---
_id: '61873'
author:
- first_name: Payam
full_name: Khanteimouri, Payam
last_name: Khanteimouri
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: 'Khanteimouri P, Campen M. C1-Smooth Parametrization of Polynomial Shapes over
Polygonal Domains. In: Proceedings of the 2025 SIAM International Meshing Roundtable.
Society for Industrial and Applied Mathematics; 2025. doi:10.1137/1.9781611978575.9'
apa: Khanteimouri, P., & Campen, M. (2025). C1-Smooth Parametrization of Polynomial
Shapes over Polygonal Domains. Proceedings of the 2025 SIAM International Meshing
Roundtable. https://doi.org/10.1137/1.9781611978575.9
bibtex: '@inproceedings{Khanteimouri_Campen_2025, place={Philadelphia, PA}, title={C1-Smooth
Parametrization of Polynomial Shapes over Polygonal Domains}, DOI={10.1137/1.9781611978575.9},
booktitle={Proceedings of the 2025 SIAM International Meshing Roundtable}, publisher={Society
for Industrial and Applied Mathematics}, author={Khanteimouri, Payam and Campen,
Marcel}, year={2025} }'
chicago: 'Khanteimouri, Payam, and Marcel Campen. “C1-Smooth Parametrization of
Polynomial Shapes over Polygonal Domains.” In Proceedings of the 2025 SIAM
International Meshing Roundtable. Philadelphia, PA: Society for Industrial
and Applied Mathematics, 2025. https://doi.org/10.1137/1.9781611978575.9.'
ieee: 'P. Khanteimouri and M. Campen, “C1-Smooth Parametrization of Polynomial Shapes
over Polygonal Domains,” 2025, doi: 10.1137/1.9781611978575.9.'
mla: Khanteimouri, Payam, and Marcel Campen. “C1-Smooth Parametrization of Polynomial
Shapes over Polygonal Domains.” Proceedings of the 2025 SIAM International
Meshing Roundtable, Society for Industrial and Applied Mathematics, 2025,
doi:10.1137/1.9781611978575.9.
short: 'P. Khanteimouri, M. Campen, in: Proceedings of the 2025 SIAM International
Meshing Roundtable, Society for Industrial and Applied Mathematics, Philadelphia,
PA, 2025.'
date_created: 2025-10-17T08:37:38Z
date_updated: 2025-10-17T08:39:39Z
department:
- _id: '969'
doi: 10.1137/1.9781611978575.9
extern: '1'
language:
- iso: eng
place: Philadelphia, PA
publication: Proceedings of the 2025 SIAM International Meshing Roundtable
publication_identifier:
isbn:
- '9781611978575'
publication_status: published
publisher: Society for Industrial and Applied Mathematics
status: public
title: C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains
type: conference
user_id: '114904'
year: '2025'
...
---
_id: '60189'
abstract:
- lang: eng
text: AbstractSeveral state‐of‐the‐art algorithms
for semi‐structured hexahedral meshing involve a so called quantization
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 integer
quadratic programs (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 linear programs
(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.
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. Comput Graph Forum. 2024;43(5). doi:10.1111/cgf.15131
apa: Brückler, H., Bommes, D., & Campen, M. (2024). Integer‐Sheet‐Pump Quantization
for Hexahedral Meshing. Comput. Graph. Forum, 43(5). https://doi.org/10.1111/cgf.15131
bibtex: '@article{Brückler_Bommes_Campen_2024, title={Integer‐Sheet‐Pump Quantization
for Hexahedral Meshing}, volume={43}, DOI={10.1111/cgf.15131},
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.” Comput. Graph. Forum 43, no. 5 (2024).
https://doi.org/10.1111/cgf.15131.
ieee: 'H. Brückler, D. Bommes, and M. Campen, “Integer‐Sheet‐Pump Quantization for
Hexahedral Meshing,” Comput. Graph. Forum, vol. 43, no. 5, 2024, doi: 10.1111/cgf.15131.'
mla: Brückler, Hendrik, et al. “Integer‐Sheet‐Pump Quantization for Hexahedral Meshing.”
Comput. Graph. Forum, vol. 43, no. 5, Wiley, 2024, doi:10.1111/cgf.15131.
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: '60240'
author:
- first_name: Ingmar
full_name: Ludwig, Ingmar
id: '116667'
last_name: Ludwig
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: Ludwig I, Campen M. Strictly Conservative Neural Implicits. Comput Graph
Forum. 2024;43(7):i–xxii. doi:10.1111/CGF.15241
apa: Ludwig, I., & Campen, M. (2024). Strictly Conservative Neural Implicits.
Comput. Graph. Forum, 43(7), i–xxii. https://doi.org/10.1111/CGF.15241
bibtex: '@article{Ludwig_Campen_2024, title={Strictly Conservative Neural Implicits},
volume={43}, DOI={10.1111/CGF.15241},
number={7}, journal={Comput. Graph. Forum}, author={Ludwig, Ingmar and Campen,
Marcel}, year={2024}, pages={i–xxii} }'
chicago: 'Ludwig, Ingmar, and Marcel Campen. “Strictly Conservative Neural Implicits.”
Comput. Graph. Forum 43, no. 7 (2024): i–xxii. https://doi.org/10.1111/CGF.15241.'
ieee: 'I. Ludwig and M. Campen, “Strictly Conservative Neural Implicits,” Comput.
Graph. Forum, vol. 43, no. 7, pp. i–xxii, 2024, doi: 10.1111/CGF.15241.'
mla: Ludwig, Ingmar, and Marcel Campen. “Strictly Conservative Neural Implicits.”
Comput. Graph. Forum, vol. 43, no. 7, 2024, pp. i–xxii, doi:10.1111/CGF.15241.
short: I. Ludwig, M. Campen, Comput. Graph. Forum 43 (2024) i–xxii.
date_created: 2025-06-17T07:46:09Z
date_updated: 2025-06-23T09:01:59Z
department:
- _id: '969'
doi: 10.1111/CGF.15241
extern: '1'
intvolume: ' 43'
issue: '7'
language:
- iso: eng
page: i–xxii
publication: Comput. Graph. Forum
status: public
title: Strictly Conservative Neural Implicits
type: journal_article
user_id: '114904'
volume: 43
year: '2024'
...
