---
_id: '60437'
abstract:
- lang: eng
  text: <jats:p>Parametrization based methods have recently become very popular for
    the generation of high quality quad meshes. In contrast to previous approaches,
    they allow for intuitive user control in order to accommodate all kinds of application
    driven constraints and design intentions. A major obstacle in practice, however,
    are the relatively long computations that lead to response times of several minutes
    already for input models of moderate complexity. In this paper we introduce a
    novel strategy to handle highly complex input meshes with up to several millions
    of triangles such that quad meshes can still be created and edited within an interactive
    workflow. Our method is based on representing the input model on different levels
    of resolution with a mechanism to propagate parametrizations from coarser to finer
    levels. The major challenge is to guarantee consistent parametrizations even in
    the presence of charts, transition functions, and singularities. Moreover, the
    remaining degrees of freedom on coarser levels of resolution have to be chosen
    carefully in order to still achieve low distortion parametrizations. We demonstrate
    a prototypic system where the user can interactively edit quad meshes with powerful
    high-level operations such as guiding constraints, singularity repositioning,
    and singularity connections.</jats:p>
author:
- first_name: Hans-Christian
  full_name: Ebke, Hans-Christian
  last_name: Ebke
- 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: Ebke H-C, Schmidt P, Campen M, Kobbelt L. Interactively controlled quad remeshing
    of high resolution 3D models. <i>ACM Transactions on Graphics</i>. 2016;35(6):1-13.
    doi:<a href="https://doi.org/10.1145/2980179.2982413">10.1145/2980179.2982413</a>
  apa: Ebke, H.-C., Schmidt, P., Campen, M., &#38; Kobbelt, L. (2016). Interactively
    controlled quad remeshing of high resolution 3D models. <i>ACM Transactions on
    Graphics</i>, <i>35</i>(6), 1–13. <a href="https://doi.org/10.1145/2980179.2982413">https://doi.org/10.1145/2980179.2982413</a>
  bibtex: '@article{Ebke_Schmidt_Campen_Kobbelt_2016, title={Interactively controlled
    quad remeshing of high resolution 3D models}, volume={35}, DOI={<a href="https://doi.org/10.1145/2980179.2982413">10.1145/2980179.2982413</a>},
    number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Ebke, Hans-Christian and Schmidt, Patrick
    and Campen, Marcel and Kobbelt, Leif}, year={2016}, pages={1–13} }'
  chicago: 'Ebke, Hans-Christian, Patrick Schmidt, Marcel Campen, and Leif Kobbelt.
    “Interactively Controlled Quad Remeshing of High Resolution 3D Models.” <i>ACM
    Transactions on Graphics</i> 35, no. 6 (2016): 1–13. <a href="https://doi.org/10.1145/2980179.2982413">https://doi.org/10.1145/2980179.2982413</a>.'
  ieee: 'H.-C. Ebke, P. Schmidt, M. Campen, and L. Kobbelt, “Interactively controlled
    quad remeshing of high resolution 3D models,” <i>ACM Transactions on Graphics</i>,
    vol. 35, no. 6, pp. 1–13, 2016, doi: <a href="https://doi.org/10.1145/2980179.2982413">10.1145/2980179.2982413</a>.'
  mla: Ebke, Hans-Christian, et al. “Interactively Controlled Quad Remeshing of High
    Resolution 3D Models.” <i>ACM Transactions on Graphics</i>, vol. 35, no. 6, Association
    for Computing Machinery (ACM), 2016, pp. 1–13, doi:<a href="https://doi.org/10.1145/2980179.2982413">10.1145/2980179.2982413</a>.
  short: H.-C. Ebke, P. Schmidt, M. Campen, L. Kobbelt, ACM Transactions on Graphics
    35 (2016) 1–13.
date_created: 2025-06-27T07:54:23Z
date_updated: 2025-07-14T12:41:54Z
department:
- _id: '969'
doi: 10.1145/2980179.2982413
extern: '1'
intvolume: '        35'
issue: '6'
language:
- iso: eng
page: 1-13
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
  - 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Interactively controlled quad remeshing of high resolution 3D models
type: journal_article
user_id: '117512'
volume: 35
year: '2016'
...
---
_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: '60436'
abstract:
- lang: eng
  text: <jats:p>This paper presents a method for bijective parametrization of 2D and
    3D objects over canonical domains. While a range of solutions for the two-dimensional
    case are well-known, our method guarantees bijectivity of mappings also for a
    large, combinatorially-defined class of tetrahedral meshes (shellable meshes).
    The key concept in our method is the piecewise-linear (PL) foliation, decomposing
    the mesh into one-dimensional submanifolds and reducing the mapping problem to
    parametrization of a lower-dimensional manifold (a foliation section). The maps
    resulting from these foliations are proved to be bijective and continuous, and
    shown to have provably bijective PL approximations. We describe exact, numerically
    robust evaluation methods and demonstrate our implementation's capabilities on
    a large variety of meshes.</jats:p>
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
- first_name: Cláudio T.
  full_name: Silva, Cláudio T.
  last_name: Silva
- first_name: Denis
  full_name: Zorin, Denis
  last_name: Zorin
citation:
  ama: Campen M, Silva CT, Zorin D. Bijective maps from simplicial foliations. <i>ACM
    Transactions on Graphics</i>. 2016;35(4):1-15. doi:<a href="https://doi.org/10.1145/2897824.2925890">10.1145/2897824.2925890</a>
  apa: Campen, M., Silva, C. T., &#38; Zorin, D. (2016). Bijective maps from simplicial
    foliations. <i>ACM Transactions on Graphics</i>, <i>35</i>(4), 1–15. <a href="https://doi.org/10.1145/2897824.2925890">https://doi.org/10.1145/2897824.2925890</a>
  bibtex: '@article{Campen_Silva_Zorin_2016, title={Bijective maps from simplicial
    foliations}, volume={35}, DOI={<a href="https://doi.org/10.1145/2897824.2925890">10.1145/2897824.2925890</a>},
    number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Campen, Marcel and Silva, Cláudio T. and Zorin,
    Denis}, year={2016}, pages={1–15} }'
  chicago: 'Campen, Marcel, Cláudio T. Silva, and Denis Zorin. “Bijective Maps from
    Simplicial Foliations.” <i>ACM Transactions on Graphics</i> 35, no. 4 (2016):
    1–15. <a href="https://doi.org/10.1145/2897824.2925890">https://doi.org/10.1145/2897824.2925890</a>.'
