---
_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: '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: '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: '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'
...
---
_id: '60378'
abstract:
- lang: eng
text: We describe an efficient algorithm to compute a discrete metric with
prescribed Gaussian curvature at all interior vertices and prescribed geodesic
curvature along the boundary of a mesh. The metric is (discretely) conformally
equivalent to the input metric. Its construction is based on theory developed
in [Gu et al. 2018b] and [Springborn 2020], relying on results on hyperbolic ideal
Delaunay triangulations. Generality is achieved by considering the surface's intrinsic
triangulation as a degree of freedom, and particular attention is paid to the
proper treatment of surface boundaries. While via a double cover approach the
case with boundary can be reduced to the case without boundary quite naturally,
the implied symmetry of the setting causes additional challenges related to stable
Delaunay-critical configurations that we address explicitly. We furthermore explore
the numerical limits of the approach and derive continuous maps from the discrete
metrics.
author:
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Ryan
full_name: Capouellez, Ryan
last_name: Capouellez
- first_name: Hanxiao
full_name: Shen, Hanxiao
last_name: Shen
- first_name: Leyi
full_name: Zhu, Leyi
last_name: Zhu
- first_name: Daniele
full_name: Panozzo, Daniele
last_name: Panozzo
- first_name: Denis
full_name: Zorin, Denis
last_name: Zorin
citation:
ama: Campen M, Capouellez R, Shen H, Zhu L, Panozzo D, Zorin D. Efficient and robust
discrete conformal equivalence with boundary. ACM Transactions on Graphics.
2021;40(6):1-16. doi:10.1145/3478513.3480557
apa: Campen, M., Capouellez, R., Shen, H., Zhu, L., Panozzo, D., & Zorin, D.
(2021). Efficient and robust discrete conformal equivalence with boundary. ACM
Transactions on Graphics, 40(6), 1–16. https://doi.org/10.1145/3478513.3480557
bibtex: '@article{Campen_Capouellez_Shen_Zhu_Panozzo_Zorin_2021, title={Efficient
and robust discrete conformal equivalence with boundary}, volume={40}, DOI={10.1145/3478513.3480557}, number={6},
journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery
(ACM)}, author={Campen, Marcel and Capouellez, Ryan and Shen, Hanxiao and Zhu,
Leyi and Panozzo, Daniele and Zorin, Denis}, year={2021}, pages={1–16} }'
chicago: 'Campen, Marcel, Ryan Capouellez, Hanxiao Shen, Leyi Zhu, Daniele Panozzo,
and Denis Zorin. “Efficient and Robust Discrete Conformal Equivalence with Boundary.”
ACM Transactions on Graphics 40, no. 6 (2021): 1–16. https://doi.org/10.1145/3478513.3480557.'
ieee: 'M. Campen, R. Capouellez, H. Shen, L. Zhu, D. Panozzo, and D. Zorin, “Efficient
and robust discrete conformal equivalence with boundary,” ACM Transactions
on Graphics, vol. 40, no. 6, pp. 1–16, 2021, doi: 10.1145/3478513.3480557.'
mla: Campen, Marcel, et al. “Efficient and Robust Discrete Conformal Equivalence
with Boundary.” ACM Transactions on Graphics, vol. 40, no. 6, Association
for Computing Machinery (ACM), 2021, pp. 1–16, doi:10.1145/3478513.3480557.
short: M. Campen, R. Capouellez, H. Shen, L. Zhu, D. Panozzo, D. Zorin, ACM Transactions
on Graphics 40 (2021) 1–16.
date_created: 2025-06-25T10:08:08Z
date_updated: 2025-07-14T12:47:47Z
department:
- _id: '969'
doi: 10.1145/3478513.3480557
extern: '1'
intvolume: ' 40'
issue: '6'
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: Efficient and robust discrete conformal equivalence with boundary
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...