---
_id: '60314'
abstract:
- lang: eng
text: A method for the construction of bijective volumetric maps between
3D shapes is presented. Arbitrary shapes of ball-topology are supported, overcoming
restrictions of previous methods to convex or star-shaped targets. In essence,
the mapping problem is decomposed into a set of simpler mapping problems, each
of which can be solved with previous methods for discrete star-shaped mapping
problems. Addressing the key challenges in this endeavor, algorithms are described
to reliably construct structurally compatible partitions of two shapes with constraints
regarding star-shapedness and to compute a parsimonious common refinement of two
triangulations.
author:
- first_name: Steffen
full_name: Hinderink, Steffen
id: '116615'
last_name: Hinderink
- first_name: Hendrik
full_name: Brückler, Hendrik
id: '115694'
last_name: Brückler
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: Hinderink S, Brückler H, Campen M. Bijective Volumetric Mapping via Star Decomposition.
ACM Transactions on Graphics. 2024;43(6):1-11. doi:10.1145/3687950
apa: Hinderink, S., Brückler, H., & Campen, M. (2024). Bijective Volumetric
Mapping via Star Decomposition. ACM Transactions on Graphics, 43(6),
1–11. https://doi.org/10.1145/3687950
bibtex: '@article{Hinderink_Brückler_Campen_2024, title={Bijective Volumetric Mapping
via Star Decomposition}, volume={43}, DOI={10.1145/3687950},
number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Hinderink, Steffen and Brückler, Hendrik and
Campen, Marcel}, year={2024}, pages={1–11} }'
chicago: 'Hinderink, Steffen, Hendrik Brückler, and Marcel Campen. “Bijective Volumetric
Mapping via Star Decomposition.” ACM Transactions on Graphics 43, no. 6
(2024): 1–11. https://doi.org/10.1145/3687950.'
ieee: 'S. Hinderink, H. Brückler, and M. Campen, “Bijective Volumetric Mapping via
Star Decomposition,” ACM Transactions on Graphics, vol. 43, no. 6, pp.
1–11, 2024, doi: 10.1145/3687950.'
mla: Hinderink, Steffen, et al. “Bijective Volumetric Mapping via Star Decomposition.”
ACM Transactions on Graphics, vol. 43, no. 6, Association for Computing
Machinery (ACM), 2024, pp. 1–11, doi:10.1145/3687950.
short: S. Hinderink, H. Brückler, M. Campen, ACM Transactions on Graphics 43 (2024)
1–11.
date_created: 2025-06-23T09:09:51Z
date_updated: 2025-07-14T12:33:54Z
department:
- _id: '969'
doi: 10.1145/3687950
extern: '1'
intvolume: ' 43'
issue: '6'
language:
- iso: eng
page: 1-11
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Bijective Volumetric Mapping via Star Decomposition
type: journal_article
user_id: '117512'
volume: 43
year: '2024'
...
---
_id: '60331'
abstract:
- lang: eng
text: "\r\n We present a novel algorithm to map ball-topology
tetrahedral meshes onto star-shaped domains with guarantees regarding bijectivity.
Our algorithm is based on the recently introduced idea of Shrink-and-Expand, where
images of interior vertices are initially clustered at one point (Shrink-), before
being sequentially moved to non-degenerate positions yielding a bijective map
(-and-Expand). In this context, we introduce the concept of the\r\n cluster
mesh\r\n , i.e. the unexpanded interior mesh consisting
of geometrically degenerate simplices. Using local, per-vertex connectivity information
solely from the cluster mesh, we show that a viable expansion sequence guaranteed
to produce a bijective map can always be found as long as the mesh is\r\n shellable.\r\n
\ In addition to robustness guarantees for this ubiquitous class of
inputs, other practically relevant benefits include improved parsimony and reduced
algorithmic complexity. While inheriting some of the worst-case high run time
requirements of the state of the art, significant acceleration for the average
case is experimentally demonstrated.\r\n "
author:
- first_name: Valentin Zénon
full_name: Nigolian, Valentin Zénon
last_name: Nigolian
- 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
citation:
ama: Nigolian VZ, Campen M, Bommes D. A Progressive Embedding Approach to Bijective
Tetrahedral Maps driven by Cluster Mesh Topology. ACM Transactions on Graphics.
2024;43(6):1-14. doi:10.1145/3687992
apa: Nigolian, V. Z., Campen, M., & Bommes, D. (2024). A Progressive Embedding
Approach to Bijective Tetrahedral Maps driven by Cluster Mesh Topology. ACM
Transactions on Graphics, 43(6), 1–14. https://doi.org/10.1145/3687992
bibtex: '@article{Nigolian_Campen_Bommes_2024, title={A Progressive Embedding Approach
to Bijective Tetrahedral Maps driven by Cluster Mesh Topology}, volume={43}, DOI={10.1145/3687992}, number={6}, journal={ACM
Transactions on Graphics}, publisher={Association for Computing Machinery (ACM)},
author={Nigolian, Valentin Zénon and Campen, Marcel and Bommes, David}, year={2024},
pages={1–14} }'
chicago: 'Nigolian, Valentin Zénon, Marcel Campen, and David Bommes. “A Progressive
Embedding Approach to Bijective Tetrahedral Maps Driven by Cluster Mesh Topology.”
ACM Transactions on Graphics 43, no. 6 (2024): 1–14. https://doi.org/10.1145/3687992.'
ieee: 'V. Z. Nigolian, M. Campen, and D. Bommes, “A Progressive Embedding Approach
to Bijective Tetrahedral Maps driven by Cluster Mesh Topology,” ACM Transactions
on Graphics, vol. 43, no. 6, pp. 1–14, 2024, doi: 10.1145/3687992.'
mla: Nigolian, Valentin Zénon, et al. “A Progressive Embedding Approach to Bijective
Tetrahedral Maps Driven by Cluster Mesh Topology.” ACM Transactions on Graphics,
vol. 43, no. 6, Association for Computing Machinery (ACM), 2024, pp. 1–14, doi:10.1145/3687992.
short: V.Z. Nigolian, M. Campen, D. Bommes, ACM Transactions on Graphics 43 (2024)
1–14.
date_created: 2025-06-23T10:32:28Z
date_updated: 2025-07-14T12:48:45Z
department:
- _id: '969'
doi: 10.1145/3687992
extern: '1'
intvolume: ' 43'
issue: '6'
language:
- iso: eng
page: 1-14
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: A Progressive Embedding Approach to Bijective Tetrahedral Maps driven by Cluster
Mesh Topology
type: journal_article
user_id: '117512'
volume: 43
year: '2024'
...