  ieee: 'M. Campen, C. T. Silva, and D. Zorin, “Bijective maps from simplicial foliations,”
    <i>ACM Transactions on Graphics</i>, vol. 35, no. 4, pp. 1–15, 2016, doi: <a href="https://doi.org/10.1145/2897824.2925890">10.1145/2897824.2925890</a>.'
  mla: Campen, Marcel, et al. “Bijective Maps from Simplicial Foliations.” <i>ACM
    Transactions on Graphics</i>, vol. 35, no. 4, Association for Computing Machinery
    (ACM), 2016, pp. 1–15, doi:<a href="https://doi.org/10.1145/2897824.2925890">10.1145/2897824.2925890</a>.
  short: M. Campen, C.T. Silva, D. Zorin, ACM Transactions on Graphics 35 (2016) 1–15.
date_created: 2025-06-27T07:52:32Z
date_updated: 2025-07-14T12:41:57Z
department:
- _id: '969'
doi: 10.1145/2897824.2925890
extern: '1'
intvolume: '        35'
issue: '4'
language:
- iso: eng
page: 1-15
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 maps from simplicial foliations
type: journal_article
user_id: '117512'
volume: 35
year: '2016'
...
---
_id: '60446'
author:
- first_name: Marcel
  full_name: Campen, Marcel
  id: '114904'
  last_name: Campen
  orcid: 0000-0003-2340-3462
citation:
  ama: 'Campen M. <i>Quad Layouts: Generation and Optimization of Conforming Quadrilateral
    Surface Partitions</i>. RWTH Aachen University, Germany; 2015.'
  apa: 'Campen, M. (2015). <i>Quad layouts: generation and optimization of conforming
    quadrilateral surface partitions</i>. RWTH Aachen University, Germany.'
  bibtex: '@book{Campen_2015, title={Quad layouts: generation and optimization of
    conforming quadrilateral surface partitions}, publisher={RWTH Aachen University,
    Germany}, author={Campen, Marcel}, year={2015} }'
  chicago: 'Campen, Marcel. <i>Quad Layouts: Generation and Optimization of Conforming
    Quadrilateral Surface Partitions</i>. RWTH Aachen University, Germany, 2015.'
  ieee: 'M. Campen, <i>Quad layouts: generation and optimization of conforming quadrilateral
    surface partitions</i>. RWTH Aachen University, Germany, 2015.'
  mla: 'Campen, Marcel. <i>Quad Layouts: Generation and Optimization of Conforming
    Quadrilateral Surface Partitions</i>. RWTH Aachen University, Germany, 2015.'
  short: 'M. Campen, Quad Layouts: Generation and Optimization of Conforming Quadrilateral
    Surface Partitions, RWTH Aachen University, Germany, 2015.'
date_created: 2025-06-27T10:25:19Z
date_updated: 2025-07-14T12:41:18Z
department:
- _id: '969'
extern: '1'
language:
- iso: eng
publisher: RWTH Aachen University, Germany
status: public
title: 'Quad layouts: generation and optimization of conforming quadrilateral surface
  partitions'
type: dissertation
user_id: '114904'
year: '2015'
...
---
_id: '60442'
abstract:
- lang: eng
  text: '<jats:p>Global surface parametrization often requires the use of cuts or
    charts due to non-trivial topology. In recent years a focus has been on so-called<jats:italic>seamless</jats:italic>parametrizations,
    where the transition functions across the cuts are rigid transformations with
    a rotation about some multiple of 90°. Of particular interest, e.g. for quadrilateral
    meshing, paneling, or texturing, are those instances where in addition the translational
    part of these transitions is integral (or more generally: quantized). We show
    that finding not even the optimal, but just an arbitrary valid quantization (one
    that does not imply parametric degeneracies), is a complex combinatorial problem.
    We present a novel method that allows us to solve it, i.e. to find valid as well
    as good quality quantizations. It is based on an original approach to quickly
    construct solutions to linear Diophantine equation systems, exploiting the specific
    geometric nature of the parametrization problem. We thereby largely outperform
    the state-of-the-art, sometimes by several orders of magnitude.</jats:p>'
author:
- 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: Campen M, Bommes D, Kobbelt L. Quantized global parametrization. <i>ACM Transactions
    on Graphics</i>. 2015;34(6):1-12. doi:<a href="https://doi.org/10.1145/2816795.2818140">10.1145/2816795.2818140</a>
  apa: Campen, M., Bommes, D., &#38; Kobbelt, L. (2015). Quantized global parametrization.
    <i>ACM Transactions on Graphics</i>, <i>34</i>(6), 1–12. <a href="https://doi.org/10.1145/2816795.2818140">https://doi.org/10.1145/2816795.2818140</a>
  bibtex: '@article{Campen_Bommes_Kobbelt_2015, title={Quantized global parametrization},
    volume={34}, DOI={<a href="https://doi.org/10.1145/2816795.2818140">10.1145/2816795.2818140</a>},
    number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Campen, Marcel and Bommes, David and Kobbelt,
    Leif}, year={2015}, pages={1–12} }'
  chicago: 'Campen, Marcel, David Bommes, and Leif Kobbelt. “Quantized Global Parametrization.”