---
_id: '60386'
abstract:
- lang: eng
text: 'We propose a novel approach to represent maps between two discrete
surfaces of the same genus and to minimize intrinsic mapping distortion. Our maps
are well-defined at every surface point and are guaranteed to be continuous bijections
(surface homeomorphisms). As a key feature of our approach, only the images of
vertices need to be represented explicitly, since the images of all other points
(on edges or in faces) are properly defined implicitly. This definition is via
unique geodesics in metrics of constant Gaussian curvature. Our method is built
upon the fact that such metrics exist on surfaces of arbitrary topology, without
the need for any cuts or cones (as asserted by the uniformization theorem). Depending
on the surfaces'' genus, these metrics exhibit one of the three classical geometries:
Euclidean, spherical or hyperbolic. Our formulation handles constructions in all
three geometries in a unified way. In addition, by considering not only the vertex
images but also the discrete metric as degrees of freedom, our formulation enables
us to simultaneously optimize the images of these vertices and images of all other
points.'
author:
- 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: Janis
full_name: Born, Janis
last_name: Born
- first_name: Leif
full_name: Kobbelt, Leif
last_name: Kobbelt
citation:
ama: Schmidt P, Campen M, Born J, Kobbelt L. Inter-surface maps via constant-curvature
metrics. ACM Transactions on Graphics. 2020;39(4). doi:10.1145/3386569.3392399
apa: Schmidt, P., Campen, M., Born, J., & Kobbelt, L. (2020). Inter-surface
maps via constant-curvature metrics. ACM Transactions on Graphics, 39(4).
https://doi.org/10.1145/3386569.3392399
bibtex: '@article{Schmidt_Campen_Born_Kobbelt_2020, title={Inter-surface maps via
constant-curvature metrics}, volume={39}, DOI={10.1145/3386569.3392399},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Schmidt, Patrick and Campen, Marcel and Born,
Janis and Kobbelt, Leif}, year={2020} }'
chicago: Schmidt, Patrick, Marcel Campen, Janis Born, and Leif Kobbelt. “Inter-Surface
Maps via Constant-Curvature Metrics.” ACM Transactions on Graphics 39,
no. 4 (2020). https://doi.org/10.1145/3386569.3392399.
ieee: 'P. Schmidt, M. Campen, J. Born, and L. Kobbelt, “Inter-surface maps via constant-curvature
metrics,” ACM Transactions on Graphics, vol. 39, no. 4, 2020, doi: 10.1145/3386569.3392399.'
mla: Schmidt, Patrick, et al. “Inter-Surface Maps via Constant-Curvature Metrics.”
ACM Transactions on Graphics, vol. 39, no. 4, Association for Computing
Machinery (ACM), 2020, doi:10.1145/3386569.3392399.
short: P. Schmidt, M. Campen, J. Born, L. Kobbelt, ACM Transactions on Graphics
39 (2020).
date_created: 2025-06-26T07:18:18Z
date_updated: 2025-07-14T12:48:27Z
department:
- _id: '969'
doi: 10.1145/3386569.3392399
extern: '1'
intvolume: ' 39'
issue: '4'
language:
- iso: eng
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Inter-surface maps via constant-curvature metrics
type: journal_article
user_id: '117512'
volume: 39
year: '2020'
...
---
_id: '60385'
abstract:
- lang: eng
text: We present a mesh generation algorithm for the curvilinear triangulation
of planar domains with piecewise polynomial boundary. The resulting mesh consists
of regular, injective higher-order triangular elements and precisely conforms
with the domain's curved boundary. No smoothness requirements are imposed on the
boundary. Prescribed piecewise polynomial curves in the interior, like material
interfaces or feature curves, can be taken into account for precise interpolation
by the resulting mesh's edges as well. In its core, the algorithm is based on
a novel explicit construction of guaranteed injective Bézier triangles with certain
edge curves and edge parametrizations prescribed. Due to the use of only rational
arithmetic, the algorithm can optionally be performed using exact number types
in practice, so as to provide robustness guarantees.
alternative_title:
- precise higher-order meshing of curved 2D domains
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. Bézier guarding. ACM Transactions on Graphics. 2020;39(4).
doi:10.1145/3386569.3392372
apa: Mandad, M., & Campen, M. (2020). Bézier guarding. ACM Transactions on
Graphics, 39(4). https://doi.org/10.1145/3386569.3392372
bibtex: '@article{Mandad_Campen_2020, title={Bézier guarding}, volume={39}, DOI={10.1145/3386569.3392372}, number={4},
journal={ACM Transactions on Graphics}, publisher={Association for Computing Machinery
(ACM)}, author={Mandad, Manish and Campen, Marcel}, year={2020} }'
chicago: Mandad, Manish, and Marcel Campen. “Bézier Guarding.” ACM Transactions
on Graphics 39, no. 4 (2020). https://doi.org/10.1145/3386569.3392372.
