions on the basis of vertices, edges, or faces. Additional interface layers
    enable support for feature data associated with such mesh entities in input and
    output as well. Due to being defined natively on mesh entities and their neighborhoods,
    lossy resampling or interpolation techniques (to enable the application of operators
    adopted from image domains) do not need to be employed. The operators have various
    degrees of freedom that can be exploited to adapt to application‐specific needs.</jats:p>
author:
- first_name: Ingmar
  full_name: Ludwig, Ingmar
  id: '116667'
  last_name: Ludwig
- first_name: Daniel
  full_name: Tyson, Daniel
  last_name: Tyson
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: Ludwig I, Tyson D, Campen M. HalfedgeCNN for Native and Flexible Deep Learning
    on Triangle Meshes. <i>Computer Graphics Forum</i>. 2023;42(5). doi:<a href="https://doi.org/10.1111/cgf.14898">10.1111/cgf.14898</a>
  apa: Ludwig, I., Tyson, D., &#38; Campen, M. (2023). HalfedgeCNN for Native and
    Flexible Deep Learning on Triangle Meshes. <i>Computer Graphics Forum</i>, <i>42</i>(5).
    <a href="https://doi.org/10.1111/cgf.14898">https://doi.org/10.1111/cgf.14898</a>
  bibtex: '@article{Ludwig_Tyson_Campen_2023, title={HalfedgeCNN for Native and Flexible
    Deep Learning on Triangle Meshes}, volume={42}, DOI={<a href="https://doi.org/10.1111/cgf.14898">10.1111/cgf.14898</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Ludwig,
    Ingmar and Tyson, Daniel and Campen, Marcel}, year={2023} }'
  chicago: Ludwig, Ingmar, Daniel Tyson, and Marcel Campen. “HalfedgeCNN for Native
    and Flexible Deep Learning on Triangle Meshes.” <i>Computer Graphics Forum</i>
    42, no. 5 (2023). <a href="https://doi.org/10.1111/cgf.14898">https://doi.org/10.1111/cgf.14898</a>.
  ieee: 'I. Ludwig, D. Tyson, and M. Campen, “HalfedgeCNN for Native and Flexible
    Deep Learning on Triangle Meshes,” <i>Computer Graphics Forum</i>, vol. 42, no.
    5, 2023, doi: <a href="https://doi.org/10.1111/cgf.14898">10.1111/cgf.14898</a>.'
  mla: Ludwig, Ingmar, et al. “HalfedgeCNN for Native and Flexible Deep Learning on
    Triangle Meshes.” <i>Computer Graphics Forum</i>, vol. 42, no. 5, Wiley, 2023,
    doi:<a href="https://doi.org/10.1111/cgf.14898">10.1111/cgf.14898</a>.
  short: I. Ludwig, D. Tyson, M. Campen, Computer Graphics Forum 42 (2023).
date_created: 2025-06-23T10:34:49Z
date_updated: 2025-07-14T12:48:40Z
department:
- _id: '969'
doi: 10.1111/cgf.14898
extern: '1'
intvolume: '        42'
issue: '5'
language:
- iso: eng
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: HalfedgeCNN for Native and Flexible Deep Learning on Triangle Meshes
type: journal_article
user_id: '117512'
volume: 42
year: '2023'
...
---
_id: '60369'
abstract:
- lang: eng
  text: '<jats:title>Abstract</jats:title><jats:p>Non‐linear optimization is essential
    to many areas of geometry processing research. However, when experimenting with
    different problem formulations or when prototyping new algorithms, a major practical
    obstacle is the need to figure out derivatives of objective functions, especially
    when second‐order derivatives are required. Deriving and manually implementing
    gradients and Hessians is both time‐consuming and error‐prone. Automatic differentiation
    techniques address this problem, but can introduce a diverse set of obstacles
    themselves, e.g. limiting the set of supported language features, imposing restrictions
    on a program''s control flow, incurring a significant run time overhead, or making
    it hard to exploit sparsity patterns common in geometry processing. We show that
    for many geometric problems, in particular on meshes, the simplest form of forward‐mode
    automatic differentiation is not only the most flexible, but also actually the
    most efficient choice. We introduce TinyAD: a lightweight C++ library that automatically
    computes gradients and Hessians, in particular of sparse problems, by differentiating
    small (tiny) sub‐problems. Its simplicity enables easy integration; no restrictions
    on, e.g., looping and branching are imposed. TinyAD provides the basic ingredients
    to quickly implement first and second order Newton‐style solvers, allowing for
    flexible adjustment of both problem formulations and solver details. By showcasing
    compact implementations of methods from parametrization, deformation, and direction
    field design, we demonstrate how TinyAD lowers the barrier to exploring non‐linear
    optimization techniques. This enables not only fast prototyping of new research
    ideas, but also improves replicability of existing algorithms in geometry processing.
    TinyAD is available to the community as an open source library.</jats:p>'
author:
- first_name: Patrick
  full_name: Schmidt, Patrick
  last_name: Schmidt
- first_name: Janis
  full_name: Born, Janis
  last_name: Born
- first_name: David
  full_name: Bommes, David
  last_name: Bommes
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: 'Schmidt P, Born J, Bommes D, Campen M, Kobbelt L. TinyAD: Automatic Differentiation
    in Geometry Processing Made Simple. <i>Computer Graphics Forum</i>. 2022;41(5):113-124.
    doi:<a href="https://doi.org/10.1111/cgf.14607">10.1111/cgf.14607</a>'
  apa: 'Schmidt, P., Born, J., Bommes, D., Campen, M., &#38; Kobbelt, L. (2022). TinyAD:
    Automatic Differentiation in Geometry Processing Made Simple. <i>Computer Graphics
    Forum</i>, <i>41</i>(5), 113–124. <a href="https://doi.org/10.1111/cgf.14607">https://doi.org/10.1111/cgf.14607</a>'
  bibtex: '@article{Schmidt_Born_Bommes_Campen_Kobbelt_2022, title={TinyAD: Automatic
    Differentiation in Geometry Processing Made Simple}, volume={41}, DOI={<a href="https://doi.org/10.1111/cgf.14607">10.1111/cgf.14607</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Schmidt,
    Patrick and Born, Janis and Bommes, David and Campen, Marcel and Kobbelt, Leif},
    year={2022}, pages={113–124} }'
  chicago: 'Schmidt, Patrick, Janis Born, David Bommes, Marcel Campen, and Leif Kobbelt.
    “TinyAD: Automatic Differentiation in Geometry Processing Made Simple.” <i>Computer
    Graphics Forum</i> 41, no. 5 (2022): 113–24. <a href="https://doi.org/10.1111/cgf.14607">https://doi.org/10.1111/cgf.14607</a>.'
  ieee: 'P. Schmidt, J. Born, D. Bommes, M. Campen, and L. Kobbelt, “TinyAD: Automatic
    Differentiation in Geometry Processing Made Simple,” <i>Computer Graphics Forum</i>,
    vol. 41, no. 5, pp. 113–124, 2022, doi: <a href="https://doi.org/10.1111/cgf.14607">10.1111/cgf.14607</a>.'
  mla: 'Schmidt, Patrick, et al. “TinyAD: Automatic Differentiation in Geometry Processing
    Made Simple.” <i>Computer Graphics Forum</i>, vol. 41, no. 5, Wiley, 2022, pp.
    113–24, doi:<a href="https://doi.org/10.1111/cgf.14607">10.1111/cgf.14607</a>.'
  short: P. Schmidt, J. Born, D. Bommes, M. Campen, L. Kobbelt, Computer Graphics
    Forum 41 (2022) 113–124.
date_created: 2025-06-25T09:02:28Z
date_updated: 2025-07-14T12:47:14Z
department:
- _id: '969'
doi: 10.1111/cgf.14607
extern: '1'
intvolume: '        41'
issue: '5'
language:
- iso: eng
page: 113-124
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: 'TinyAD: Automatic Differentiation in Geometry Processing Made Simple'
type: journal_article
user_id: '117512'
volume: 41
year: '2022'
...
---
_id: '60366'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The so‐called motorcycle graph has
    been employed in recent years for various purposes in the context of structured
    and aligned block decomposition of 2D shapes and 2‐manifold surfaces. Applications
    are in the fields of surface parametrization, spline space construction, semi‐structured
    quad mesh generation, or geometry data compression. We describe a generalization
    of this motorcycle graph concept to the three‐dimensional volumetric setting.