    <i>ACM Transactions on Graphics</i> 34, no. 6 (2015): 1–12. <a href="https://doi.org/10.1145/2816795.2818140">https://doi.org/10.1145/2816795.2818140</a>.'
  ieee: 'M. Campen, D. Bommes, and L. Kobbelt, “Quantized global parametrization,”
    <i>ACM Transactions on Graphics</i>, vol. 34, no. 6, pp. 1–12, 2015, doi: <a href="https://doi.org/10.1145/2816795.2818140">10.1145/2816795.2818140</a>.'
  mla: Campen, Marcel, et al. “Quantized Global Parametrization.” <i>ACM Transactions
    on Graphics</i>, vol. 34, no. 6, Association for Computing Machinery (ACM), 2015,
    pp. 1–12, doi:<a href="https://doi.org/10.1145/2816795.2818140">10.1145/2816795.2818140</a>.
  short: M. Campen, D. Bommes, L. Kobbelt, ACM Transactions on Graphics 34 (2015)
    1–12.
date_created: 2025-06-27T10:19:04Z
date_updated: 2025-07-14T12:41:34Z
department:
- _id: '969'
doi: 10.1145/2816795.2818140
extern: '1'
intvolume: '        34'
issue: '6'
language:
- iso: eng
page: 1-12
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
  - 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Quantized global parametrization
type: journal_article
user_id: '117512'
volume: 34
year: '2015'
...
---
_id: '60444'
abstract:
- lang: eng
  text: "<jats:p>\r\n            We introduce\r\n            <jats:italic>Dual Strip
    Weaving</jats:italic>\r\n            , a novel concept for the interactive design
    of quad layouts, i.e. partitionings of freeform surfaces into quadrilateral patch
    networks. In contrast to established tools for the design of quad layouts or subdivision
    base meshes, which are often based on creating individual vertices, edges, and
    quads, our method takes a more global perspective, operating on a higher level
    of abstraction: the atomic operation of our method is the creation of an entire
    cyclic strip, delineating a large number of quad patches at once. The global consistency-preserving
    nature of this approach reduces demands on the user's expertise by requiring less
    advance planning. Efficiency is achieved using a novel method at the heart of
    our system, which automatically proposes geometrically and topologically suitable
    strips to the user. Based on this we provide interaction tools to influence the
    design process to any desired degree and visual guides to support the user in
    this task.\r\n          </jats:p>"
alternative_title:
- interactive design of quad layouts using elastica strips
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. Dual strip weaving. <i>ACM Transactions on Graphics</i>.
    2014;33(6):1-10. doi:<a href="https://doi.org/10.1145/2661229.2661236">10.1145/2661229.2661236</a>
  apa: Campen, M., &#38; Kobbelt, L. (2014). Dual strip weaving. <i>ACM Transactions
    on Graphics</i>, <i>33</i>(6), 1–10. <a href="https://doi.org/10.1145/2661229.2661236">https://doi.org/10.1145/2661229.2661236</a>
  bibtex: '@article{Campen_Kobbelt_2014, title={Dual strip weaving}, volume={33},
    DOI={<a href="https://doi.org/10.1145/2661229.2661236">10.1145/2661229.2661236</a>},
    number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Campen, Marcel and Kobbelt, Leif}, year={2014},
    pages={1–10} }'
  chicago: 'Campen, Marcel, and Leif Kobbelt. “Dual Strip Weaving.” <i>ACM Transactions
    on Graphics</i> 33, no. 6 (2014): 1–10. <a href="https://doi.org/10.1145/2661229.2661236">https://doi.org/10.1145/2661229.2661236</a>.'
  ieee: 'M. Campen and L. Kobbelt, “Dual strip weaving,” <i>ACM Transactions on Graphics</i>,
    vol. 33, no. 6, pp. 1–10, 2014, doi: <a href="https://doi.org/10.1145/2661229.2661236">10.1145/2661229.2661236</a>.'
  mla: Campen, Marcel, and Leif Kobbelt. “Dual Strip Weaving.” <i>ACM Transactions
    on Graphics</i>, vol. 33, no. 6, Association for Computing Machinery (ACM), 2014,
    pp. 1–10, doi:<a href="https://doi.org/10.1145/2661229.2661236">10.1145/2661229.2661236</a>.
  short: M. Campen, L. Kobbelt, ACM Transactions on Graphics 33 (2014) 1–10.
date_created: 2025-06-27T10:22:29Z
date_updated: 2025-07-14T12:41:30Z
department:
- _id: '969'
doi: 10.1145/2661229.2661236
extern: '1'
intvolume: '        33'
issue: '6'
language:
- iso: eng
page: 1-10
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
  - 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Dual strip weaving
type: journal_article
user_id: '117512'
volume: 33
year: '2014'
...
---
_id: '60445'
abstract:
- lang: eng
  text: '<jats:p>The most effective and popular tools for obtaining feature aligned
    quad meshes from triangular input meshes are based on cross field guided parametrization.
    These methods are incarnations of a conceptual three-step pipeline: (1) cross
    field computation, (2) field-guided surface parametrization, (3) quad mesh extraction.
    While in most meshing scenarios the user prescribes a desired target quad size
    or edge length, this information is typically taken into account from step 2 onwards
    only, but not in the cross field computation step. This turns into a problem in
    the presence of small scale geometric or topological features or noise in the
    input mesh: closely placed singularities are induced in the cross field, which
    are not properly reproducible by vertices in a quad mesh with the prescribed edge
    length, causing severe distortions or even failure of the meshing algorithm. We
    reformulate the construction of cross fields as well as field-guided parametrizations
    in a scale-aware manner which effectively suppresses densely spaced features and
    noise of geometric as well as topological kind. Dominant large-scale features
    are adequately preserved in the output by relying on the unaltered input mesh
    as the computational domain.</jats:p>'
author:
- first_name: Hans-Christian
  full_name: Ebke, Hans-Christian
  last_name: Ebke
- 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: Ebke H-C, Campen M, Bommes D, Kobbelt L. Level-of-detail quad meshing. <i>ACM
    Transactions on Graphics</i>. 2014;33(6):1-11. doi:<a href="https://doi.org/10.1145/2661229.2661240">10.1145/2661229.2661240</a>
  apa: Ebke, H.-C., Campen, M., Bommes, D., &#38; Kobbelt, L. (2014). Level-of-detail
    quad meshing. <i>ACM Transactions on Graphics</i>, <i>33</i>(6), 1–11. <a href="https://doi.org/10.1145/2661229.2661240">https://doi.org/10.1145/2661229.2661240</a>
  bibtex: '@article{Ebke_Campen_Bommes_Kobbelt_2014, title={Level-of-detail quad meshing},
    volume={33}, DOI={<a href="https://doi.org/10.1145/2661229.2661240">10.1145/2661229.2661240</a>},
    number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Ebke, Hans-Christian and Campen, Marcel and
    Bommes, David and Kobbelt, Leif}, year={2014}, pages={1–11} }'
  chicago: 'Ebke, Hans-Christian, Marcel Campen, David Bommes, and Leif Kobbelt. “Level-of-Detail
    Quad Meshing.” <i>ACM Transactions on Graphics</i> 33, no. 6 (2014): 1–11. <a
    href="https://doi.org/10.1145/2661229.2661240">https://doi.org/10.1145/2661229.2661240</a>.'