ieee: 'M. Mandad and M. Campen, “Bézier guarding,” ACM Transactions on Graphics,
vol. 39, no. 4, 2020, doi: 10.1145/3386569.3392372.'
mla: Mandad, Manish, and Marcel Campen. “Bézier Guarding.” ACM Transactions on
Graphics, vol. 39, no. 4, Association for Computing Machinery (ACM), 2020,
doi:10.1145/3386569.3392372.
short: M. Mandad, M. Campen, ACM Transactions on Graphics 39 (2020).
date_created: 2025-06-26T07:16:40Z
date_updated: 2025-07-14T12:48:24Z
department:
- _id: '969'
doi: 10.1145/3386569.3392372
extern: '1'
intvolume: ' 39'
issue: '4'
language:
- iso: eng
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery (ACM)
status: public
title: Bézier guarding
type: journal_article
user_id: '117512'
volume: 39
year: '2020'
...
---
_id: '60390'
abstract:
- lang: eng
text: "\r\n The problem of discrete surface parametrization,
i.e. mapping a mesh to a planar domain, has been investigated extensively. We
address the more general problem of mapping\r\n between\r\n
\ surfaces. In particular, we provide a formulation that yields a map
between two disk-topology meshes, which is continuous and injective by construction
and which locally minimizes intrinsic distortion. A common approach is to express
such a map as the composition of two maps via a simple intermediate domain such
as the plane, and to independently optimize the individual maps. However, even
if both individual maps are of minimal distortion, there is potentially high distortion
in the composed map. In contrast to many previous works, we minimize distortion
in an end-to-end manner, directly optimizing the quality of the composed map.
This setting poses additional challenges due to the discrete nature of both the
source and the target domain. We propose a formulation that, despite the combinatorial
aspects of the problem, allows for a purely continuous optimization. Further,
our approach addresses the non-smooth nature of discrete distortion measures in
this context which hinders straightforward application of off-the-shelf optimization
techniques. We demonstrate that, despite the challenges inherent to the more involved
setting, discrete surface-to-surface maps can be optimized effectively.\r\n "
author:
- first_name: Patrick
full_name: Schmidt, Patrick
last_name: Schmidt
- first_name: Janis
full_name: Born, Janis
last_name: Born
- 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, Campen M, Kobbelt L. Distortion-minimizing injective maps
between surfaces. ACM Transactions on Graphics. 2019;38(6):1-15. doi:10.1145/3355089.3356519
apa: Schmidt, P., Born, J., Campen, M., & Kobbelt, L. (2019). Distortion-minimizing
injective maps between surfaces. ACM Transactions on Graphics, 38(6),
1–15. https://doi.org/10.1145/3355089.3356519
bibtex: '@article{Schmidt_Born_Campen_Kobbelt_2019, title={Distortion-minimizing
injective maps between surfaces}, volume={38}, DOI={10.1145/3355089.3356519},
number={6}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Schmidt, Patrick and Born, Janis and Campen,
Marcel and Kobbelt, Leif}, year={2019}, pages={1–15} }'
chicago: 'Schmidt, Patrick, Janis Born, Marcel Campen, and Leif Kobbelt. “Distortion-Minimizing
Injective Maps between Surfaces.” ACM Transactions on Graphics 38, no.
6 (2019): 1–15. https://doi.org/10.1145/3355089.3356519.'
ieee: 'P. Schmidt, J. Born, M. Campen, and L. Kobbelt, “Distortion-minimizing injective
maps between surfaces,” ACM Transactions on Graphics, vol. 38, no. 6, pp.
1–15, 2019, doi: 10.1145/3355089.3356519.'
mla: Schmidt, Patrick, et al. “Distortion-Minimizing Injective Maps between Surfaces.”
ACM Transactions on Graphics, vol. 38, no. 6, Association for Computing
Machinery (ACM), 2019, pp. 1–15, doi:10.1145/3355089.3356519.
short: P. Schmidt, J. Born, M. Campen, L. Kobbelt, ACM Transactions on Graphics
38 (2019) 1–15.
date_created: 2025-06-26T07:44:21Z
date_updated: 2025-07-14T12:44:37Z
department:
- _id: '969'
doi: 10.1145/3355089.3356519
extern: '1'
intvolume: ' 38'
issue: '6'
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: Distortion-minimizing injective maps between surfaces
type: journal_article
user_id: '117512'
volume: 38
year: '2019'
...
