---
_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: '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: '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: '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: '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'
...