  ieee: 'H.-C. Ebke, M. Campen, D. Bommes, and L. Kobbelt, “Level-of-detail quad meshing,”
    <i>ACM Transactions on Graphics</i>, vol. 33, no. 6, pp. 1–11, 2014, doi: <a href="https://doi.org/10.1145/2661229.2661240">10.1145/2661229.2661240</a>.'
  mla: Ebke, Hans-Christian, et al. “Level-of-Detail Quad Meshing.” <i>ACM Transactions
    on Graphics</i>, vol. 33, no. 6, Association for Computing Machinery (ACM), 2014,
    pp. 1–11, doi:<a href="https://doi.org/10.1145/2661229.2661240">10.1145/2661229.2661240</a>.
  short: H.-C. Ebke, M. Campen, D. Bommes, L. Kobbelt, ACM Transactions on Graphics
    33 (2014) 1–11.
date_created: 2025-06-27T10:23:37Z
date_updated: 2025-07-14T12:41:24Z
department:
- _id: '969'
doi: 10.1145/2661229.2661240
extern: '1'
intvolume: '        33'
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: Level-of-detail quad meshing
type: journal_article
user_id: '117512'
volume: 33
year: '2014'
...
---
_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: '60453'
abstract:
- lang: eng
  text: "<jats:p>\r\n            The most popular and actively researched class of
    quad remeshing techniques is the family of\r\n            <jats:italic>parametrization
    based quad meshing methods</jats:italic>\r\n            . They all strive to generate
    an\r\n            <jats:italic>integer-grid map</jats:italic>\r\n            ,
    i.e. a parametrization of the input surface into R\r\n            <jats:sup>2</jats:sup>\r\n
    \           such that the canonical grid of integer iso-lines forms a quad mesh
    when mapped back onto the surface in R\r\n            <jats:sup>3</jats:sup>\r\n
    \           . An essential, albeit broadly neglected aspect of these methods is
    the\r\n            <jats:italic>quad extraction</jats:italic>\r\n            step,
    i.e. the materialization of an actual quad mesh from the mere \"quad texture\".
    Quad (mesh) extraction is often believed to be a trivial matter but quite the
    opposite is true: numerous special cases, ambiguities induced by numerical inaccuracies
    and limited solver precision, as well as imperfections in the maps produced by
    most methods (unless costly countermeasures are taken) pose significant challenges
    to the quad extractor. We present a method to sanitize a provided parametrization
    such that it becomes numerically consistent even in a limited precision floating
    point representation. Based on this we are able to provide a comprehensive and
    sound description of how to perform quad extraction robustly and without the need
    for any complex tolerance thresholds or disambiguation rules. On top of that we
    develop a novel strategy to cope with common local fold-overs in the parametrization.
    This allows our method, dubbed\r\n            <jats:italic>QEx</jats:italic>\r\n
    \           , to generate all-quadrilateral meshes where otherwise holes, non-quad
    polygons or no output at all would have been produced. We thus enable the practical
    use of an entire class of maps that was previously considered defective. Since
    state of the art quad meshing methods spend a significant share of their run time
    solely to prevent local fold-overs, using our method it is now possible to obtain
    quad meshes significantly quicker than before. We also provide libQEx, an open
    source C++ reference implementation of our method and thus significantly lower
    the bar to enter the field of quad meshing.\r\n          </jats:p>"
alternative_title:
- robust quad mesh extraction
author:
- first_name: Hans-Christian
  full_name: Ebke, Hans-Christian
  last_name: Ebke
- 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: Ebke H-C, Bommes D, Campen M, Kobbelt L. QEx. <i>ACM Transactions on Graphics</i>.
    2013;32(6):1-10. doi:<a href="https://doi.org/10.1145/2508363.2508372">10.1145/2508363.2508372</a>
  apa: Ebke, H.-C., Bommes, D., Campen, M., &#38; Kobbelt, L. (2013). QEx. <i>ACM
    Transactions on Graphics</i>, <i>32</i>(6), 1–10. <a href="https://doi.org/10.1145/2508363.2508372">https://doi.org/10.1145/2508363.2508372</a>
  bibtex: '@article{Ebke_Bommes_Campen_Kobbelt_2013, title={QEx}, volume={32}, DOI={<a
    href="https://doi.org/10.1145/2508363.2508372">10.1145/2508363.2508372</a>}, number={6},
    journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery
    (ACM)}, author={Ebke, Hans-Christian and Bommes, David and Campen, Marcel and
    Kobbelt, Leif}, year={2013}, pages={1–10} }'
  chicago: 'Ebke, Hans-Christian, David Bommes, Marcel Campen, and Leif Kobbelt. “QEx.”
    <i>ACM Transactions on Graphics</i> 32, no. 6 (2013): 1–10. <a href="https://doi.org/10.1145/2508363.2508372">https://doi.org/10.1145/2508363.2508372</a>.'
  ieee: 'H.-C. Ebke, D. Bommes, M. Campen, and L. Kobbelt, “QEx,” <i>ACM Transactions
    on Graphics</i>, vol. 32, no. 6, pp. 1–10, 2013, doi: <a href="https://doi.org/10.1145/2508363.2508372">10.1145/2508363.2508372</a>.'
  mla: Ebke, Hans-Christian, et al. “QEx.” <i>ACM Transactions on Graphics</i>, vol.