---
_id: '60389'
abstract:
- lang: eng
text: The generation of quad meshes based on surface parametrization techniques
has proven to be a versatile approach. These techniques quantize an initial seamless
parametrization so as to obtain an integer grid map implying a pure quad mesh.
State-of-the-art methods following this approach have to assume that the surface
to be meshed either has no boundary, or has a boundary which the resulting mesh
is supposed to be aligned to. In a variety of applications this is not desirable
and non-boundary-aligned meshes or grid-parametrizations are preferred. We thus
present a technique to robustly generate integer grid maps which are either boundary-aligned,
non-boundary-aligned, or partially boundary-aligned, just as required by different
applications. We thereby generalize previous work to this broader setting. This
enables the reliable generation of trimmed quad meshes with partial elements along
the boundary, preferable in various scenarios, from tiled texturing over design
and modeling to fabrication and architecture, due to fewer constraints and hence
higher overall mesh quality and other benefits in terms of aesthetics and flexibility.
author:
- first_name: Max
full_name: Lyon, Max
last_name: Lyon
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: David
full_name: Bommes, David
last_name: Bommes
- first_name: Leif
full_name: Kobbelt, Leif
last_name: Kobbelt
citation:
ama: Lyon M, Campen M, Bommes D, Kobbelt L. Parametrization quantization with free
boundaries for trimmed quad meshing. ACM Transactions on Graphics. 2019;38(4):1-14.
doi:10.1145/3306346.3323019
apa: Lyon, M., Campen, M., Bommes, D., & Kobbelt, L. (2019). Parametrization
quantization with free boundaries for trimmed quad meshing. ACM Transactions
on Graphics, 38(4), 1–14. https://doi.org/10.1145/3306346.3323019
bibtex: '@article{Lyon_Campen_Bommes_Kobbelt_2019, title={Parametrization quantization
with free boundaries for trimmed quad meshing}, volume={38}, DOI={10.1145/3306346.3323019},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Lyon, Max and Campen, Marcel and Bommes, David
and Kobbelt, Leif}, year={2019}, pages={1–14} }'
chicago: 'Lyon, Max, Marcel Campen, David Bommes, and Leif Kobbelt. “Parametrization
Quantization with Free Boundaries for Trimmed Quad Meshing.” ACM Transactions
on Graphics 38, no. 4 (2019): 1–14. https://doi.org/10.1145/3306346.3323019.'
ieee: 'M. Lyon, M. Campen, D. Bommes, and L. Kobbelt, “Parametrization quantization
with free boundaries for trimmed quad meshing,” ACM Transactions on Graphics,
vol. 38, no. 4, pp. 1–14, 2019, doi: 10.1145/3306346.3323019.'
mla: Lyon, Max, et al. “Parametrization Quantization with Free Boundaries for Trimmed
Quad Meshing.” ACM Transactions on Graphics, vol. 38, no. 4, Association
for Computing Machinery (ACM), 2019, pp. 1–14, doi:10.1145/3306346.3323019.
short: M. Lyon, M. Campen, D. Bommes, L. Kobbelt, ACM Transactions on Graphics 38
(2019) 1–14.
date_created: 2025-06-26T07:40:49Z
date_updated: 2025-07-14T12:44:32Z
department:
- _id: '969'
doi: 10.1145/3306346.3323019
extern: '1'
intvolume: ' 38'
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: Parametrization quantization with free boundaries for trimmed quad meshing
type: journal_article
user_id: '117512'
volume: 38
year: '2019'
...
---
_id: '60384'
abstract:
- lang: eng
text: "Seamless global parametrization of surfaces is a key operation in
geometry processing, e.g., for high-quality quad mesh generation. A common approach
is to prescribe the parametric domain structure, in particular, the locations
of parametrization singularities (cones), and solve a non-convex optimization
problem minimizing a distortion measure, with local injectivity imposed through
either constraints or barrier terms. In both cases, an initial valid parametrization
is essential to serve as a feasible starting point for obtaining an optimized
solution. While convexified versions of the constraints eliminate this initialization
requirement, they narrow the range of solutions, causing some problem instances
that actually do have a solution to become infeasible.\r\n We
demonstrate that for arbitrary given sets of topologically admissible parametric
cones with prescribed curvature, a global seamless parametrization always exists
(with the exception of one well-known case). Importantly, our proof is constructive
and directly leads to a general algorithm for computing such parametrizations.