    Through careful extensions aware of topological intricacies of this higher‐dimensional
    setting, we are able to guarantee important block decomposition properties also
    in this case. We describe algorithms for the construction of this 3D motorcycle
    complex on the basis of either hexahedral meshes or seamless volumetric parametrizations.
    Its utility is illustrated on examples in hexahedral mesh generation and volumetric
    T‐spline construction.</jats:p>
author:
- first_name: Hendrik
  full_name: Brückler, Hendrik
  id: '115694'
  last_name: Brückler
- first_name: Ojaswi
  full_name: Gupta, Ojaswi
  last_name: Gupta
- 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: Brückler H, Gupta O, Mandad M, Campen M. The 3D Motorcycle Complex for Structured
    Volume Decomposition. <i>Computer Graphics Forum</i>. 2022;41(2):221-235. doi:<a
    href="https://doi.org/10.1111/cgf.14470">10.1111/cgf.14470</a>
  apa: Brückler, H., Gupta, O., Mandad, M., &#38; Campen, M. (2022). The 3D Motorcycle
    Complex for Structured Volume Decomposition. <i>Computer Graphics Forum</i>, <i>41</i>(2),
    221–235. <a href="https://doi.org/10.1111/cgf.14470">https://doi.org/10.1111/cgf.14470</a>
  bibtex: '@article{Brückler_Gupta_Mandad_Campen_2022, title={The 3D Motorcycle Complex
    for Structured Volume Decomposition}, volume={41}, DOI={<a href="https://doi.org/10.1111/cgf.14470">10.1111/cgf.14470</a>},
    number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Brückler,
    Hendrik and Gupta, Ojaswi and Mandad, Manish and Campen, Marcel}, year={2022},
    pages={221–235} }'
  chicago: 'Brückler, Hendrik, Ojaswi Gupta, Manish Mandad, and Marcel Campen. “The
    3D Motorcycle Complex for Structured Volume Decomposition.” <i>Computer Graphics
    Forum</i> 41, no. 2 (2022): 221–35. <a href="https://doi.org/10.1111/cgf.14470">https://doi.org/10.1111/cgf.14470</a>.'
  ieee: 'H. Brückler, O. Gupta, M. Mandad, and M. Campen, “The 3D Motorcycle Complex
    for Structured Volume Decomposition,” <i>Computer Graphics Forum</i>, vol. 41,
    no. 2, pp. 221–235, 2022, doi: <a href="https://doi.org/10.1111/cgf.14470">10.1111/cgf.14470</a>.'
  mla: Brückler, Hendrik, et al. “The 3D Motorcycle Complex for Structured Volume
    Decomposition.” <i>Computer Graphics Forum</i>, vol. 41, no. 2, Wiley, 2022, pp.
    221–35, doi:<a href="https://doi.org/10.1111/cgf.14470">10.1111/cgf.14470</a>.
  short: H. Brückler, O. Gupta, M. Mandad, M. Campen, Computer Graphics Forum 41 (2022)
    221–235.
date_created: 2025-06-25T08:52:53Z
date_updated: 2025-07-14T12:47:02Z
department:
- _id: '969'
doi: 10.1111/cgf.14470
extern: '1'
intvolume: '        41'
issue: '2'
language:
- iso: eng
page: 221-235
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: The 3D Motorcycle Complex for Structured Volume Decomposition
type: journal_article
user_id: '117512'
volume: 41
year: '2022'
...
---
_id: '60368'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We present a reliable method to generate
    planar meshes of nonlinear rational triangular elements. The elements are guaranteed
    to be valid, i.e. defined by injective rational functions. The mesh is guaranteed
    to conform exactly, without geometric error, to arbitrary rational domain boundary
    and feature curves. The method generalizes the recent Bézier Guarding technique,
    which is applicable only to polynomial curves and elements. This generalization
    enables the accurate handling of practically important cases involving, for instance,
    circular or elliptic arcs and NURBS curves, which cannot be matched by polynomial
    elements. Furthermore, although many practical scenarios are concerned with rational
    functions of quadratic and cubic degree only, our method is fully general and
    supports arbitrary degree. We demonstrate the method on a variety of test cases.</jats:p>
author:
- first_name: Payam
  full_name: Khanteimouri, Payam
  last_name: Khanteimouri
- 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: Khanteimouri P, Mandad M, Campen M. Rational Bézier Guarding. <i>Computer Graphics
    Forum</i>. 2022;41(5):89-99. doi:<a href="https://doi.org/10.1111/cgf.14605">10.1111/cgf.14605</a>
  apa: Khanteimouri, P., Mandad, M., &#38; Campen, M. (2022). Rational Bézier Guarding.
    <i>Computer Graphics Forum</i>, <i>41</i>(5), 89–99. <a href="https://doi.org/10.1111/cgf.14605">https://doi.org/10.1111/cgf.14605</a>
  bibtex: '@article{Khanteimouri_Mandad_Campen_2022, title={Rational Bézier Guarding},
    volume={41}, DOI={<a href="https://doi.org/10.1111/cgf.14605">10.1111/cgf.14605</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Khanteimouri,
    Payam and Mandad, Manish and Campen, Marcel}, year={2022}, pages={89–99} }'
  chicago: 'Khanteimouri, Payam, Manish Mandad, and Marcel Campen. “Rational Bézier
    Guarding.” <i>Computer Graphics Forum</i> 41, no. 5 (2022): 89–99. <a href="https://doi.org/10.1111/cgf.14605">https://doi.org/10.1111/cgf.14605</a>.'
  ieee: 'P. Khanteimouri, M. Mandad, and M. Campen, “Rational Bézier Guarding,” <i>Computer
    Graphics Forum</i>, vol. 41, no. 5, pp. 89–99, 2022, doi: <a href="https://doi.org/10.1111/cgf.14605">10.1111/cgf.14605</a>.'
  mla: Khanteimouri, Payam, et al. “Rational Bézier Guarding.” <i>Computer Graphics
    Forum</i>, vol. 41, no. 5, Wiley, 2022, pp. 89–99, doi:<a href="https://doi.org/10.1111/cgf.14605">10.1111/cgf.14605</a>.
  short: P. Khanteimouri, M. Mandad, M. Campen, Computer Graphics Forum 41 (2022)
    89–99.
date_created: 2025-06-25T08:56:35Z
date_updated: 2025-07-14T12:46:58Z
department:
- _id: '969'
doi: 10.1111/cgf.14605
extern: '1'
intvolume: '        41'
issue: '5'
language:
- iso: eng
page: 89-99
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Rational Bézier Guarding
type: journal_article
user_id: '117512'
volume: 41
year: '2022'
...
---
_id: '60376'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>A homeomorphism between two surfaces
    not only defines a (continuous and bijective) geometric correspondence of points
    but also (by implication) an identification of topological features, i.e. handles
    and tunnels, and how the map twists around them. However, in practice, surface
    maps are often encoded via sparse correspondences or fuzzy representations that
    merely approximate a homeomorphism and are therefore inherently ambiguous about
    map topology. In this work, we show a way to infer topological information from
    an imperfect input map between two shapes. In particular, we compute a homology
    map, a linear map that transports homology classes of cycles from one surface
    to the other, subject to a global consistency constraint. Our inference robustly
    handles imperfect (e.g., partial, sparse, fuzzy, noisy, outlier‐ridden, non‐injective)
    input maps and is guaranteed to produce homology maps that are compatible with
    true homeomorphisms between the input shapes. Homology maps inferred by our method
    can be directly used to transfer homological information between shapes, or serve
    as foundation for the construction of a proper homeomorphism guided by the input
    map, e.g., via compatible surface decomposition.</jats:p>
author:
- first_name: Janis
  full_name: Born, Janis
  last_name: Born
- first_name: Patrick
  full_name: Schmidt, Patrick
  last_name: Schmidt
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Born J, Schmidt P, Campen M, Kobbelt L. Surface Map Homology Inference. <i>Computer
    Graphics Forum</i>. 2021;40(5):193-204. doi:<a href="https://doi.org/10.1111/cgf.14367">10.1111/cgf.14367</a>
  apa: Born, J., Schmidt, P., Campen, M., &#38; Kobbelt, L. (2021). Surface Map Homology
    Inference. <i>Computer Graphics Forum</i>, <i>40</i>(5), 193–204. <a href="https://doi.org/10.1111/cgf.14367">https://doi.org/10.1111/cgf.14367</a>
  bibtex: '@article{Born_Schmidt_Campen_Kobbelt_2021, title={Surface Map Homology
    Inference}, volume={40}, DOI={<a href="https://doi.org/10.1111/cgf.14367">10.1111/cgf.14367</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Born,
    Janis and Schmidt, Patrick and Campen, Marcel and Kobbelt, Leif}, year={2021},
    pages={193–204} }'
  chicago: 'Born, Janis, Patrick Schmidt, Marcel Campen, and Leif Kobbelt. “Surface
    Map Homology Inference.” <i>Computer Graphics Forum</i> 40, no. 5 (2021): 193–204.