    32, no. 6, Association for Computing Machinery (ACM), 2013, pp. 1–10, doi:<a href="https://doi.org/10.1145/2508363.2508372">10.1145/2508363.2508372</a>.
  short: H.-C. Ebke, D. Bommes, M. Campen, L. Kobbelt, ACM Transactions on Graphics
    32 (2013) 1–10.
date_created: 2025-06-30T07:11:12Z
date_updated: 2025-07-14T12:39:54Z
department:
- _id: '969'
doi: 10.1145/2508363.2508372
extern: '1'
intvolume: '        32'
issue: '6'
language:
- iso: eng
page: 1-10
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
  - 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: QEx
type: journal_article
user_id: '117512'
volume: 32
year: '2013'
...
---
_id: '60452'
abstract:
- lang: eng
  text: '<jats:p>Quadrilateral remeshing approaches based on global parametrization
    enable many desirable mesh properties. Two of the most important ones are (1)
    high regularity due to explicit control over irregular vertices and (2) smooth
    distribution of distortion achieved by convex variational formulations. Apart
    from these strengths, state-of-the-art techniques suffer from limited reliability
    on real-world input data, i.e. the determined map might have degeneracies like
    (local) non-injectivities and consequently often cannot be used directly to generate
    a quadrilateral mesh. In this paper we propose a novel convex Mixed-Integer Quadratic
    Programming (MIQP) formulation which ensures by construction that the resulting
    map is within the class of so called Integer-Grid Maps that are guaranteed to
    imply a quad mesh. In order to overcome the NP-hardness of MIQP and to be able
    to remesh typical input geometries in acceptable time we propose two additional
    problem specific optimizations: a complexity reduction algorithm and singularity
    separating conditions. While the former decouples the dimension of the MIQP search
    space from the input complexity of the triangle mesh and thus is able to dramatically
    speed up the computation without inducing inaccuracies, the latter improves the
    continuous relaxation, which is crucial for the success of modern MIQP optimizers.
    Our experiments show that the reliability of the resulting algorithm does not
    only annihilate the main drawback of parametrization based quad-remeshing but
    moreover enables the global search for high-quality coarse quad layouts - a difficult
    task solely tackled by greedy methodologies before.</jats:p>'
author:
- 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: Hans-Christian
  full_name: Ebke, Hans-Christian
  last_name: Ebke
- first_name: Pierre
  full_name: Alliez, Pierre
  last_name: Alliez
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: Bommes D, Campen M, Ebke H-C, Alliez P, Kobbelt L. Integer-grid maps for reliable
    quad meshing. <i>ACM Transactions on Graphics</i>. 2013;32(4):1-12. doi:<a href="https://doi.org/10.1145/2461912.2462014">10.1145/2461912.2462014</a>
  apa: Bommes, D., Campen, M., Ebke, H.-C., Alliez, P., &#38; Kobbelt, L. (2013).
    Integer-grid maps for reliable quad meshing. <i>ACM Transactions on Graphics</i>,
    <i>32</i>(4), 1–12. <a href="https://doi.org/10.1145/2461912.2462014">https://doi.org/10.1145/2461912.2462014</a>
  bibtex: '@article{Bommes_Campen_Ebke_Alliez_Kobbelt_2013, title={Integer-grid maps
    for reliable quad meshing}, volume={32}, DOI={<a href="https://doi.org/10.1145/2461912.2462014">10.1145/2461912.2462014</a>},
    number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Bommes, David and Campen, Marcel and Ebke,
    Hans-Christian and Alliez, Pierre and Kobbelt, Leif}, year={2013}, pages={1–12}
    }'
  chicago: 'Bommes, David, Marcel Campen, Hans-Christian Ebke, Pierre Alliez, and
    Leif Kobbelt. “Integer-Grid Maps for Reliable Quad Meshing.” <i>ACM Transactions
    on Graphics</i> 32, no. 4 (2013): 1–12. <a href="https://doi.org/10.1145/2461912.2462014">https://doi.org/10.1145/2461912.2462014</a>.'
  ieee: 'D. Bommes, M. Campen, H.-C. Ebke, P. Alliez, and L. Kobbelt, “Integer-grid
    maps for reliable quad meshing,” <i>ACM Transactions on Graphics</i>, vol. 32,
    no. 4, pp. 1–12, 2013, doi: <a href="https://doi.org/10.1145/2461912.2462014">10.1145/2461912.2462014</a>.'
  mla: Bommes, David, et al. “Integer-Grid Maps for Reliable Quad Meshing.” <i>ACM
    Transactions on Graphics</i>, vol. 32, no. 4, Association for Computing Machinery
    (ACM), 2013, pp. 1–12, doi:<a href="https://doi.org/10.1145/2461912.2462014">10.1145/2461912.2462014</a>.
  short: D. Bommes, M. Campen, H.-C. Ebke, P. Alliez, L. Kobbelt, ACM Transactions
    on Graphics 32 (2013) 1–12.
date_created: 2025-06-30T07:06:50Z
date_updated: 2025-07-14T12:39:58Z
department:
- _id: '969'
doi: 10.1145/2461912.2462014
extern: '1'
intvolume: '        32'
issue: '4'
language:
- iso: eng
page: 1-12
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
  - 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Integer-grid maps for reliable quad meshing
type: journal_article
user_id: '117512'
volume: 32
year: '2013'
...
---
_id: '60451'
abstract:
- lang: eng
  text: "<jats:p>Nowadays, digital 3D models are in widespread and ubiquitous use,
    and each specific application dealing with 3D geometry has its own quality requirements
    that restrict the class of acceptable and supported models. This article analyzes
    typical defects that make a 3D model unsuitable for key application contexts,
    and surveys existing algorithms that process, repair, and improve its structure,
    geometry, and topology to make it appropriate to case-by-case requirements.</jats:p>\r\n
    \         <jats:p>The analysis is focused on polygon meshes, which constitute
    by far the most common 3D object representation. In particular, this article provides
    a structured overview of mesh repairing techniques from the point of view of the
    application context. Different types of mesh defects are classified according
    to the upstream application that produced the mesh, whereas mesh quality requirements
    are grouped by representative sets of downstream applications where the mesh is
    to be used. The numerous mesh repair methods that have been proposed during the
    last two decades are analyzed and classified in terms of their capabilities, properties,
    and guarantees. Based on these classifications, guidelines can be derived to support
    the identification of repairing algorithms best-suited to bridge the compatibility
    gap between the quality provided by the upstream process and the quality required
    by the downstream applications in a given geometry processing scenario.</jats:p>"
alternative_title:
- An application perspective
author:
- first_name: Marco
  full_name: Attene, Marco
  last_name: Attene
- 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: Attene M, Campen M, Kobbelt L. Polygon mesh repairing. <i>ACM Computing Surveys</i>.