Most distinctively, this algorithm is bootstrapped with a convex optimization
problem (solving for a conformal map), in tandem with a simple linear equation
system (determining a seamless modification of this map). This initial map can
then serve as a valid starting point and be optimized for low distortion using
existing injectivity preserving methods."
author:
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Hanxiao
full_name: Shen, Hanxiao
last_name: Shen
- first_name: Jiaran
full_name: Zhou, Jiaran
last_name: Zhou
- first_name: Denis
full_name: Zorin, Denis
last_name: Zorin
citation:
ama: Campen M, Shen H, Zhou J, Zorin D. Seamless Parametrization with Arbitrary
Cones for Arbitrary Genus. ACM Transactions on Graphics. 2019;39(1):1-19.
doi:10.1145/3360511
apa: Campen, M., Shen, H., Zhou, J., & Zorin, D. (2019). Seamless Parametrization
with Arbitrary Cones for Arbitrary Genus. ACM Transactions on Graphics,
39(1), 1–19. https://doi.org/10.1145/3360511
bibtex: '@article{Campen_Shen_Zhou_Zorin_2019, title={Seamless Parametrization with
Arbitrary Cones for Arbitrary Genus}, volume={39}, DOI={10.1145/3360511},
number={1}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Campen, Marcel and Shen, Hanxiao and Zhou,
Jiaran and Zorin, Denis}, year={2019}, pages={1–19} }'
chicago: 'Campen, Marcel, Hanxiao Shen, Jiaran Zhou, and Denis Zorin. “Seamless
Parametrization with Arbitrary Cones for Arbitrary Genus.” ACM Transactions
on Graphics 39, no. 1 (2019): 1–19. https://doi.org/10.1145/3360511.'
ieee: 'M. Campen, H. Shen, J. Zhou, and D. Zorin, “Seamless Parametrization with
Arbitrary Cones for Arbitrary Genus,” ACM Transactions on Graphics, vol.
39, no. 1, pp. 1–19, 2019, doi: 10.1145/3360511.'
mla: Campen, Marcel, et al. “Seamless Parametrization with Arbitrary Cones for Arbitrary
Genus.” ACM Transactions on Graphics, vol. 39, no. 1, Association for Computing
Machinery (ACM), 2019, pp. 1–19, doi:10.1145/3360511.
short: M. Campen, H. Shen, J. Zhou, D. Zorin, ACM Transactions on Graphics 39 (2019)
1–19.
date_created: 2025-06-26T07:05:13Z
date_updated: 2025-07-14T12:48:21Z
department:
- _id: '969'
doi: 10.1145/3360511
extern: '1'
intvolume: ' 39'
issue: '1'
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: Seamless Parametrization with Arbitrary Cones for Arbitrary Genus
type: journal_article
user_id: '117512'
volume: 39
year: '2019'
...
---
_id: '60399'
abstract:
- lang: eng
text: "A variety of techniques were proposed to model smooth surfaces based
on tensor product splines (e.g. subdivision surfaces, free-form splines, T-splines).
Conversion of an input surface into such a representation is commonly achieved
by constructing a global seamless parametrization, possibly aligned to a guiding
cross-field (e.g. of principal curvature directions), and using this parametrization
as domain to construct the spline-based surface.\r\n One
major fundamental difficulty in designing robust algorithms for this task is the
fact that for common types, e.g. subdivision surfaces (requiring a conforming
domain mesh) or T-spline surfaces (requiring a globally consistent knot interval
assignment) reliably obtaining a suitable parametrization that has the same topological
structure as the guiding field poses a major challenge. Even worse, not all fields
do admit suitable parametrizations, and no concise conditions are known as to
which fields do.\r\n \r\n We present a class
of surface constructions (T-splines with\r\n halfedge
knots\r\n ) and a class of parametrizations (\r\n seamless
similarity maps\r\n ) that are, in a sense, a perfect
match for the task: for\r\n any\r\n given
guiding field structure, a compatible parametrization of this kind exists and
a smooth piecewise rational surface with exactly the same structure as the input
field can be constructed from it. As a byproduct, this enables full control over
extraordinary points. The construction is backward compatible with classical NURBS.