    <a href="https://doi.org/10.1111/cgf.14367">https://doi.org/10.1111/cgf.14367</a>.'
  ieee: 'J. Born, P. Schmidt, M. Campen, and L. Kobbelt, “Surface Map Homology Inference,”
    <i>Computer Graphics Forum</i>, vol. 40, no. 5, pp. 193–204, 2021, doi: <a href="https://doi.org/10.1111/cgf.14367">10.1111/cgf.14367</a>.'
  mla: Born, Janis, et al. “Surface Map Homology Inference.” <i>Computer Graphics
    Forum</i>, vol. 40, no. 5, Wiley, 2021, pp. 193–204, doi:<a href="https://doi.org/10.1111/cgf.14367">10.1111/cgf.14367</a>.
  short: J. Born, P. Schmidt, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021)
    193–204.
date_created: 2025-06-25T09:54:02Z
date_updated: 2025-07-14T12:47:40Z
department:
- _id: '969'
doi: 10.1111/cgf.14367
extern: '1'
intvolume: '        40'
issue: '5'
language:
- iso: eng
page: 193-204
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Surface Map Homology Inference
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...
---
_id: '60374'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We present a robust and fast method
    for the creation of conforming quad layouts on surfaces. Our algorithm is based
    on the quantization of a T‐mesh, i.e. an assignment of integer lengths to the
    sides of a non‐conforming rectangular partition of the surface. This representation
    has the benefit of being able to encode an infinite number of layout connectivity
    options in a finite manner, which guarantees that a valid layout can always be
    found. We carefully construct the T‐mesh from a given seamless parametrization
    such that the algorithm can provide guarantees on the results' quality. In particular,
    the user can specify a bound on the angular deviation of layout edges from prescribed
    directions. We solve an integer linear program (ILP) to find a coarse quad layout
    adhering to that maximal deviation. Our algorithm is guaranteed to yield a conforming
    quad layout free of T‐junctions together with bounded angle distortion. Our results
    show that the presented method is fast, reliable, and achieves high quality layouts.</jats:p>
author:
- first_name: Max
  full_name: Lyon, Max
  last_name: Lyon
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Lyon M, Campen M, Kobbelt L. Quad Layouts via Constrained T‐Mesh Quantization.
    <i>Computer Graphics Forum</i>. 2021;40(2):305-314. doi:<a href="https://doi.org/10.1111/cgf.142634">10.1111/cgf.142634</a>
  apa: Lyon, M., Campen, M., &#38; Kobbelt, L. (2021). Quad Layouts via Constrained
    T‐Mesh Quantization. <i>Computer Graphics Forum</i>, <i>40</i>(2), 305–314. <a
    href="https://doi.org/10.1111/cgf.142634">https://doi.org/10.1111/cgf.142634</a>
  bibtex: '@article{Lyon_Campen_Kobbelt_2021, title={Quad Layouts via Constrained
    T‐Mesh Quantization}, volume={40}, DOI={<a href="https://doi.org/10.1111/cgf.142634">10.1111/cgf.142634</a>},
    number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Lyon,
    Max and Campen, Marcel and Kobbelt, Leif}, year={2021}, pages={305–314} }'
  chicago: 'Lyon, Max, Marcel Campen, and Leif Kobbelt. “Quad Layouts via Constrained
    T‐Mesh Quantization.” <i>Computer Graphics Forum</i> 40, no. 2 (2021): 305–14.
    <a href="https://doi.org/10.1111/cgf.142634">https://doi.org/10.1111/cgf.142634</a>.'
  ieee: 'M. Lyon, M. Campen, and L. Kobbelt, “Quad Layouts via Constrained T‐Mesh
    Quantization,” <i>Computer Graphics Forum</i>, vol. 40, no. 2, pp. 305–314, 2021,
    doi: <a href="https://doi.org/10.1111/cgf.142634">10.1111/cgf.142634</a>.'
  mla: Lyon, Max, et al. “Quad Layouts via Constrained T‐Mesh Quantization.” <i>Computer
    Graphics Forum</i>, vol. 40, no. 2, Wiley, 2021, pp. 305–14, doi:<a href="https://doi.org/10.1111/cgf.142634">10.1111/cgf.142634</a>.
  short: M. Lyon, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021) 305–314.
date_created: 2025-06-25T09:17:15Z
date_updated: 2025-07-14T12:47:35Z
department:
- _id: '969'
doi: 10.1111/cgf.142634
extern: '1'
intvolume: '        40'
issue: '2'
language:
- iso: eng
page: 305-314
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Quad Layouts via Constrained T‐Mesh Quantization
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...
---
_id: '60375'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>A common approach to automatic quad
    layout generation on surfaces is to, in a first stage, decide on the positioning
    of irregular layout vertices, followed by finding sensible layout edges connecting
    these vertices and partitioning the surface into quadrilateral patches in a second
    stage. While this two‐step approach reduces the problem's complexity, this separation
    also limits the result quality. In the worst case, the set of layout vertices
    fixed in the first stage without consideration of the second may not even permit
    a valid quad layout. We propose an algorithm for the creation of quad layouts
    in which the initial layout vertices can be adjusted in the second stage. Whenever
    beneficial for layout quality or even validity, these vertices may be moved within
    a prescribed radius or even be removed. Our algorithm is based on a robust quantization
    strategy, turning a continuous T‐mesh structure into a discrete layout. We show
    the effectiveness of our algorithm on a variety of inputs.</jats:p>
author:
- first_name: Max
  full_name: Lyon, Max
  last_name: Lyon
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Lyon M, Campen M, Kobbelt L. Simpler Quad Layouts using Relaxed Singularities.
    <i>Computer Graphics Forum</i>. 2021;40(5):169-180. doi:<a href="https://doi.org/10.1111/cgf.14365">10.1111/cgf.14365</a>
  apa: Lyon, M., Campen, M., &#38; Kobbelt, L. (2021). Simpler Quad Layouts using
    Relaxed Singularities. <i>Computer Graphics Forum</i>, <i>40</i>(5), 169–180.
    <a href="https://doi.org/10.1111/cgf.14365">https://doi.org/10.1111/cgf.14365</a>
  bibtex: '@article{Lyon_Campen_Kobbelt_2021, title={Simpler Quad Layouts using Relaxed
    Singularities}, volume={40}, DOI={<a href="https://doi.org/10.1111/cgf.14365">10.1111/cgf.14365</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Lyon,
    Max and Campen, Marcel and Kobbelt, Leif}, year={2021}, pages={169–180} }'
  chicago: 'Lyon, Max, Marcel Campen, and Leif Kobbelt. “Simpler Quad Layouts Using
    Relaxed Singularities.” <i>Computer Graphics Forum</i> 40, no. 5 (2021): 169–80.
    <a href="https://doi.org/10.1111/cgf.14365">https://doi.org/10.1111/cgf.14365</a>.'
  ieee: 'M. Lyon, M. Campen, and L. Kobbelt, “Simpler Quad Layouts using Relaxed Singularities,”
    <i>Computer Graphics Forum</i>, vol. 40, no. 5, pp. 169–180, 2021, doi: <a href="https://doi.org/10.1111/cgf.14365">10.1111/cgf.14365</a>.'
  mla: Lyon, Max, et al. “Simpler Quad Layouts Using Relaxed Singularities.” <i>Computer
    Graphics Forum</i>, vol. 40, no. 5, Wiley, 2021, pp. 169–80, doi:<a href="https://doi.org/10.1111/cgf.14365">10.1111/cgf.14365</a>.
  short: M. Lyon, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021) 169–180.
date_created: 2025-06-25T09:39:31Z
date_updated: 2025-07-14T12:47:37Z
department:
- _id: '969'
doi: 10.1111/cgf.14365
extern: '1'
intvolume: '        40'
issue: '5'
language:
- iso: eng
page: 169-180
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Simpler Quad Layouts using Relaxed Singularities
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...