    2013;45(2):1-33. doi:<a href="https://doi.org/10.1145/2431211.2431214">10.1145/2431211.2431214</a>
  apa: Attene, M., Campen, M., &#38; Kobbelt, L. (2013). Polygon mesh repairing. <i>ACM
    Computing Surveys</i>, <i>45</i>(2), 1–33. <a href="https://doi.org/10.1145/2431211.2431214">https://doi.org/10.1145/2431211.2431214</a>
  bibtex: '@article{Attene_Campen_Kobbelt_2013, title={Polygon mesh repairing}, volume={45},
    DOI={<a href="https://doi.org/10.1145/2431211.2431214">10.1145/2431211.2431214</a>},
    number={2}, journal={ACM Computing Surveys}, publisher={Association for Computing
    Machinery (ACM)}, author={Attene, Marco and Campen, Marcel and Kobbelt, Leif},
    year={2013}, pages={1–33} }'
  chicago: 'Attene, Marco, Marcel Campen, and Leif Kobbelt. “Polygon Mesh Repairing.”
    <i>ACM Computing Surveys</i> 45, no. 2 (2013): 1–33. <a href="https://doi.org/10.1145/2431211.2431214">https://doi.org/10.1145/2431211.2431214</a>.'
  ieee: 'M. Attene, M. Campen, and L. Kobbelt, “Polygon mesh repairing,” <i>ACM Computing
    Surveys</i>, vol. 45, no. 2, pp. 1–33, 2013, doi: <a href="https://doi.org/10.1145/2431211.2431214">10.1145/2431211.2431214</a>.'
  mla: Attene, Marco, et al. “Polygon Mesh Repairing.” <i>ACM Computing Surveys</i>,
    vol. 45, no. 2, Association for Computing Machinery (ACM), 2013, pp. 1–33, doi:<a
    href="https://doi.org/10.1145/2431211.2431214">10.1145/2431211.2431214</a>.
  short: M. Attene, M. Campen, L. Kobbelt, ACM Computing Surveys 45 (2013) 1–33.
date_created: 2025-06-30T07:05:12Z
date_updated: 2025-07-14T12:40:08Z
department:
- _id: '969'
doi: 10.1145/2431211.2431214
extern: '1'
intvolume: '        45'
issue: '2'
language:
- iso: eng
page: 1-33
publication: ACM Computing Surveys
publication_identifier:
  issn:
  - 0360-0300
  - 1557-7341
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Polygon mesh repairing
type: journal_article
user_id: '114904'
volume: 45
year: '2013'
...
---
_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: '60454'
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: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: 'Zimmer H, Campen M, Kobbelt L. Efficient Computation of Shortest Path-Concavity
    for 3D Meshes. In: <i>2013 IEEE Conference on Computer Vision and Pattern Recognition</i>.
    IEEE; 2013. doi:<a href="https://doi.org/10.1109/cvpr.2013.280">10.1109/cvpr.2013.280</a>'
  apa: Zimmer, H., Campen, M., &#38; Kobbelt, L. (2013). Efficient Computation of
    Shortest Path-Concavity for 3D Meshes. <i>2013 IEEE Conference on Computer Vision
    and Pattern Recognition</i>. <a href="https://doi.org/10.1109/cvpr.2013.280">https://doi.org/10.1109/cvpr.2013.280</a>
  bibtex: '@inproceedings{Zimmer_Campen_Kobbelt_2013, title={Efficient Computation
    of Shortest Path-Concavity for 3D Meshes}, DOI={<a href="https://doi.org/10.1109/cvpr.2013.280">10.1109/cvpr.2013.280</a>},
    booktitle={2013 IEEE Conference on Computer Vision and Pattern Recognition}, publisher={IEEE},
    author={Zimmer, Henrik and Campen, Marcel and Kobbelt, Leif}, year={2013} }'
  chicago: Zimmer, Henrik, Marcel Campen, and Leif Kobbelt. “Efficient Computation
    of Shortest Path-Concavity for 3D Meshes.” In <i>2013 IEEE Conference on Computer
    Vision and Pattern Recognition</i>. IEEE, 2013. <a href="https://doi.org/10.1109/cvpr.2013.280">https://doi.org/10.1109/cvpr.2013.280</a>.
  ieee: 'H. Zimmer, M. Campen, and L. Kobbelt, “Efficient Computation of Shortest
    Path-Concavity for 3D Meshes,” 2013, doi: <a href="https://doi.org/10.1109/cvpr.2013.280">10.1109/cvpr.2013.280</a>.'
  mla: Zimmer, Henrik, et al. “Efficient Computation of Shortest Path-Concavity for
    3D Meshes.” <i>2013 IEEE Conference on Computer Vision and Pattern Recognition</i>,
    IEEE, 2013, doi:<a href="https://doi.org/10.1109/cvpr.2013.280">10.1109/cvpr.2013.280</a>.
  short: 'H. Zimmer, M. Campen, L. Kobbelt, in: 2013 IEEE Conference on Computer Vision
    and Pattern Recognition, IEEE, 2013.'
date_created: 2025-06-30T07:17:02Z
date_updated: 2025-07-14T12:39:49Z
department:
- _id: '969'
doi: 10.1109/cvpr.2013.280
language:
- iso: eng
publication: 2013 IEEE Conference on Computer Vision and Pattern Recognition
publication_status: published
publisher: IEEE
status: public
title: Efficient Computation of Shortest Path-Concavity for 3D Meshes
type: conference
user_id: '117512'
year: '2013'
...
---
_id: '60456'
abstract:
- lang: eng
  text: <jats:p>We present a theoretical framework and practical method for the automatic
    construction of simple, all-quadrilateral patch layouts on manifold surfaces.