---
_id: '60355'
abstract:
- lang: eng
text: We present a method for the generation of higher-order tetrahedral
meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed
to be free of degeneracies and inversions while conforming exactly to prescribed
piecewise polynomial surfaces, such as domain boundaries or material interfaces.
Arbitrary polynomial order is supported. Algorithmically, the polynomial input
surfaces are first covered by a single layer of carefully constructed curved elements
using a recursive refinement procedure that provably avoids degeneracies and inversions.
These tetrahedral elements are designed such that the remaining space is bounded
piecewise linearly. In this way, our method effectively reduces the curved meshing
problem to the classical problem of linear mesh generation (for the remaining
space).
author:
- first_name: Payam
full_name: Khanteimouri, Payam
last_name: Khanteimouri
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: 'Khanteimouri P, Campen M. 3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral
Meshing. ACM Transactions on Graphics. 2023;42(6):1-19. doi:10.1145/3618332'
apa: 'Khanteimouri, P., & Campen, M. (2023). 3D Bézier Guarding: Boundary-Conforming
Curved Tetrahedral Meshing. ACM Transactions on Graphics, 42(6),
1–19. https://doi.org/10.1145/3618332'
bibtex: '@article{Khanteimouri_Campen_2023, title={3D Bézier Guarding: Boundary-Conforming
Curved Tetrahedral Meshing}, volume={42}, DOI={10.1145/3618332},
number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Khanteimouri, Payam and Campen, Marcel}, year={2023},
pages={1–19} }'
chicago: 'Khanteimouri, Payam, and Marcel Campen. “3D Bézier Guarding: Boundary-Conforming
Curved Tetrahedral Meshing.” ACM Transactions on Graphics 42, no. 6 (2023):
1–19. https://doi.org/10.1145/3618332.'
ieee: 'P. Khanteimouri and M. Campen, “3D Bézier Guarding: Boundary-Conforming Curved
Tetrahedral Meshing,” ACM Transactions on Graphics, vol. 42, no. 6, pp.
1–19, 2023, doi: 10.1145/3618332.'
mla: 'Khanteimouri, Payam, and Marcel Campen. “3D Bézier Guarding: Boundary-Conforming
Curved Tetrahedral Meshing.” ACM Transactions on Graphics, vol. 42, no.
6, Association for Computing Machinery (ACM), 2023, pp. 1–19, doi:10.1145/3618332.'
short: P. Khanteimouri, M. Campen, ACM Transactions on Graphics 42 (2023) 1–19.
date_created: 2025-06-24T07:46:53Z
date_updated: 2025-07-14T12:46:54Z
department:
- _id: '969'
doi: 10.1145/3618332
extern: '1'
intvolume: ' 42'
issue: '6'
language:
- iso: eng
page: 1-19
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: '3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing'
type: journal_article
user_id: '117512'
volume: 42
year: '2023'
...
---
_id: '60337'
abstract:
- lang: eng
text: "\r\n Volumetric mapping is a ubiquitous and difficult
problem in Geometry Processing and has been the subject of research in numerous
and various directions. While several methods show encouraging results, the field
still lacks a general approach with guarantees regarding map bijectivity. Through
this work, we aim at opening the door to a new family of methods by providing
a novel framework based on the concept of\r\n progressive
expansion.\r\n Starting from an initial map of a tetrahedral
mesh whose image may contain degeneracies but no inversions, we incrementally
adjust vertex images to expand degenerate elements. By restricting movement to
so-called\r\n expansion cones\r\n ,
it is done in such a way that the number of degenerate elements decreases in a
strictly monotonic manner, without ever introducing any inversion. Adaptive local
refinement of the mesh is performed to facilitate this process. We describe a
prototype algorithm in the realm of this framework for the computation of maps
from ball-topology tetrahedral meshes to convex or star-shaped domains. This algorithm
is evaluated and compared to state-of-the-art methods, demonstrating its benefits
in terms of bijectivity. We also discuss the associated cost in terms of sometimes
significant mesh refinement to obtain the necessary degrees of freedom required
for establishing a valid mapping. Our conclusions include that while this algorithm
is only of limited immediate practical utility due to efficiency concerns, the
general framework has the potential to inspire a range of novel methods improving
on the efficiency aspect.\r\n "
author:
- first_name: Valentin Zénon
full_name: Nigolian, Valentin Zénon
last_name: Nigolian
- 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
citation:
ama: 'Nigolian VZ, Campen M, Bommes D. Expansion Cones: A Progressive Volumetric
Mapping Framework. ACM Transactions on Graphics. 2023;42(4):1-19. doi:10.1145/3592421'
apa: 'Nigolian, V. Z., Campen, M., & Bommes, D. (2023). Expansion Cones: A Progressive
Volumetric Mapping Framework. ACM Transactions on Graphics, 42(4),
1–19. https://doi.org/10.1145/3592421'
bibtex: '@article{Nigolian_Campen_Bommes_2023, title={Expansion Cones: A Progressive
Volumetric Mapping Framework}, volume={42}, DOI={10.1145/3592421},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Nigolian, Valentin Zénon and Campen, Marcel
and Bommes, David}, year={2023}, pages={1–19} }'
chicago: 'Nigolian, Valentin Zénon, Marcel Campen, and David Bommes. “Expansion
Cones: A Progressive Volumetric Mapping Framework.” ACM Transactions on Graphics
42, no. 4 (2023): 1–19. https://doi.org/10.1145/3592421.'
ieee: 'V. Z. Nigolian, M. Campen, and D. Bommes, “Expansion Cones: A Progressive
Volumetric Mapping Framework,” ACM Transactions on Graphics, vol. 42, no.
4, pp. 1–19, 2023, doi: 10.1145/3592421.'
mla: 'Nigolian, Valentin Zénon, et al. “Expansion Cones: A Progressive Volumetric
Mapping Framework.” ACM Transactions on Graphics, vol. 42, no. 4, Association
for Computing Machinery (ACM), 2023, pp. 1–19, doi:10.1145/3592421.'
short: V.Z. Nigolian, M. Campen, D. Bommes, ACM Transactions on Graphics 42 (2023)
1–19.
date_created: 2025-06-23T10:58:12Z
date_updated: 2025-07-14T12:47:55Z
department:
- _id: '969'
doi: 10.1145/3592421
extern: '1'
intvolume: ' 42'
issue: '4'
language:
- iso: eng
page: 1-19
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: 'Expansion Cones: A Progressive Volumetric Mapping Framework'
type: journal_article
user_id: '117512'
volume: 42
year: '2023'
...