---
_id: '60383'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The problem of seamless parametrization
    of surfaces is of interest in the context of structured quadrilateral mesh generation
    and spline‐based surface approximation. It has been tackled by a variety of approaches,
    commonly relying on continuous numerical optimization to ultimately obtain suitable
    parameter domains. We present a general combinatorial seamless parameter domain
    construction, free from the potential numerical issues inherent to continuous
    optimization techniques in practice. The domains are constructed as abstract polygonal
    complexes which can be embedded in a discrete planar grid space, as unions of
    unit squares. We ensure that the domain structure matches any prescribed parametrization
    singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary
    genus are supported. Once a domain suitable for a given surface is constructed,
    a seamless and locally injective parametrization over this domain can be obtained
    using existing planar disk mapping techniques, making recourse to Tutte's classical
    embedding theorem.</jats:p>
author:
- first_name: Jiaran
  full_name: Zhou, Jiaran
  last_name: Zhou
- first_name: Changhe
  full_name: Tu, Changhe
  last_name: Tu
- first_name: Denis
  full_name: Zorin, Denis
  last_name: Zorin
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: Zhou J, Tu C, Zorin D, Campen M. Combinatorial Construction of Seamless Parameter
    Domains. <i>Computer Graphics Forum</i>. 2020;39(2):179-190. doi:<a href="https://doi.org/10.1111/cgf.13922">10.1111/cgf.13922</a>
  apa: Zhou, J., Tu, C., Zorin, D., &#38; Campen, M. (2020). Combinatorial Construction
    of Seamless Parameter Domains. <i>Computer Graphics Forum</i>, <i>39</i>(2), 179–190.
    <a href="https://doi.org/10.1111/cgf.13922">https://doi.org/10.1111/cgf.13922</a>
  bibtex: '@article{Zhou_Tu_Zorin_Campen_2020, title={Combinatorial Construction of
    Seamless Parameter Domains}, volume={39}, DOI={<a href="https://doi.org/10.1111/cgf.13922">10.1111/cgf.13922</a>},
    number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Zhou,
    Jiaran and Tu, Changhe and Zorin, Denis and Campen, Marcel}, year={2020}, pages={179–190}
    }'
  chicago: 'Zhou, Jiaran, Changhe Tu, Denis Zorin, and Marcel Campen. “Combinatorial
    Construction of Seamless Parameter Domains.” <i>Computer Graphics Forum</i> 39,
    no. 2 (2020): 179–90. <a href="https://doi.org/10.1111/cgf.13922">https://doi.org/10.1111/cgf.13922</a>.'
  ieee: 'J. Zhou, C. Tu, D. Zorin, and M. Campen, “Combinatorial Construction of Seamless
    Parameter Domains,” <i>Computer Graphics Forum</i>, vol. 39, no. 2, pp. 179–190,
    2020, doi: <a href="https://doi.org/10.1111/cgf.13922">10.1111/cgf.13922</a>.'
  mla: Zhou, Jiaran, et al. “Combinatorial Construction of Seamless Parameter Domains.”
    <i>Computer Graphics Forum</i>, vol. 39, no. 2, Wiley, 2020, pp. 179–90, doi:<a
    href="https://doi.org/10.1111/cgf.13922">10.1111/cgf.13922</a>.
  short: J. Zhou, C. Tu, D. Zorin, M. Campen, Computer Graphics Forum 39 (2020) 179–190.
date_created: 2025-06-26T06:52:07Z
date_updated: 2025-07-14T12:48:19Z
department:
- _id: '969'
doi: 10.1111/cgf.13922
extern: '1'
intvolume: '        39'
issue: '2'
language:
- iso: eng
page: 179-190
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Combinatorial Construction of Seamless Parameter Domains
type: journal_article
user_id: '117512'
volume: 39
year: '2020'
...
---
_id: '16337'
author:
- first_name: Sascha
  full_name: Brandt, Sascha
  id: '11648'
  last_name: Brandt
  orcid: https://orcid.org/0000-0003-3546-203X
- first_name: Claudius
  full_name: Jähn, Claudius
  last_name: Jähn
- first_name: Matthias
  full_name: Fischer, Matthias
  id: '146'
  last_name: Fischer
- first_name: Friedhelm
  full_name: Meyer auf der Heide, Friedhelm
  id: '15523'
  last_name: Meyer auf der Heide
citation:
  ama: Brandt S, Jähn C, Fischer M, Meyer auf der Heide F. Visibility‐Aware Progressive
    Farthest Point Sampling on the GPU. <i>Computer Graphics Forum</i>. 2019;38(7):413-424.
    doi:<a href="https://doi.org/10.1111/cgf.13848">10.1111/cgf.13848</a>
  apa: Brandt, S., Jähn, C., Fischer, M., &#38; Meyer auf der Heide, F. (2019). Visibility‐Aware
    Progressive Farthest Point Sampling on the GPU. <i>Computer Graphics Forum</i>,
    <i>38</i>(7), 413–424. <a href="https://doi.org/10.1111/cgf.13848">https://doi.org/10.1111/cgf.13848</a>
  bibtex: '@article{Brandt_Jähn_Fischer_Meyer auf der Heide_2019, title={Visibility‐Aware
    Progressive Farthest Point Sampling on the GPU}, volume={38}, DOI={<a href="https://doi.org/10.1111/cgf.13848">10.1111/cgf.13848</a>},
    number={7}, journal={Computer Graphics Forum}, author={Brandt, Sascha and Jähn,
    Claudius and Fischer, Matthias and Meyer auf der Heide, Friedhelm}, year={2019},
    pages={413–424} }'
  chicago: 'Brandt, Sascha, Claudius Jähn, Matthias Fischer, and Friedhelm Meyer auf
    der Heide. “Visibility‐Aware Progressive Farthest Point Sampling on the GPU.”
    <i>Computer Graphics Forum</i> 38, no. 7 (2019): 413–24. <a href="https://doi.org/10.1111/cgf.13848">https://doi.org/10.1111/cgf.13848</a>.'
  ieee: S. Brandt, C. Jähn, M. Fischer, and F. Meyer auf der Heide, “Visibility‐Aware
    Progressive Farthest Point Sampling on the GPU,” <i>Computer Graphics Forum</i>,
    vol. 38, no. 7, pp. 413–424, 2019.
  mla: Brandt, Sascha, et al. “Visibility‐Aware Progressive Farthest Point Sampling
    on the GPU.” <i>Computer Graphics Forum</i>, vol. 38, no. 7, 2019, pp. 413–24,
    doi:<a href="https://doi.org/10.1111/cgf.13848">10.1111/cgf.13848</a>.
  short: S. Brandt, C. Jähn, M. Fischer, F. Meyer auf der Heide, Computer Graphics
    Forum 38 (2019) 413–424.
conference:
  end_date: 2019-10-17
  location: Seoul, South Korea
  name: Pacific Graphics 2019
  start_date: 2019-10-14
date_created: 2020-03-24T08:24:11Z
date_updated: 2022-01-06T06:52:49Z
doi: 10.1111/cgf.13848
intvolume: '        38'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13848
oa: '1'
page: 413-424
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
status: public
title: Visibility‐Aware Progressive Farthest Point Sampling on the GPU
type: journal_article
user_id: '11648'
volume: 38
year: '2019'
...
---
_id: '60388'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>In the field of global surface parametrization
    a recent focus has been on so‐called seamless parametrization. This term refers
    to parametrization approaches which, while using an atlas of charts to enable
    the handling of surfaces of arbitrary topology, relate the parametrization across
    the cuts between charts via transition functions from special classes of transformations.
    This effectively makes the cuts invisible to applications which are invariant
    to these specific transformations in some sense. In actual implementations of
    these parametrization approaches, however, these restrictions are obeyed only
    approximately; errors stem from the tolerances of numerical solvers employed and,
    ultimately, from the limited accuracy of floating point arithmetic. In practice,
    robustness issues arise from these flaws in the seamlessness of a parametrization,
    no matter how small. We present a robust global algorithm that turns a given approximately
    seamless parametrization into an exactly seamless one ‐ that still is representable
    by standard floating point numbers. It supports common practically relevant additional
    constraints regarding boundary and feature curve alignment or isocurve connectivity,
    and ensures that these are likewise fulfilled exactly. This allows subsequent
    algorithms to operate robustly on the resulting truly seamless parametrization.
    We believe that the core of our method will furthermore be of benefit in a broader
    range of applications involving linearly constrained numerical optimization.</jats:p>
author:
- 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: Mandad M, Campen M. Exact Constraint Satisfaction for Truly Seamless Parametrization.