    The resulting layouts are coarse, surface-embedded cell complexes well adapted
    to the geometric structure, hence they are ideally suited as domains and base
    complexes for surface parameterization, spline fitting, or subdivision surfaces
    and can be used to generate quad meshes with a high-level patch structure that
    are advantageous in many application scenarios. Our approach is based on the careful
    construction of the layout graph's combinatorial dual. In contrast to the primal
    this dual perspective provides direct control over the globally interdependent
    structural constraints inherent to quad layouts. The dual layout is built from
    curvature-guided, crossing loops on the surface. A novel method to construct these
    efficiently in a geometry- and structure-aware manner constitutes the core of
    our approach.</jats:p>
alternative_title:
- quality quad layouts on manifolds
author:
- 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: Campen M, Bommes D, Kobbelt L. Dual loops meshing. <i>ACM Transactions on Graphics</i>.
    2012;31(4):1-11. doi:<a href="https://doi.org/10.1145/2185520.2185606">10.1145/2185520.2185606</a>
  apa: Campen, M., Bommes, D., &#38; Kobbelt, L. (2012). Dual loops meshing. <i>ACM
    Transactions on Graphics</i>, <i>31</i>(4), 1–11. <a href="https://doi.org/10.1145/2185520.2185606">https://doi.org/10.1145/2185520.2185606</a>
  bibtex: '@article{Campen_Bommes_Kobbelt_2012, title={Dual loops meshing}, volume={31},
    DOI={<a href="https://doi.org/10.1145/2185520.2185606">10.1145/2185520.2185606</a>},
    number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
    Computing Machinery (ACM)}, author={Campen, Marcel and Bommes, David and Kobbelt,
    Leif}, year={2012}, pages={1–11} }'
  chicago: 'Campen, Marcel, David Bommes, and Leif Kobbelt. “Dual Loops Meshing.”
    <i>ACM Transactions on Graphics</i> 31, no. 4 (2012): 1–11. <a href="https://doi.org/10.1145/2185520.2185606">https://doi.org/10.1145/2185520.2185606</a>.'
  ieee: 'M. Campen, D. Bommes, and L. Kobbelt, “Dual loops meshing,” <i>ACM Transactions
    on Graphics</i>, vol. 31, no. 4, pp. 1–11, 2012, doi: <a href="https://doi.org/10.1145/2185520.2185606">10.1145/2185520.2185606</a>.'
  mla: Campen, Marcel, et al. “Dual Loops Meshing.” <i>ACM Transactions on Graphics</i>,
    vol. 31, no. 4, Association for Computing Machinery (ACM), 2012, pp. 1–11, doi:<a
    href="https://doi.org/10.1145/2185520.2185606">10.1145/2185520.2185606</a>.
  short: M. Campen, D. Bommes, L. Kobbelt, ACM Transactions on Graphics 31 (2012)
    1–11.
date_created: 2025-06-30T07:32:26Z
date_updated: 2025-07-14T12:39:21Z
department:
- _id: '969'
doi: 10.1145/2185520.2185606
extern: '1'
intvolume: '        31'
issue: '4'
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: Dual loops meshing
type: journal_article
user_id: '117512'
volume: 31
year: '2012'
...
---
_id: '60457'
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: Ralf
  full_name: Herkrath, Ralf
  last_name: Herkrath
- first_name: Leif
  full_name: Kobbelt, Leif
  last_name: Kobbelt
citation:
  ama: 'Zimmer H, Campen M, Herkrath R, Kobbelt L. Variational Tangent Plane Intersection
    for Planar Polygonal Meshing. In: Hesselgren L, Sharma S, Wallner J, Baldassini
    N, Bompas P, Raynaud J, eds. <i>Advances in Architectural Geometry, AAG 2012,
    Paris, France, September 27-28, 2012</i>. Springer; 2012:319–332. doi:<a href="https://doi.org/10.1007/978-3-7091-1251-9_26">10.1007/978-3-7091-1251-9_26</a>'
  apa: Zimmer, H., Campen, M., Herkrath, R., &#38; Kobbelt, L. (2012). Variational
    Tangent Plane Intersection for Planar Polygonal Meshing. In L. Hesselgren, S.
    Sharma, J. Wallner, N. Baldassini, P. Bompas, &#38; J. Raynaud (Eds.), <i>Advances
    in Architectural Geometry, AAG 2012, Paris, France, September 27-28, 2012</i>
    (pp. 319–332). Springer. <a href="https://doi.org/10.1007/978-3-7091-1251-9_26">https://doi.org/10.1007/978-3-7091-1251-9_26</a>
  bibtex: '@inproceedings{Zimmer_Campen_Herkrath_Kobbelt_2012, title={Variational
    Tangent Plane Intersection for Planar Polygonal Meshing}, DOI={<a href="https://doi.org/10.1007/978-3-7091-1251-9_26">10.1007/978-3-7091-1251-9_26</a>},
    booktitle={Advances in Architectural Geometry, AAG 2012, Paris, France, September
    27-28, 2012}, publisher={Springer}, author={Zimmer, Henrik and Campen, Marcel
    and Herkrath, Ralf and Kobbelt, Leif}, editor={Hesselgren, Lars and Sharma, Shrikant
    and Wallner, Johannes and Baldassini, Niccolo and Bompas, Philippe and Raynaud,
    Jacques}, year={2012}, pages={319–332} }'
  chicago: Zimmer, Henrik, Marcel Campen, Ralf Herkrath, and Leif Kobbelt. “Variational
    Tangent Plane Intersection for Planar Polygonal Meshing.” In <i>Advances in Architectural
    Geometry, AAG 2012, Paris, France, September 27-28, 2012</i>, edited by Lars Hesselgren,
    Shrikant Sharma, Johannes Wallner, Niccolo Baldassini, Philippe Bompas, and Jacques
    Raynaud, 319–332. Springer, 2012. <a href="https://doi.org/10.1007/978-3-7091-1251-9_26">https://doi.org/10.1007/978-3-7091-1251-9_26</a>.