---
_id: '60354'
abstract:
- lang: eng
text: We present a set of operators to perform modifications, in particular
collapses and splits, in volumetric cell complexes which are discretely embedded
in a background mesh. Topological integrity and geometric embedding validity are
carefully maintained. We apply these operators strategically to volumetric block
decompositions, so-called T-meshes or base complexes, in the context of hexahedral
mesh generation. This allows circumventing the expensive and unreliable global
volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid
maps. In essence, we reduce this step to simpler local cube mapping problems,
for which reliable solutions are available. As a consequence, the robustness of
the mesh generation process is increased, especially when targeting coarse or
block-structured hexahedral meshes. We furthermore extend this pipeline to support
feature alignment constraints, and systematically respect these throughout, enabling
the generation of meshes that align to points, curves, and surfaces of special
interest, whether on the boundary or in the interior of the domain.
author:
- first_name: Hendrik
full_name: Brückler, Hendrik
id: '115694'
last_name: Brückler
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: Brückler H, Campen M. Collapsing Embedded Cell Complexes for Safer Hexahedral
Meshing. ACM Transactions on Graphics. 2023;42(6):1-24. doi:10.1145/3618384
apa: Brückler, H., & Campen, M. (2023). Collapsing Embedded Cell Complexes for
Safer Hexahedral Meshing. ACM Transactions on Graphics, 42(6), 1–24.
https://doi.org/10.1145/3618384
bibtex: '@article{Brückler_Campen_2023, title={Collapsing Embedded Cell Complexes
for Safer Hexahedral Meshing}, volume={42}, DOI={10.1145/3618384},
number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Brückler, Hendrik and Campen, Marcel}, year={2023},
pages={1–24} }'
chicago: 'Brückler, Hendrik, and Marcel Campen. “Collapsing Embedded Cell Complexes
for Safer Hexahedral Meshing.” ACM Transactions on Graphics 42, no. 6 (2023):
1–24. https://doi.org/10.1145/3618384.'
ieee: 'H. Brückler and M. Campen, “Collapsing Embedded Cell Complexes for Safer
Hexahedral Meshing,” ACM Transactions on Graphics, vol. 42, no. 6, pp.
1–24, 2023, doi: 10.1145/3618384.'
mla: Brückler, Hendrik, and Marcel Campen. “Collapsing Embedded Cell Complexes for
Safer Hexahedral Meshing.” ACM Transactions on Graphics, vol. 42, no. 6,
Association for Computing Machinery (ACM), 2023, pp. 1–24, doi:10.1145/3618384.
short: H. Brückler, M. Campen, ACM Transactions on Graphics 42 (2023) 1–24.
date_created: 2025-06-24T07:45:44Z
date_updated: 2025-07-14T12:47:30Z
department:
- _id: '969'
doi: 10.1145/3618384
extern: '1'
intvolume: ' 42'
issue: '6'
language:
- iso: eng
page: 1-24
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing
type: journal_article
user_id: '117512'
volume: 42
year: '2023'
...
---
_id: '60335'
abstract:
- lang: eng
text: A method is presented to compute volumetric maps and parametrizations
of objects over 3D domains. As a key feature, continuity and bijectivity are ensured
by construction. Arbitrary objects of ball topology, represented as tetrahedral
meshes, are supported. Arbitrary convex as well as star-shaped domains are supported.
Full control over the boundary mapping is provided. The method is based on the
technique of simplicial foliations, generalized to a broader class of domain shapes
and applied adaptively in a novel localized manner. This increases flexibility
as well as efficiency over the state of the art, while maintaining reliability
in guaranteeing map bijectivity.
author:
- first_name: Steffen
full_name: Hinderink, Steffen
id: '116615'
last_name: Hinderink
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: 'Hinderink S, Campen M. Galaxy Maps: Localized Foliations for Bijective Volumetric
Mapping. ACM Transactions on Graphics. 2023;42(4):1-16. doi:10.1145/3592410'
apa: 'Hinderink, S., & Campen, M. (2023). Galaxy Maps: Localized Foliations
for Bijective Volumetric Mapping. ACM Transactions on Graphics, 42(4),
1–16. https://doi.org/10.1145/3592410'
bibtex: '@article{Hinderink_Campen_2023, title={Galaxy Maps: Localized Foliations
for Bijective Volumetric Mapping}, volume={42}, DOI={10.1145/3592410},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Hinderink, Steffen and Campen, Marcel}, year={2023},
pages={1–16} }'
chicago: 'Hinderink, Steffen, and Marcel Campen. “Galaxy Maps: Localized Foliations
for Bijective Volumetric Mapping.” ACM Transactions on Graphics 42, no.
4 (2023): 1–16. https://doi.org/10.1145/3592410.'
ieee: 'S. Hinderink and M. Campen, “Galaxy Maps: Localized Foliations for Bijective
Volumetric Mapping,” ACM Transactions on Graphics, vol. 42, no. 4, pp.
1–16, 2023, doi: 10.1145/3592410.'
mla: 'Hinderink, Steffen, and Marcel Campen. “Galaxy Maps: Localized Foliations
for Bijective Volumetric Mapping.” ACM Transactions on Graphics, vol. 42,
no. 4, Association for Computing Machinery (ACM), 2023, pp. 1–16, doi:10.1145/3592410.'
short: S. Hinderink, M. Campen, ACM Transactions on Graphics 42 (2023) 1–16.
date_created: 2025-06-23T10:38:02Z
date_updated: 2025-07-14T12:48:12Z
department:
- _id: '969'
doi: 10.1145/3592410
extern: '1'
intvolume: ' 42'
issue: '4'
language:
- iso: eng
page: 1-16
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: 'Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping'
type: journal_article
user_id: '117512'
volume: 42
year: '2023'
...
---
_id: '60333'
abstract:
- lang: eng
text: AbstractWe 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.