    <i>Computer Graphics Forum</i>. 2019;38(2):135-145. doi:<a href="https://doi.org/10.1111/cgf.13625">10.1111/cgf.13625</a>
  apa: Mandad, M., &#38; Campen, M. (2019). Exact Constraint Satisfaction for Truly
    Seamless Parametrization. <i>Computer Graphics Forum</i>, <i>38</i>(2), 135–145.
    <a href="https://doi.org/10.1111/cgf.13625">https://doi.org/10.1111/cgf.13625</a>
  bibtex: '@article{Mandad_Campen_2019, title={Exact Constraint Satisfaction for Truly
    Seamless Parametrization}, volume={38}, DOI={<a href="https://doi.org/10.1111/cgf.13625">10.1111/cgf.13625</a>},
    number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Mandad,
    Manish and Campen, Marcel}, year={2019}, pages={135–145} }'
  chicago: 'Mandad, Manish, and Marcel Campen. “Exact Constraint Satisfaction for
    Truly Seamless Parametrization.” <i>Computer Graphics Forum</i> 38, no. 2 (2019):
    135–45. <a href="https://doi.org/10.1111/cgf.13625">https://doi.org/10.1111/cgf.13625</a>.'
  ieee: 'M. Mandad and M. Campen, “Exact Constraint Satisfaction for Truly Seamless
    Parametrization,” <i>Computer Graphics Forum</i>, vol. 38, no. 2, pp. 135–145,
    2019, doi: <a href="https://doi.org/10.1111/cgf.13625">10.1111/cgf.13625</a>.'
  mla: Mandad, Manish, and Marcel Campen. “Exact Constraint Satisfaction for Truly
    Seamless Parametrization.” <i>Computer Graphics Forum</i>, vol. 38, no. 2, Wiley,
    2019, pp. 135–45, doi:<a href="https://doi.org/10.1111/cgf.13625">10.1111/cgf.13625</a>.
  short: M. Mandad, M. Campen, Computer Graphics Forum 38 (2019) 135–145.
date_created: 2025-06-26T07:35:31Z
date_updated: 2025-07-14T12:44:26Z
department:
- _id: '969'
doi: 10.1111/cgf.13625
extern: '1'
intvolume: '        38'
issue: '2'
language:
- iso: eng
page: 135-145
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Exact Constraint Satisfaction for Truly Seamless Parametrization
type: journal_article
user_id: '117512'
volume: 38
year: '2019'
...
---
_id: '60398'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The efficient and practical representation
    and processing of geometrically or topologically complex shapes often demands
    a partitioning into simpler patches. Possibilities range from unstructured arrangements
    of arbitrarily shaped patches on the one end, to highly structured conforming
    networks of all‐quadrilateral patches on the other end of the spectrum. Due to
    its regularity, this latter extreme of conforming partitions with quadrilateral
    patches, called quad layouts, is most beneficial in many application scenarios,
    for instance enabling the use of tensor‐product representations based on splines
    or Bézier patches, grid‐based multi‐resolution techniques and discrete pixel‐based
    map representations. However, this type of partition is also most complicated
    to create due to the strict inherent structural restrictions. Traditionally often
    performed manually in a tedious and demanding process, research in computer graphics
    and geometry processing has led to a number of computer‐assisted, semi‐automatic,
    as well as fully automatic approaches to address this problem more efficiently.
    This survey provides a detailed discussion of this range of methods, treats their
    strengths and weaknesses and outlines open problems in this field of research.</jats:p>
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: 'Campen M. Partitioning Surfaces Into Quadrilateral Patches: A Survey. <i>Computer
    Graphics Forum</i>. 2017;36(8):567-588. doi:<a href="https://doi.org/10.1111/cgf.13153">10.1111/cgf.13153</a>'
  apa: 'Campen, M. (2017). Partitioning Surfaces Into Quadrilateral Patches: A Survey.
    <i>Computer Graphics Forum</i>, <i>36</i>(8), 567–588. <a href="https://doi.org/10.1111/cgf.13153">https://doi.org/10.1111/cgf.13153</a>'
  bibtex: '@article{Campen_2017, title={Partitioning Surfaces Into Quadrilateral Patches:
    A Survey}, volume={36}, DOI={<a href="https://doi.org/10.1111/cgf.13153">10.1111/cgf.13153</a>},
    number={8}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
    Marcel}, year={2017}, pages={567–588} }'
  chicago: 'Campen, Marcel. “Partitioning Surfaces Into Quadrilateral Patches: A Survey.”
    <i>Computer Graphics Forum</i> 36, no. 8 (2017): 567–88. <a href="https://doi.org/10.1111/cgf.13153">https://doi.org/10.1111/cgf.13153</a>.'
  ieee: 'M. Campen, “Partitioning Surfaces Into Quadrilateral Patches: A Survey,”
    <i>Computer Graphics Forum</i>, vol. 36, no. 8, pp. 567–588, 2017, doi: <a href="https://doi.org/10.1111/cgf.13153">10.1111/cgf.13153</a>.'
  mla: 'Campen, Marcel. “Partitioning Surfaces Into Quadrilateral Patches: A Survey.”
    <i>Computer Graphics Forum</i>, vol. 36, no. 8, Wiley, 2017, pp. 567–88, doi:<a
    href="https://doi.org/10.1111/cgf.13153">10.1111/cgf.13153</a>.'
  short: M. Campen, Computer Graphics Forum 36 (2017) 567–588.
date_created: 2025-06-26T08:14:22Z
date_updated: 2025-07-14T12:42:33Z
department:
- _id: '969'
doi: 10.1111/cgf.13153
extern: '1'
intvolume: '        36'
issue: '8'
language:
- iso: eng
page: 567-588
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: 'Partitioning Surfaces Into Quadrilateral Patches: A Survey'
type: journal_article
user_id: '117512'
volume: 36
year: '2017'
...
---
_id: '60435'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Various applications of global surface
    parametrization benefit from the alignment of parametrization isolines with principal
    curvature directions. This is particularly true for recent parametrization‐based
    meshing approaches, where this directly translates into a shape‐aware edge flow,
    better approximation quality, and reduced meshing artifacts. Existing methods
    to influence a parametrization based on principal curvature directions suffer
    from scale‐dependence, which implies the necessity of parameter variation, or
    try to capture complex directional shape features using simple 1D curves. Especially
    for non‐sharp features, such as chamfers, fillets, blends, and even more for organic
    variants thereof, these abstractions can be unfit. We present a novel approach
    which respects and exploits the 2D nature of such directional feature regions,
    detects them based on coherence and homogeneity properties, and controls the parametrization
    process accordingly. This approach enables us to provide an intuitive, scale‐invariant
    control parameter to the user. It also allows us to consider non‐local aspects
    like the topology of a feature, enabling further improvements. We demonstrate
    that, compared to previous approaches, global parametrizations of higher quality
    can be generated without user intervention.</jats:p>
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Moritz
  full_name: Ibing, Moritz
  last_name: Ibing
- first_name: Hans‐Christian
  full_name: Ebke, Hans‐Christian
  last_name: Ebke
- first_name: Denis
  full_name: Zorin, Denis
  last_name: Zorin
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Campen M, Ibing M, Ebke H, Zorin D, Kobbelt L. Scale‐Invariant Directional
    Alignment of Surface Parametrizations. <i>Computer Graphics Forum</i>. 2016;35(5):1-10.
    doi:<a href="https://doi.org/10.1111/cgf.12958">10.1111/cgf.12958</a>
  apa: Campen, M., Ibing, M., Ebke, H., Zorin, D., &#38; Kobbelt, L. (2016). Scale‐Invariant
    Directional Alignment of Surface Parametrizations. <i>Computer Graphics Forum</i>,
    <i>35</i>(5), 1–10. <a href="https://doi.org/10.1111/cgf.12958">https://doi.org/10.1111/cgf.12958</a>
  bibtex: '@article{Campen_Ibing_Ebke_Zorin_Kobbelt_2016, title={Scale‐Invariant Directional
    Alignment of Surface Parametrizations}, volume={35}, DOI={<a href="https://doi.org/10.1111/cgf.12958">10.1111/cgf.12958</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
    Marcel and Ibing, Moritz and Ebke, Hans‐Christian and Zorin, Denis and Kobbelt,
    Leif}, year={2016}, pages={1–10} }'
  chicago: 'Campen, Marcel, Moritz Ibing, Hans‐Christian Ebke, Denis Zorin, and Leif
    Kobbelt. “Scale‐Invariant Directional Alignment of Surface Parametrizations.”