  ieee: 'H. Zimmer, M. Campen, R. Herkrath, and L. Kobbelt, “Variational Tangent Plane
    Intersection for Planar Polygonal Meshing,” in <i>Advances in Architectural Geometry,
    AAG 2012, Paris, France, September 27-28, 2012</i>, 2012, pp. 319–332, doi: <a
    href="https://doi.org/10.1007/978-3-7091-1251-9_26">10.1007/978-3-7091-1251-9_26</a>.'
  mla: Zimmer, Henrik, et al. “Variational Tangent Plane Intersection for Planar Polygonal
    Meshing.” <i>Advances in Architectural Geometry, AAG 2012, Paris, France, September
    27-28, 2012</i>, edited by Lars Hesselgren et al., Springer, 2012, pp. 319–332,
    doi:<a href="https://doi.org/10.1007/978-3-7091-1251-9_26">10.1007/978-3-7091-1251-9_26</a>.
  short: 'H. Zimmer, M. Campen, R. Herkrath, L. Kobbelt, in: L. Hesselgren, S. Sharma,
    J. Wallner, N. Baldassini, P. Bompas, J. Raynaud (Eds.), Advances in Architectural
    Geometry, AAG 2012, Paris, France, September 27-28, 2012, Springer, 2012, pp.
    319–332.'
date_created: 2025-06-30T07:39:33Z
date_updated: 2025-07-14T12:38:54Z
department:
- _id: '969'
doi: 10.1007/978-3-7091-1251-9_26
editor:
- first_name: Lars
  full_name: Hesselgren, Lars
  last_name: Hesselgren
- first_name: Shrikant
  full_name: Sharma, Shrikant
  last_name: Sharma
- first_name: Johannes
  full_name: Wallner, Johannes
  last_name: Wallner
- first_name: Niccolo
  full_name: Baldassini, Niccolo
  last_name: Baldassini
- first_name: Philippe
  full_name: Bompas, Philippe
  last_name: Bompas
- first_name: Jacques
  full_name: Raynaud, Jacques
  last_name: Raynaud
extern: '1'
language:
- iso: eng
page: 319–332
publication: Advances in Architectural Geometry, AAG 2012, Paris, France, September
  27-28, 2012
publisher: Springer
status: public
title: Variational Tangent Plane Intersection for Planar Polygonal Meshing
type: conference
user_id: '117512'
year: '2012'
...
---
_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'
...
---
_id: '60464'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We present a novel technique for
    the efficient boundary evaluation of sweep operations applied to objects in polygonal
    boundary representation. These sweep operations include Minkowski addition, offsetting,
    and sweeping along a discrete rigid motion trajectory. Many previous methods focus
    on the construction of a polygonal superset (containing self‐intersections and
    spurious internal geometry) of the boundary of the volumes which are swept. Only
    few are able to determine a clean representation of the actual boundary, most
    of them in a discrete volumetric setting. We unify such superset constructions
    into a succinct common formulation and present a technique for the robust extraction
    of a polygonal mesh representing the outer boundary, i.e. it makes no general
    position assumptions and always yields a manifold, watertight mesh. It is exact
    for Minkowski sums and approximates swept volumes polygonally. By using plane‐based
    geometry in conjunction with hierarchical arrangement computations we avoid the
    necessity of arbitrary precision arithmetics and extensive special case handling.
    By restricting operations to regions containing pieces of the boundary, we significantly
    enhance the performance of the algorithm.</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. Polygonal Boundary Evaluation of Minkowski Sums and Swept
    Volumes. <i>Computer Graphics Forum</i>. 2010;29(5):1613-1622. doi:<a href="https://doi.org/10.1111/j.1467-8659.2010.01770.x">10.1111/j.1467-8659.2010.01770.x</a>
  apa: Campen, M., &#38; Kobbelt, L. (2010). Polygonal Boundary Evaluation of Minkowski
    Sums and Swept Volumes. <i>Computer Graphics Forum</i>, <i>29</i>(5), 1613–1622.
    <a href="https://doi.org/10.1111/j.1467-8659.2010.01770.x">https://doi.org/10.1111/j.1467-8659.2010.01770.x</a>
  bibtex: '@article{Campen_Kobbelt_2010, title={Polygonal Boundary Evaluation of Minkowski
    Sums and Swept Volumes}, volume={29}, DOI={<a href="https://doi.org/10.1111/j.1467-8659.2010.01770.x">10.1111/j.1467-8659.2010.01770.x</a>},
    number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
    Marcel and Kobbelt, Leif}, year={2010}, pages={1613–1622} }'
  chicago: 'Campen, Marcel, and Leif Kobbelt. “Polygonal Boundary Evaluation of Minkowski
    Sums and Swept Volumes.” <i>Computer Graphics Forum</i> 29, no. 5 (2010): 1613–22.
    <a href="https://doi.org/10.1111/j.1467-8659.2010.01770.x">https://doi.org/10.1111/j.1467-8659.2010.01770.x</a>.'
  ieee: 'M. Campen and L. Kobbelt, “Polygonal Boundary Evaluation of Minkowski Sums
    and Swept Volumes,” <i>Computer Graphics Forum</i>, vol. 29, no. 5, pp. 1613–1622,
    2010, doi: <a href="https://doi.org/10.1111/j.1467-8659.2010.01770.x">10.1111/j.1467-8659.2010.01770.x</a>.'
  mla: Campen, Marcel, and Leif Kobbelt. “Polygonal Boundary Evaluation of Minkowski
    Sums and Swept Volumes.” <i>Computer Graphics Forum</i>, vol. 29, no. 5, Wiley,
    2010, pp. 1613–22, doi:<a href="https://doi.org/10.1111/j.1467-8659.2010.01770.x">10.1111/j.1467-8659.2010.01770.x</a>.
  short: M. Campen, L. Kobbelt, Computer Graphics Forum 29 (2010) 1613–1622.
date_created: 2025-06-30T08:34:20Z
date_updated: 2025-07-14T12:35:40Z
department:
- _id: '969'
doi: 10.1111/j.1467-8659.2010.01770.x
extern: '1'
intvolume: '        29'
issue: '5'
language:
- iso: eng
page: 1613-1622
publication: Computer Graphics Forum
publication_identifier:
  issn:
  - 0167-7055
  - 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes
type: journal_article
user_id: '117512'
volume: 29
year: '2010'
...