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. Computer Graphics Forum. 2023;42(5). doi:10.1111/cgf.14898
apa: Ludwig, I., Tyson, D., & Campen, M. (2023). HalfedgeCNN for Native and
Flexible Deep Learning on Triangle Meshes. Computer Graphics Forum, 42(5).
https://doi.org/10.1111/cgf.14898
bibtex: '@article{Ludwig_Tyson_Campen_2023, title={HalfedgeCNN for Native and Flexible
Deep Learning on Triangle Meshes}, volume={42}, DOI={10.1111/cgf.14898},
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.” Computer Graphics Forum
42, no. 5 (2023). https://doi.org/10.1111/cgf.14898.
ieee: 'I. Ludwig, D. Tyson, and M. Campen, “HalfedgeCNN for Native and Flexible
Deep Learning on Triangle Meshes,” Computer Graphics Forum, vol. 42, no.
5, 2023, doi: 10.1111/cgf.14898.'
mla: Ludwig, Ingmar, et al. “HalfedgeCNN for Native and Flexible Deep Learning on
Triangle Meshes.” Computer Graphics Forum, vol. 42, no. 5, Wiley, 2023,
doi:10.1111/cgf.14898.
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: 'AbstractNon‐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.'
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. Computer Graphics Forum. 2022;41(5):113-124.
doi:10.1111/cgf.14607'
apa: 'Schmidt, P., Born, J., Bommes, D., Campen, M., & Kobbelt, L. (2022). TinyAD:
Automatic Differentiation in Geometry Processing Made Simple. Computer Graphics
Forum, 41(5), 113–124. https://doi.org/10.1111/cgf.14607'
bibtex: '@article{Schmidt_Born_Bommes_Campen_Kobbelt_2022, title={TinyAD: Automatic
Differentiation in Geometry Processing Made Simple}, volume={41}, DOI={10.1111/cgf.14607},
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.” Computer
Graphics Forum 41, no. 5 (2022): 113–24. https://doi.org/10.1111/cgf.14607.'
ieee: 'P. Schmidt, J. Born, D. Bommes, M. Campen, and L. Kobbelt, “TinyAD: Automatic
Differentiation in Geometry Processing Made Simple,” Computer Graphics Forum,
vol. 41, no. 5, pp. 113–124, 2022, doi: 10.1111/cgf.14607.'
mla: 'Schmidt, Patrick, et al. “TinyAD: Automatic Differentiation in Geometry Processing
Made Simple.” Computer Graphics Forum, vol. 41, no. 5, Wiley, 2022, pp.
113–24, doi:10.1111/cgf.14607.'
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: '60371'
abstract:
- lang: eng
text: We describe a method for the generation of seamless surface parametrizations
with guaranteed local injectivity and full control over holonomy. Previous methods
guarantee only one of the two. Local injectivity is required to enable these parametrizations'
use in applications such as surface quadrangulation and spline construction. Holonomy
control is crucial to enable guidance or prescription of the parametrization's
isocurves based on directional information, in particular from cross-fields or
feature curves, and more generally to constrain the parametrization topologically.
To this end we investigate the relation between cross-field topology and seamless
parametrization topology. Leveraging previous results on locally injective parametrization
and combining them with insights on this relation in terms of holonomy, we propose
an algorithm that meets these requirements. A key component relies on the insight
that arbitrary surface cut graphs, as required for global parametrization, can
be homeomorphically modified to assume almost any set of turning numbers with
respect to a given target cross-field.
alternative_title:
- global parameterization from prescribed holonomy signatures
author:
- first_name: Hanxiao
full_name: Shen, Hanxiao
last_name: Shen
- first_name: Leyi
full_name: Zhu, Leyi
last_name: Zhu
- first_name: Ryan
full_name: Capouellez, Ryan
last_name: Capouellez
- first_name: Daniele
full_name: Panozzo, Daniele
last_name: Panozzo
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Denis
full_name: Zorin, Denis
last_name: Zorin
citation:
ama: Shen H, Zhu L, Capouellez R, Panozzo D, Campen M, Zorin D. Which cross fields
can be quadrangulated? ACM Transactions on Graphics. 2022;41(4):1-12. doi:10.1145/3528223.3530187
apa: Shen, H., Zhu, L., Capouellez, R., Panozzo, D., Campen, M., & Zorin, D.
(2022). Which cross fields can be quadrangulated? ACM Transactions on Graphics,
41(4), 1–12. https://doi.org/10.1145/3528223.3530187
bibtex: '@article{Shen_Zhu_Capouellez_Panozzo_Campen_Zorin_2022, title={Which cross
fields can be quadrangulated?}, volume={41}, DOI={10.1145/3528223.3530187},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Shen, Hanxiao and Zhu, Leyi and Capouellez,
Ryan and Panozzo, Daniele and Campen, Marcel and Zorin, Denis}, year={2022}, pages={1–12}
}'
chicago: 'Shen, Hanxiao, Leyi Zhu, Ryan Capouellez, Daniele Panozzo, Marcel Campen,
and Denis Zorin. “Which Cross Fields Can Be Quadrangulated?” ACM Transactions
on Graphics 41, no. 4 (2022): 1–12. https://doi.org/10.1145/3528223.3530187.'
ieee: 'H. Shen, L. Zhu, R. Capouellez, D. Panozzo, M. Campen, and D. Zorin, “Which
cross fields can be quadrangulated?,” ACM Transactions on Graphics, vol.
41, no. 4, pp. 1–12, 2022, doi: 10.1145/3528223.3530187.'
mla: Shen, Hanxiao, et al. “Which Cross Fields Can Be Quadrangulated?” ACM Transactions
on Graphics, vol. 41, no. 4, Association for Computing Machinery (ACM), 2022,
pp. 1–12, doi:10.1145/3528223.3530187.
short: H. Shen, L. Zhu, R. Capouellez, D. Panozzo, M. Campen, D. Zorin, ACM Transactions
on Graphics 41 (2022) 1–12.
date_created: 2025-06-25T09:05:57Z
date_updated: 2025-07-14T12:47:19Z
department:
- _id: '969'
doi: 10.1145/3528223.3530187
extern: '1'
intvolume: ' 41'
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: Which cross fields can be quadrangulated?
type: journal_article
user_id: '117512'
volume: 41
year: '2022'
...
---
_id: '60366'
abstract:
- lang: eng
text: AbstractThe 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.