    <i>Computer Graphics Forum</i> 35, no. 5 (2016): 1–10. <a href="https://doi.org/10.1111/cgf.12958">https://doi.org/10.1111/cgf.12958</a>.'
  ieee: 'M. Campen, M. Ibing, H. Ebke, D. Zorin, and L. Kobbelt, “Scale‐Invariant
    Directional Alignment of Surface Parametrizations,” <i>Computer Graphics Forum</i>,
    vol. 35, no. 5, pp. 1–10, 2016, doi: <a href="https://doi.org/10.1111/cgf.12958">10.1111/cgf.12958</a>.'
  mla: Campen, Marcel, et al. “Scale‐Invariant Directional Alignment of Surface Parametrizations.”
    <i>Computer Graphics Forum</i>, vol. 35, no. 5, Wiley, 2016, pp. 1–10, doi:<a
    href="https://doi.org/10.1111/cgf.12958">10.1111/cgf.12958</a>.
  short: M. Campen, M. Ibing, H. Ebke, D. Zorin, L. Kobbelt, Computer Graphics Forum
    35 (2016) 1–10.
date_created: 2025-06-27T07:51:00Z
date_updated: 2025-07-14T12:42:01Z
department:
- _id: '969'
doi: 10.1111/cgf.12958
extern: '1'
intvolume: '        35'
issue: '5'
language:
- iso: eng
page: 1-10
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Scale‐Invariant Directional Alignment of Surface Parametrizations
type: journal_article
user_id: '117512'
volume: 35
year: '2016'
...
---
_id: '60434'
abstract:
- lang: eng
  text: '<jats:title>Abstract</jats:title><jats:p>Direction fields and vector fields
    play an increasingly important role in computer graphics and geometry processing.
    The synthesis of directional fields on surfaces, or other spatial domains, is
    a fundamental step in numerous applications, such as mesh generation, deformation,
    texture mapping, and many more. The wide range of applications resulted in definitions
    for many types of directional fields: from vector and tensor fields, over line
    and cross fields, to frame and vector‐set fields. Depending on the application
    at hand, researchers have used various notions of objectives and constraints to
    synthesize such fields. These notions are defined in terms of fairness, feature
    alignment, symmetry, or field topology, to mention just a few. To facilitate these
    objectives, various representations, discretizations, and optimization strategies
    have been developed. These choices come with varying strengths and weaknesses.
    This report provides a systematic overview of directional field synthesis for
    graphics applications, the challenges it poses, and the methods developed in recent
    years to address these challenges.</jats:p>'
author:
- first_name: Amir
  full_name: Vaxman, Amir
  last_name: Vaxman
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Olga
  full_name: Diamanti, Olga
  last_name: Diamanti
- first_name: Daniele
  full_name: Panozzo, Daniele
  last_name: Panozzo
- first_name: David
  full_name: Bommes, David
  last_name: Bommes
- first_name: Klaus
  full_name: Hildebrandt, Klaus
  last_name: Hildebrandt
- first_name: Mirela
  full_name: Ben‐Chen, Mirela
  last_name: Ben‐Chen
citation:
  ama: Vaxman A, Campen M, Diamanti O, et al. Directional Field Synthesis, Design,
    and Processing. <i>Computer Graphics Forum</i>. 2016;35(2):545-572. doi:<a href="https://doi.org/10.1111/cgf.12864">10.1111/cgf.12864</a>
  apa: Vaxman, A., Campen, M., Diamanti, O., Panozzo, D., Bommes, D., Hildebrandt,
    K., &#38; Ben‐Chen, M. (2016). Directional Field Synthesis, Design, and Processing.
    <i>Computer Graphics Forum</i>, <i>35</i>(2), 545–572. <a href="https://doi.org/10.1111/cgf.12864">https://doi.org/10.1111/cgf.12864</a>
  bibtex: '@article{Vaxman_Campen_Diamanti_Panozzo_Bommes_Hildebrandt_Ben‐Chen_2016,
    title={Directional Field Synthesis, Design, and Processing}, volume={35}, DOI={<a
    href="https://doi.org/10.1111/cgf.12864">10.1111/cgf.12864</a>}, number={2}, journal={Computer
    Graphics Forum}, publisher={Wiley}, author={Vaxman, Amir and Campen, Marcel and
    Diamanti, Olga and Panozzo, Daniele and Bommes, David and Hildebrandt, Klaus and
    Ben‐Chen, Mirela}, year={2016}, pages={545–572} }'
  chicago: 'Vaxman, Amir, Marcel Campen, Olga Diamanti, Daniele Panozzo, David Bommes,
    Klaus Hildebrandt, and Mirela Ben‐Chen. “Directional Field Synthesis, Design,
    and Processing.” <i>Computer Graphics Forum</i> 35, no. 2 (2016): 545–72. <a href="https://doi.org/10.1111/cgf.12864">https://doi.org/10.1111/cgf.12864</a>.'
  ieee: 'A. Vaxman <i>et al.</i>, “Directional Field Synthesis, Design, and Processing,”
    <i>Computer Graphics Forum</i>, vol. 35, no. 2, pp. 545–572, 2016, doi: <a href="https://doi.org/10.1111/cgf.12864">10.1111/cgf.12864</a>.'
  mla: Vaxman, Amir, et al. “Directional Field Synthesis, Design, and Processing.”
    <i>Computer Graphics Forum</i>, vol. 35, no. 2, Wiley, 2016, pp. 545–72, doi:<a
    href="https://doi.org/10.1111/cgf.12864">10.1111/cgf.12864</a>.
  short: A. Vaxman, M. Campen, O. Diamanti, D. Panozzo, D. Bommes, K. Hildebrandt,
    M. Ben‐Chen, Computer Graphics Forum 35 (2016) 545–572.
date_created: 2025-06-27T07:45:00Z
date_updated: 2025-07-14T12:42:05Z
department:
- _id: '969'
doi: 10.1111/cgf.12864
extern: '1'
intvolume: '        35'
issue: '2'
language:
- iso: eng
page: 545-572
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Directional Field Synthesis, Design, and Processing
type: journal_article
user_id: '117512'
volume: 35
year: '2016'
...
---
_id: '60443'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p><jats:italic>Quad layouting, i.e.
    the partitioning of a surface into a coarse network of quadrilateral patches,
    is a fundamental step in application scenarios ranging from animation and simulation
    to reverse engineering and meshing. This process involves determining the layout's
    combinatorial structure as well as its geometric embedding in the surface. We
    present a novel quad layout algorithm that focuses on the embedding optimization,
    thereby complementing recent methods focusing on the structure optimization aspect.
    It takes as input a description of the target layout structure and computes a
    complete embedding in form of a parameterization globally optimized for isometry
    and, in particular, principal direction alignment. Besides being suited for fully
    automatic workflows, our method can also incorporate user constraints and support
    the tedious but common procedure of manual layouting</jats:italic>.</jats:p>
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Campen M, Kobbelt L. Quad Layout Embedding via Aligned Parameterization. <i>Computer
    Graphics Forum</i>. 2014;33(8):69-81. doi:<a href="https://doi.org/10.1111/cgf.12401">10.1111/cgf.12401</a>
  apa: Campen, M., &#38; Kobbelt, L. (2014). Quad Layout Embedding via Aligned Parameterization.
    <i>Computer Graphics Forum</i>, <i>33</i>(8), 69–81. <a href="https://doi.org/10.1111/cgf.12401">https://doi.org/10.1111/cgf.12401</a>
  bibtex: '@article{Campen_Kobbelt_2014, title={Quad Layout Embedding via Aligned
    Parameterization}, volume={33}, DOI={<a href="https://doi.org/10.1111/cgf.12401">10.1111/cgf.12401</a>},
    number={8}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
    Marcel and Kobbelt, Leif}, year={2014}, pages={69–81} }'
  chicago: 'Campen, Marcel, and Leif Kobbelt. “Quad Layout Embedding via Aligned Parameterization.”
    <i>Computer Graphics Forum</i> 33, no. 8 (2014): 69–81. <a href="https://doi.org/10.1111/cgf.12401">https://doi.org/10.1111/cgf.12401</a>.'
  ieee: 'M. Campen and L. Kobbelt, “Quad Layout Embedding via Aligned Parameterization,”
    <i>Computer Graphics Forum</i>, vol. 33, no. 8, pp. 69–81, 2014, doi: <a href="https://doi.org/10.1111/cgf.12401">10.1111/cgf.12401</a>.'
  mla: Campen, Marcel, and Leif Kobbelt. “Quad Layout Embedding via Aligned Parameterization.”