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. Computer Graphics Forum. 2022;41(2):221-235. doi:10.1111/cgf.14470
apa: Brückler, H., Gupta, O., Mandad, M., & Campen, M. (2022). The 3D Motorcycle
Complex for Structured Volume Decomposition. Computer Graphics Forum, 41(2),
221–235. https://doi.org/10.1111/cgf.14470
bibtex: '@article{Brückler_Gupta_Mandad_Campen_2022, title={The 3D Motorcycle Complex
for Structured Volume Decomposition}, volume={41}, DOI={10.1111/cgf.14470},
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.” Computer Graphics
Forum 41, no. 2 (2022): 221–35. https://doi.org/10.1111/cgf.14470.'
ieee: 'H. Brückler, O. Gupta, M. Mandad, and M. Campen, “The 3D Motorcycle Complex
for Structured Volume Decomposition,” Computer Graphics Forum, vol. 41,
no. 2, pp. 221–235, 2022, doi: 10.1111/cgf.14470.'
mla: Brückler, Hendrik, et al. “The 3D Motorcycle Complex for Structured Volume
Decomposition.” Computer Graphics Forum, vol. 41, no. 2, Wiley, 2022, pp.
221–35, doi:10.1111/cgf.14470.
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: AbstractWe 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.
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. Computer Graphics
Forum. 2022;41(5):89-99. doi:10.1111/cgf.14605
apa: Khanteimouri, P., Mandad, M., & Campen, M. (2022). Rational Bézier Guarding.
Computer Graphics Forum, 41(5), 89–99. https://doi.org/10.1111/cgf.14605
bibtex: '@article{Khanteimouri_Mandad_Campen_2022, title={Rational Bézier Guarding},
volume={41}, DOI={10.1111/cgf.14605},
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.” Computer Graphics Forum 41, no. 5 (2022): 89–99. https://doi.org/10.1111/cgf.14605.'
ieee: 'P. Khanteimouri, M. Mandad, and M. Campen, “Rational Bézier Guarding,” Computer
Graphics Forum, vol. 41, no. 5, pp. 89–99, 2022, doi: 10.1111/cgf.14605.'
mla: Khanteimouri, Payam, et al. “Rational Bézier Guarding.” Computer Graphics
Forum, vol. 41, no. 5, Wiley, 2022, pp. 89–99, doi:10.1111/cgf.14605.
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: '60363'
article_number: '102078'
author:
- first_name: Manish
full_name: Mandad, Manish
last_name: Mandad
- first_name: Ruizhi
full_name: Chen, Ruizhi
last_name: Chen
- 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: Mandad M, Chen R, Bommes D, Campen M. Intrinsic mixed-integer polycubes for
hexahedral meshing. Computer Aided Geometric Design. 2022;94. doi:10.1016/j.cagd.2022.102078
apa: Mandad, M., Chen, R., Bommes, D., & Campen, M. (2022). Intrinsic mixed-integer
polycubes for hexahedral meshing. Computer Aided Geometric Design, 94,
Article 102078. https://doi.org/10.1016/j.cagd.2022.102078
bibtex: '@article{Mandad_Chen_Bommes_Campen_2022, title={Intrinsic mixed-integer
polycubes for hexahedral meshing}, volume={94}, DOI={10.1016/j.cagd.2022.102078},
number={102078}, journal={Computer Aided Geometric Design}, publisher={Elsevier
BV}, author={Mandad, Manish and Chen, Ruizhi and Bommes, David and Campen, Marcel},
year={2022} }'
chicago: Mandad, Manish, Ruizhi Chen, David Bommes, and Marcel Campen. “Intrinsic
Mixed-Integer Polycubes for Hexahedral Meshing.” Computer Aided Geometric Design
94 (2022). https://doi.org/10.1016/j.cagd.2022.102078.
ieee: 'M. Mandad, R. Chen, D. Bommes, and M. Campen, “Intrinsic mixed-integer polycubes
for hexahedral meshing,” Computer Aided Geometric Design, vol. 94, Art.
no. 102078, 2022, doi: 10.1016/j.cagd.2022.102078.'
mla: Mandad, Manish, et al. “Intrinsic Mixed-Integer Polycubes for Hexahedral Meshing.”
Computer Aided Geometric Design, vol. 94, 102078, Elsevier BV, 2022, doi:10.1016/j.cagd.2022.102078.
short: M. Mandad, R. Chen, D. Bommes, M. Campen, Computer Aided Geometric Design
94 (2022).
date_created: 2025-06-25T08:44:09Z
date_updated: 2025-07-14T12:47:12Z
department:
- _id: '969'
doi: 10.1016/j.cagd.2022.102078
extern: '1'
intvolume: ' 94'
language:
- iso: eng
publication: Computer Aided Geometric Design
publication_identifier:
issn:
- 0167-8396
publication_status: published
publisher: Elsevier BV
status: public
title: Intrinsic mixed-integer polycubes for hexahedral meshing
type: journal_article
user_id: '117512'
volume: 94
year: '2022'
...
---
_id: '60365'
article_number: '102085'
author:
- first_name: Steffen
full_name: Hinderink, Steffen
id: '116615'
last_name: Hinderink
- first_name: Manish
full_name: Mandad, Manish
last_name: Mandad
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: Hinderink S, Mandad M, Campen M. Angle-bounded 2D mesh simplification. Computer
Aided Geometric Design. 2022;95. doi:10.1016/j.cagd.2022.102085
apa: Hinderink, S., Mandad, M., & Campen, M. (2022). Angle-bounded 2D mesh simplification.
Computer Aided Geometric Design, 95, Article 102085. https://doi.org/10.1016/j.cagd.2022.102085
bibtex: '@article{Hinderink_Mandad_Campen_2022, title={Angle-bounded 2D mesh simplification},
volume={95}, DOI={10.1016/j.cagd.2022.102085},
number={102085}, journal={Computer Aided Geometric Design}, publisher={Elsevier
BV}, author={Hinderink, Steffen and Mandad, Manish and Campen, Marcel}, year={2022}
}'
chicago: Hinderink, Steffen, Manish Mandad, and Marcel Campen. “Angle-Bounded 2D
Mesh Simplification.” Computer Aided Geometric Design 95 (2022). https://doi.org/10.1016/j.cagd.2022.102085.
ieee: 'S. Hinderink, M. Mandad, and M. Campen, “Angle-bounded 2D mesh simplification,”
Computer Aided Geometric Design, vol. 95, Art. no. 102085, 2022, doi: 10.1016/j.cagd.2022.102085.'
mla: Hinderink, Steffen, et al. “Angle-Bounded 2D Mesh Simplification.” Computer
Aided Geometric Design, vol. 95, 102085, Elsevier BV, 2022, doi:10.1016/j.cagd.2022.102085.
short: S. Hinderink, M. Mandad, M. Campen, Computer Aided Geometric Design 95 (2022).
date_created: 2025-06-25T08:50:14Z
date_updated: 2025-07-14T12:47:05Z
department:
- _id: '969'
doi: 10.1016/j.cagd.2022.102085
extern: '1'
intvolume: ' 95'
language:
- iso: eng
publication: Computer Aided Geometric Design
publication_identifier:
issn:
- 0167-8396
publication_status: published
publisher: Elsevier BV
status: public
title: Angle-bounded 2D mesh simplification
type: journal_article
user_id: '117512'
volume: 95
year: '2022'
...
---
_id: '60372'
abstract:
- lang: eng
text: Developments in the field of parametrization-based quad mesh generation
on surfaces have been impactful over the past decade. In this context, an important
advance has been the replacement of error-prone rounding in the generation of
integer-grid maps, by robust quantization methods. In parallel, parametrization-based
hex mesh generation for volumes has been advanced. In this volumetric context,
however, the state-of-the-art still relies on fragile rounding, not rarely producing
defective meshes, especially when targeting a coarse mesh resolution. We present
a method to robustly quantize volume parametrizations, i.e., to determine guaranteed
valid choices of integers for 3D integer-grid maps. Inspired by the 2D case, we
base our construction on a non-conforming cell decomposition of the volume, a
3D analogue of a T-mesh. In particular, we leverage the motorcycle complex, a
recent generalization of the motorcycle graph, for this purpose. Integer values
are expressed in a differential manner on the edges of this complex, enabling
the efficient formulation of the conditions required to strictly prevent forcing
the map into degeneration. Applying our method in the context of hexahedral meshing,
we demonstrate that hexahedral meshes can be generated with significantly improved
flexibility.
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. Volume parametrization quantization for hexahedral
meshing. ACM Transactions on Graphics. 2022;41(4):1-19. doi:10.1145/3528223.3530123
apa: Brückler, H., Bommes, D., & Campen, M. (2022). Volume parametrization quantization
for hexahedral meshing. ACM Transactions on Graphics, 41(4), 1–19.
https://doi.org/10.1145/3528223.3530123
bibtex: '@article{Brückler_Bommes_Campen_2022, title={Volume parametrization quantization
for hexahedral meshing}, volume={41}, DOI={10.1145/3528223.3530123},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Brückler, Hendrik and Bommes, David and Campen,
Marcel}, year={2022}, pages={1–19} }'
chicago: 'Brückler, Hendrik, David Bommes, and Marcel Campen. “Volume Parametrization
Quantization for Hexahedral Meshing.” ACM Transactions on Graphics 41,
no. 4 (2022): 1–19. https://doi.org/10.1145/3528223.3530123.'
ieee: 'H. Brückler, D. Bommes, and M. Campen, “Volume parametrization quantization
for hexahedral meshing,” ACM Transactions on Graphics, vol. 41, no. 4,
pp. 1–19, 2022, doi: 10.1145/3528223.3530123.'
mla: Brückler, Hendrik, et al. “Volume Parametrization Quantization for Hexahedral
Meshing.” ACM Transactions on Graphics, vol. 41, no. 4, Association for
Computing Machinery (ACM), 2022, pp. 1–19, doi:10.1145/3528223.3530123.
short: H. Brückler, D. Bommes, M. Campen, ACM Transactions on Graphics 41 (2022)
1–19.
date_created: 2025-06-25T09:07:20Z
date_updated: 2025-07-14T12:47:23Z
department:
- _id: '969'
doi: 10.1145/3528223.3530123
extern: '1'
intvolume: ' 41'
issue: '4'
language:
- iso: eng
page: 1-19
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Volume parametrization quantization for hexahedral meshing
type: journal_article
user_id: '117512'
volume: 41
year: '2022'
...
---
_id: '60334'
abstract:
- lang: eng
text: In this article, we provide a detailed survey of techniques for hexahedral
mesh generation. We cover the whole spectrum of alternative approaches to mesh
generation, as well as post-processing algorithms for connectivity editing and
mesh optimization. For each technique, we highlight capabilities and limitations,
also pointing out the associated unsolved challenges. Recent relaxed approaches,
aiming to generate not pure-hex but hex-dominant meshes, are also discussed. The
required background, pertaining to geometrical as well as combinatorial aspects,
is introduced along the way.
author:
- first_name: Nico
full_name: Pietroni, Nico
last_name: Pietroni
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Alla
full_name: Sheffer, Alla
last_name: Sheffer
- first_name: Gianmarco
full_name: Cherchi, Gianmarco
last_name: Cherchi
- first_name: David
full_name: Bommes, David
last_name: Bommes
- first_name: Xifeng
full_name: Gao, Xifeng
last_name: Gao
- first_name: Riccardo
full_name: Scateni, Riccardo
last_name: Scateni
- first_name: Franck
full_name: Ledoux, Franck
last_name: Ledoux
- first_name: Jean
full_name: Remacle, Jean
last_name: Remacle
- first_name: Marco
full_name: Livesu, Marco
last_name: Livesu
citation:
ama: 'Pietroni N, Campen M, Sheffer A, et al. Hex-Mesh Generation and Processing:
A Survey. ACM Transactions on Graphics. 2022;42(2):1-44. doi:10.1145/3554920'
apa: 'Pietroni, N., Campen, M., Sheffer, A., Cherchi, G., Bommes, D., Gao, X., Scateni,
R., Ledoux, F., Remacle, J., & Livesu, M. (2022). Hex-Mesh Generation and
Processing: A Survey. ACM Transactions on Graphics, 42(2), 1–44.
https://doi.org/10.1145/3554920'
bibtex: '@article{Pietroni_Campen_Sheffer_Cherchi_Bommes_Gao_Scateni_Ledoux_Remacle_Livesu_2022,
title={Hex-Mesh Generation and Processing: A Survey}, volume={42}, DOI={10.1145/3554920},
number={2}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Pietroni, Nico and Campen, Marcel and Sheffer,
Alla and Cherchi, Gianmarco and Bommes, David and Gao, Xifeng and Scateni, Riccardo
and Ledoux, Franck and Remacle, Jean and Livesu, Marco}, year={2022}, pages={1–44}
}'
chicago: 'Pietroni, Nico, Marcel Campen, Alla Sheffer, Gianmarco Cherchi, David
Bommes, Xifeng Gao, Riccardo Scateni, Franck Ledoux, Jean Remacle, and Marco Livesu.