    <i>Computer Graphics Forum</i>, vol. 33, no. 8, Wiley, 2014, pp. 69–81, doi:<a
    href="https://doi.org/10.1111/cgf.12401">10.1111/cgf.12401</a>.
  short: M. Campen, L. Kobbelt, Computer Graphics Forum 33 (2014) 69–81.
date_created: 2025-06-27T10:20:46Z
date_updated: 2025-07-14T12:41:33Z
department:
- _id: '969'
doi: 10.1111/cgf.12401
extern: '1'
intvolume: '        33'
issue: '8'
language:
- iso: eng
page: 69-81
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Quad Layout Embedding via Aligned Parameterization
type: journal_article
user_id: '117512'
volume: 33
year: '2014'
...
---
_id: '60450'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The computation of intrinsic, geodesic
    distances and geodesic paths on surfaces is a fundamental low‐level building block
    in countless Computer Graphics and Geometry Processing applications. This demand
    led to the development of numerous algorithms – some for the exact, others for
    the approximative computation, some focussing on speed, others providing strict
    guarantees. Most of these methods are designed for computing distances according
    to the standard Riemannian metric induced by the surface's embedding in Euclidean
    space. Generalization to other, especially anisotropic, metrics – which more recently
    gained interest in several application areas – is not rarely hampered by fundamental
    problems. We explore and discuss possibilities for the generalization and extension
    of well‐known methods to the anisotropic case, evaluate their relative performance
    in terms of accuracy and speed, and propose a novel algorithm, the <jats:italic>Short‐Term
    Vector Dijkstra</jats:italic>. This algorithm is strikingly simple to implement
    and proves to provide practical accuracy at a higher speed than generalized previous
    methods.</jats:p>
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Martin
  full_name: Heistermann, Martin
  last_name: Heistermann
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Campen M, Heistermann M, Kobbelt L. Practical Anisotropic Geodesy. <i>Computer
    Graphics Forum</i>. 2013;32(5):63-71. doi:<a href="https://doi.org/10.1111/cgf.12173">10.1111/cgf.12173</a>
  apa: Campen, M., Heistermann, M., &#38; Kobbelt, L. (2013). Practical Anisotropic
    Geodesy. <i>Computer Graphics Forum</i>, <i>32</i>(5), 63–71. <a href="https://doi.org/10.1111/cgf.12173">https://doi.org/10.1111/cgf.12173</a>
  bibtex: '@article{Campen_Heistermann_Kobbelt_2013, title={Practical Anisotropic
    Geodesy}, volume={32}, DOI={<a href="https://doi.org/10.1111/cgf.12173">10.1111/cgf.12173</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
    Marcel and Heistermann, Martin and Kobbelt, Leif}, year={2013}, pages={63–71}
    }'
  chicago: 'Campen, Marcel, Martin Heistermann, and Leif Kobbelt. “Practical Anisotropic
    Geodesy.” <i>Computer Graphics Forum</i> 32, no. 5 (2013): 63–71. <a href="https://doi.org/10.1111/cgf.12173">https://doi.org/10.1111/cgf.12173</a>.'
  ieee: 'M. Campen, M. Heistermann, and L. Kobbelt, “Practical Anisotropic Geodesy,”
    <i>Computer Graphics Forum</i>, vol. 32, no. 5, pp. 63–71, 2013, doi: <a href="https://doi.org/10.1111/cgf.12173">10.1111/cgf.12173</a>.'
  mla: Campen, Marcel, et al. “Practical Anisotropic Geodesy.” <i>Computer Graphics
    Forum</i>, vol. 32, no. 5, Wiley, 2013, pp. 63–71, doi:<a href="https://doi.org/10.1111/cgf.12173">10.1111/cgf.12173</a>.
  short: M. Campen, M. Heistermann, L. Kobbelt, Computer Graphics Forum 32 (2013)
    63–71.
date_created: 2025-06-30T06:53:20Z
date_updated: 2025-07-14T12:40:27Z
department:
- _id: '969'
doi: 10.1111/cgf.12173
extern: '1'
intvolume: '        32'
issue: '5'
language:
- iso: eng
page: 63-71
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Practical Anisotropic Geodesy
type: journal_article
user_id: '117512'
volume: 32
year: '2013'
...
---
_id: '60455'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>In mechanical engineering and architecture,
    structural elements with low material consumption and high load‐bearing capabilities
    are essential for light‐weight and even self‐supporting constructions. This paper
    deals with so called point‐folding elements – non‐planar, pyramidal panels, usually
    formed from thin metal sheets, which exploit the increased structural capabilities
    emerging from folds or creases. Given a triangulated free‐form surface, a corresponding
    point‐folding structure is a collection of pyramidal elements basing on the triangles.
    User‐specified or material‐induced geometric constraints often imply that each
    individual folding element has a different shape, leading to immense fabrication
    costs. We present a rationalization method for such structures which respects
    the prescribed aesthetic and production constraints and finds a minimal set of
    molds for the production process, leading to drastically reduced costs. For each
    base triangle we compute and parametrize the range of feasible folding elements
    that satisfy the given constraints within the allowed tolerances. Then we pose
    the rationalization task as a geometric intersection problem, which we solve so
    as to maximize the re‐use of mold dies. Major challenges arise from the high precision
    requirements and the non‐trivial parametrization of the search space. We evaluate
    our method on a number of practical examples where we achieve rationalization
    gains of more than 90%.</jats:p>
author:
- first_name: Henrik
  full_name: Zimmer, Henrik
  last_name: Zimmer
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: David
  full_name: Bommes, David
  last_name: Bommes
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Zimmer H, Campen M, Bommes D, Kobbelt L. Rationalization of Triangle‐Based
    Point‐Folding Structures. <i>Computer Graphics Forum</i>. 2012;31(2pt3):611-620.
    doi:<a href="https://doi.org/10.1111/j.1467-8659.2012.03040.x">10.1111/j.1467-8659.2012.03040.x</a>
  apa: Zimmer, H., Campen, M., Bommes, D., &#38; Kobbelt, L. (2012). Rationalization
    of Triangle‐Based Point‐Folding Structures. <i>Computer Graphics Forum</i>, <i>31</i>(2pt3),
    611–620. <a href="https://doi.org/10.1111/j.1467-8659.2012.03040.x">https://doi.org/10.1111/j.1467-8659.2012.03040.x</a>
  bibtex: '@article{Zimmer_Campen_Bommes_Kobbelt_2012, title={Rationalization of Triangle‐Based
    Point‐Folding Structures}, volume={31}, DOI={<a href="https://doi.org/10.1111/j.1467-8659.2012.03040.x">10.1111/j.1467-8659.2012.03040.x</a>},
    number={2pt3}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Zimmer,
    Henrik and Campen, Marcel and Bommes, David and Kobbelt, Leif}, year={2012}, pages={611–620}
    }'
  chicago: 'Zimmer, Henrik, Marcel Campen, David Bommes, and Leif Kobbelt. “Rationalization
    of Triangle‐Based Point‐Folding Structures.” <i>Computer Graphics Forum</i> 31,
    no. 2pt3 (2012): 611–20. <a href="https://doi.org/10.1111/j.1467-8659.2012.03040.x">https://doi.org/10.1111/j.1467-8659.2012.03040.x</a>.'
  ieee: 'H. Zimmer, M. Campen, D. Bommes, and L. Kobbelt, “Rationalization of Triangle‐Based
    Point‐Folding Structures,” <i>Computer Graphics Forum</i>, vol. 31, no. 2pt3,
    pp. 611–620, 2012, doi: <a href="https://doi.org/10.1111/j.1467-8659.2012.03040.x">10.1111/j.1467-8659.2012.03040.x</a>.'
  mla: Zimmer, Henrik, et al. “Rationalization of Triangle‐Based Point‐Folding Structures.”
    <i>Computer Graphics Forum</i>, vol. 31, no. 2pt3, Wiley, 2012, pp. 611–20, doi:<a
    href="https://doi.org/10.1111/j.1467-8659.2012.03040.x">10.1111/j.1467-8659.2012.03040.x</a>.
  short: H. Zimmer, M. Campen, D. Bommes, L. Kobbelt, Computer Graphics Forum 31 (2012)
    611–620.
date_created: 2025-06-30T07:19:54Z
date_updated: 2025-07-14T12:39:35Z
department:
- _id: '969'
doi: 10.1111/j.1467-8659.2012.03040.x
extern: '1'
intvolume: '        31'
issue: 2pt3
language:
- iso: eng
page: 611-620
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Rationalization of Triangle‐Based Point‐Folding Structures
type: journal_article
user_id: '117512'
volume: 31
year: '2012'
...
---
_id: '60461'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Efficient methods to compute intrinsic
    distances and geodesic paths have been presented for various types of surface
    representations, most importantly polygon meshes. These meshes are usually assumed
    to be well‐structured and manifold. In practice, however, they often contain defects
    like holes, gaps, degeneracies, non‐manifold configurations – or they might even
    be just a soup of polygons. The task of repairing these defects is computationally
    complex and in many cases exhibits various ambiguities demanding tedious manual
    efforts. We present a computational framework that enables the computation of
    meaningful approximate intrinsic distances and geodesic paths on raw meshes in
    a way which is tolerant to such defects. Holes and gaps are bridged up to a user‐specified
    tolerance threshold such that distances can be computed plausibly even across
    multiple connected components of inconsistent meshes. Further, we show ways to
    locally parameterize a surface based on geodesic distance fields, easily facilitating
    the application of textures and decals on raw meshes. We do all this without explicitly
    repairing the input, thereby avoiding the costly additional efforts. In order
    to enable broad applicability we provide details on two implementation variants,
    one optimized for performance, the other optimized for memory efficiency. Using
    the presented framework many applications can readily be extended to deal with
    imperfect meshes. Since we abstract from the input applicability is not even limited
    to meshes, other representations can be handled as well.</jats:p>
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: 'Campen M, Kobbelt L. Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances
    and Parameterizations. <i>Computer Graphics Forum</i>. 2011;30(2):623-632. doi:<a
    href="https://doi.org/10.1111/j.1467-8659.2011.01896.x">10.1111/j.1467-8659.2011.01896.x</a>'
  apa: 'Campen, M., &#38; Kobbelt, L. (2011). Walking On Broken Mesh: Defect‐Tolerant
    Geodesic Distances and Parameterizations. <i>Computer Graphics Forum</i>, <i>30</i>(2),
    623–632. <a href="https://doi.org/10.1111/j.1467-8659.2011.01896.x">https://doi.org/10.1111/j.1467-8659.2011.01896.x</a>'
  bibtex: '@article{Campen_Kobbelt_2011, title={Walking On Broken Mesh: Defect‐Tolerant
    Geodesic Distances and Parameterizations}, volume={30}, DOI={<a href="https://doi.org/10.1111/j.1467-8659.2011.01896.x">10.1111/j.1467-8659.2011.01896.x</a>},
    number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
    Marcel and Kobbelt, Leif}, year={2011}, pages={623–632} }'
  chicago: 'Campen, Marcel, and Leif Kobbelt. “Walking On Broken Mesh: Defect‐Tolerant
    Geodesic Distances and Parameterizations.” <i>Computer Graphics Forum</i> 30,
    no. 2 (2011): 623–32. <a href="https://doi.org/10.1111/j.1467-8659.2011.01896.x">https://doi.org/10.1111/j.1467-8659.2011.01896.x</a>.'
  ieee: 'M. Campen and L. Kobbelt, “Walking On Broken Mesh: Defect‐Tolerant Geodesic
    Distances and Parameterizations,” <i>Computer Graphics Forum</i>, vol. 30, no.
    2, pp. 623–632, 2011, doi: <a href="https://doi.org/10.1111/j.1467-8659.2011.01896.x">10.1111/j.1467-8659.2011.01896.x</a>.'
  mla: 'Campen, Marcel, and Leif Kobbelt. “Walking On Broken Mesh: Defect‐Tolerant
    Geodesic Distances and Parameterizations.” <i>Computer Graphics Forum</i>, vol.
    30, no. 2, Wiley, 2011, pp. 623–32, doi:<a href="https://doi.org/10.1111/j.1467-8659.2011.01896.x">10.1111/j.1467-8659.2011.01896.x</a>.'
  short: M. Campen, L. Kobbelt, Computer Graphics Forum 30 (2011) 623–632.
date_created: 2025-06-30T08:14:56Z
date_updated: 2025-07-14T12:35:50Z
department:
- _id: '969'
doi: 10.1111/j.1467-8659.2011.01896.x
extern: '1'
intvolume: '        30'
issue: '2'
language:
- iso: eng
page: 623-632
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: 'Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations'
type: journal_article
user_id: '117512'
volume: 30
year: '2011'
...
---
_id: '60463'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We present a new technique to implement
    operators that modify the topology of polygonal meshes at intersections and self‐intersections.
    Depending on the modification strategy, this effectively results in operators
    for Boolean combinations or for the construction of outer hulls that are suited
    for mesh repair tasks and accurate mesh‐based front tracking of deformable materials
    that split and merge. By combining an adaptive octree with nested binary space
    partitions (BSP), we can guarantee exactness (= correctness) and robustness (=
    completeness) of the algorithm while still achieving higher performance and less
    memory consumption than previous approaches. The efficiency and scalability in
    terms of runtime and memory is obtained by an operation localization scheme. We
    restrict the essential computations to those cells in the adaptive octree where
    intersections actually occur. Within those critical cells, we convert the input
    geometry into a plane‐based BSP‐representation which allows us to perform all
    computations exactly even with fixed precision arithmetics. We carefully analyze
    the precision requirements of the involved geometric data and predicates in order
    to guarantee correctness and show how minimal input mesh quantization can be used
    to safely rely on computations with standard floating point numbers. We properly
    evaluate our method with respect to precision, robustness, and efficiency.</jats:p>
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Campen M, Kobbelt L. Exact and Robust (Self‐)Intersections for Polygonal Meshes.
    <i>Computer Graphics Forum</i>. 2010;29(2):397-406. doi:<a href="https://doi.org/10.1111/j.1467-8659.2009.01609.x">10.1111/j.1467-8659.2009.01609.x</a>
  apa: Campen, M., &#38; Kobbelt, L. (2010). Exact and Robust (Self‐)Intersections
    for Polygonal Meshes. <i>Computer Graphics Forum</i>, <i>29</i>(2), 397–406. <a
    href="https://doi.org/10.1111/j.1467-8659.2009.01609.x">https://doi.org/10.1111/j.1467-8659.2009.01609.x</a>
  bibtex: '@article{Campen_Kobbelt_2010, title={Exact and Robust (Self‐)Intersections
    for Polygonal Meshes}, volume={29}, DOI={<a href="https://doi.org/10.1111/j.1467-8659.2009.01609.x">10.1111/j.1467-8659.2009.01609.x</a>},
    number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
    Marcel and Kobbelt, Leif}, year={2010}, pages={397–406} }'
  chicago: 'Campen, Marcel, and Leif Kobbelt. “Exact and Robust (Self‐)Intersections
    for Polygonal Meshes.” <i>Computer Graphics Forum</i> 29, no. 2 (2010): 397–406.
    <a href="https://doi.org/10.1111/j.1467-8659.2009.01609.x">https://doi.org/10.1111/j.1467-8659.2009.01609.x</a>.'
  ieee: 'M. Campen and L. Kobbelt, “Exact and Robust (Self‐)Intersections for Polygonal
    Meshes,” <i>Computer Graphics Forum</i>, vol. 29, no. 2, pp. 397–406, 2010, doi:
    <a href="https://doi.org/10.1111/j.1467-8659.2009.01609.x">10.1111/j.1467-8659.2009.01609.x</a>.'
  mla: Campen, Marcel, and Leif Kobbelt. “Exact and Robust (Self‐)Intersections for
    Polygonal Meshes.” <i>Computer Graphics Forum</i>, vol. 29, no. 2, Wiley, 2010,
    pp. 397–406, doi:<a href="https://doi.org/10.1111/j.1467-8659.2009.01609.x">10.1111/j.1467-8659.2009.01609.x</a>.
  short: M. Campen, L. Kobbelt, Computer Graphics Forum 29 (2010) 397–406.
date_created: 2025-06-30T08:24:08Z
date_updated: 2025-07-14T12:35:44Z
department:
- _id: '969'
doi: 10.1111/j.1467-8659.2009.01609.x
extern: '1'
intvolume: '        29'
issue: '2'
language:
- iso: eng
page: 397-406
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Exact and Robust (Self‐)Intersections for Polygonal Meshes
type: journal_article
user_id: '117512'
volume: 29
year: '2010'
...