“Hex-Mesh Generation and Processing: A Survey.” ACM Transactions on Graphics
42, no. 2 (2022): 1–44. https://doi.org/10.1145/3554920.'
ieee: 'N. Pietroni et al., “Hex-Mesh Generation and Processing: A Survey,”
ACM Transactions on Graphics, vol. 42, no. 2, pp. 1–44, 2022, doi: 10.1145/3554920.'
mla: 'Pietroni, Nico, et al. “Hex-Mesh Generation and Processing: A Survey.” ACM
Transactions on Graphics, vol. 42, no. 2, Association for Computing Machinery
(ACM), 2022, pp. 1–44, doi:10.1145/3554920.'
short: N. Pietroni, M. Campen, A. Sheffer, G. Cherchi, D. Bommes, X. Gao, R. Scateni,
F. Ledoux, J. Remacle, M. Livesu, ACM Transactions on Graphics 42 (2022) 1–44.
date_created: 2025-06-23T10:36:34Z
date_updated: 2025-07-14T12:48:37Z
department:
- _id: '969'
doi: 10.1145/3554920
extern: '1'
intvolume: ' 42'
issue: '2'
language:
- iso: eng
page: 1-44
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: 'Hex-Mesh Generation and Processing: A Survey'
type: journal_article
user_id: '117512'
volume: 42
year: '2022'
...
---
_id: '60447'
citation:
ama: Andres B, Campen M, Sedlmair M, eds. 26th International Symposium on Vision,
Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität
Dresden, Germany, September 27-28, 2021. Eurographics Association; 2021.
apa: Andres, B., Campen, M., & Sedlmair, M. (Eds.). (2021). 26th International
Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische
Universität Dresden, Germany, September 27-28, 2021. Eurographics Association.
bibtex: '@book{Andres_Campen_Sedlmair_2021, title={26th International Symposium
on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität
Dresden, Germany, September 27-28, 2021}, publisher={Eurographics Association},
year={2021} }'
chicago: Andres, Bjoern, Marcel Campen, and Michael Sedlmair, eds. 26th International
Symposium on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische
Universität Dresden, Germany, September 27-28, 2021. Eurographics Association,
2021.
ieee: B. Andres, M. Campen, and M. Sedlmair, Eds., 26th International Symposium
on Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität
Dresden, Germany, September 27-28, 2021. Eurographics Association, 2021.
mla: Andres, Bjoern, et al., editors. 26th International Symposium on Vision,
Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität
Dresden, Germany, September 27-28, 2021. Eurographics Association, 2021.
short: B. Andres, M. Campen, M. Sedlmair, eds., 26th International Symposium on
Vision, Modeling, and Visualization, VMV 2021, Virtual Event / Technische Universität
Dresden, Germany, September 27-28, 2021, Eurographics Association, 2021.
date_created: 2025-06-27T10:28:46Z
date_updated: 2025-07-14T12:41:02Z
department:
- _id: '969'
editor:
- first_name: Bjoern
full_name: Andres, Bjoern
last_name: Andres
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Michael
full_name: Sedlmair, Michael
last_name: Sedlmair
extern: '1'
language:
- iso: eng
publication_identifier:
isbn:
- 978-3-03868-161-8
publisher: Eurographics Association
status: public
title: 26th International Symposium on Vision, Modeling, and Visualization, VMV 2021,
Virtual Event / Technische Universität Dresden, Germany, September 27-28, 2021
type: conference_editor
user_id: '114904'
year: '2021'
...
---
_id: '60377'
abstract:
- lang: eng
text: We present a guaranteed quality mesh generation algorithm for the
curvilinear triangulation of planar domains with piecewise polynomial boundary.
The resulting mesh consists of higher-order triangular elements which are not
only regular (i.e., with injective geometric map) but respect strict bounds on
quality measures like scaled Jacobian and MIPS distortion. This also implies that
the curved triangles' inner angles are bounded from above and below. These are
key quality criteria, for instance, in the field of finite element analysis. The
domain boundary is reproduced exactly, without geometric approximation error.
The central idea is to transform the curvilinear meshing problem into a linear
meshing problem via a carefully constructed transformation of bounded distortion,
enabling us to leverage key results on guaranteed-quality straight-edge triangulation.
The transformation is based on a simple yet general construction and observations
about convergence properties of curves under subdivision. Our algorithm can handle
arbitrary polynomial order, arbitrarily sharp corners, feature and interface curves,
and can be executed using rational arithmetic for strict reliability.
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. Guaranteed-quality higher-order triangular meshing of 2D
domains. ACM Transactions on Graphics. 2021;40(4):1-14. doi:10.1145/3450626.3459673
apa: Mandad, M., & Campen, M. (2021). Guaranteed-quality higher-order triangular
meshing of 2D domains. ACM Transactions on Graphics, 40(4), 1–14.
https://doi.org/10.1145/3450626.3459673
bibtex: '@article{Mandad_Campen_2021, title={Guaranteed-quality higher-order triangular
meshing of 2D domains}, volume={40}, DOI={10.1145/3450626.3459673},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Mandad, Manish and Campen, Marcel}, year={2021},
pages={1–14} }'
chicago: 'Mandad, Manish, and Marcel Campen. “Guaranteed-Quality Higher-Order Triangular
Meshing of 2D Domains.” ACM Transactions on Graphics 40, no. 4 (2021):
1–14. https://doi.org/10.1145/3450626.3459673.'
ieee: 'M. Mandad and M. Campen, “Guaranteed-quality higher-order triangular meshing
of 2D domains,” ACM Transactions on Graphics, vol. 40, no. 4, pp. 1–14,
2021, doi: 10.1145/3450626.3459673.'
mla: Mandad, Manish, and Marcel Campen. “Guaranteed-Quality Higher-Order Triangular
Meshing of 2D Domains.” ACM Transactions on Graphics, vol. 40, no. 4, Association
for Computing Machinery (ACM), 2021, pp. 1–14, doi:10.1145/3450626.3459673.
short: M. Mandad, M. Campen, ACM Transactions on Graphics 40 (2021) 1–14.
date_created: 2025-06-25T10:06:07Z
date_updated: 2025-07-14T12:47:43Z
department:
- _id: '969'
doi: 10.1145/3450626.3459673
extern: '1'
intvolume: ' 40'
issue: '4'
language:
- iso: eng
page: 1-14
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Guaranteed-quality higher-order triangular meshing of 2D domains
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...