We present efficient algorithms for building discrete conformal similarity maps
and associated T-meshes and T-spline surfaces.\r\n "
alternative_title:
- a perfect couple
author:
- 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: Campen M, Zorin D. Similarity maps and field-guided T-splines. ACM Transactions
on Graphics. 2017;36(4):1-16. doi:10.1145/3072959.3073647
apa: Campen, M., & Zorin, D. (2017). Similarity maps and field-guided T-splines.
ACM Transactions on Graphics, 36(4), 1–16. https://doi.org/10.1145/3072959.3073647
bibtex: '@article{Campen_Zorin_2017, title={Similarity maps and field-guided T-splines},
volume={36}, DOI={10.1145/3072959.3073647},
number={4}, journal={ACM Transactions on Graphics}, publisher={Association for
Computing Machinery (ACM)}, author={Campen, Marcel and Zorin, Denis}, year={2017},
pages={1–16} }'
chicago: 'Campen, Marcel, and Denis Zorin. “Similarity Maps and Field-Guided T-Splines.”
ACM Transactions on Graphics 36, no. 4 (2017): 1–16. https://doi.org/10.1145/3072959.3073647.'
ieee: 'M. Campen and D. Zorin, “Similarity maps and field-guided T-splines,” ACM
Transactions on Graphics, vol. 36, no. 4, pp. 1–16, 2017, doi: 10.1145/3072959.3073647.'
mla: Campen, Marcel, and Denis Zorin. “Similarity Maps and Field-Guided T-Splines.”
ACM Transactions on Graphics, vol. 36, no. 4, Association for Computing
Machinery (ACM), 2017, pp. 1–16, doi:10.1145/3072959.3073647.
short: M. Campen, D. Zorin, ACM Transactions on Graphics 36 (2017) 1–16.
date_created: 2025-06-26T08:16:00Z
date_updated: 2025-07-14T12:43:19Z
department:
- _id: '969'
doi: 10.1145/3072959.3073647
extern: '1'
intvolume: ' 36'
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: Similarity maps and field-guided T-splines
type: journal_article
user_id: '117512'
volume: 36
year: '2017'
...
---
_id: '60437'
abstract:
- lang: eng
text: 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.
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. ACM Transactions on Graphics. 2016;35(6):1-13.
doi:10.1145/2980179.2982413
apa: Ebke, H.-C., Schmidt, P., Campen, M., & Kobbelt, L. (2016). Interactively
controlled quad remeshing of high resolution 3D models. ACM Transactions on
Graphics, 35(6), 1–13. https://doi.org/10.1145/2980179.2982413
bibtex: '@article{Ebke_Schmidt_Campen_Kobbelt_2016, title={Interactively controlled
quad remeshing of high resolution 3D models}, volume={35}, DOI={10.1145/2980179.2982413},
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.” ACM
Transactions on Graphics 35, no. 6 (2016): 1–13. https://doi.org/10.1145/2980179.2982413.'
ieee: 'H.-C. Ebke, P. Schmidt, M. Campen, and L. Kobbelt, “Interactively controlled
quad remeshing of high resolution 3D models,” ACM Transactions on Graphics,
vol. 35, no. 6, pp. 1–13, 2016, doi: 10.1145/2980179.2982413.'
mla: Ebke, Hans-Christian, et al. “Interactively Controlled Quad Remeshing of High
Resolution 3D Models.” ACM Transactions on Graphics, vol. 35, no. 6, Association
for Computing Machinery (ACM), 2016, pp. 1–13, doi:10.1145/2980179.2982413.
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: '60436'
abstract:
- lang: eng
text: 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.
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. ACM
Transactions on Graphics. 2016;35(4):1-15. doi:10.1145/2897824.2925890
apa: Campen, M., Silva, C. T., & Zorin, D. (2016). Bijective maps from simplicial
foliations. ACM Transactions on Graphics, 35(4), 1–15. https://doi.org/10.1145/2897824.2925890
bibtex: '@article{Campen_Silva_Zorin_2016, title={Bijective maps from simplicial
foliations}, volume={35}, DOI={10.1145/2897824.2925890},
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.” ACM Transactions on Graphics 35, no. 4 (2016):
1–15. https://doi.org/10.1145/2897824.2925890.'
ieee: 'M. Campen, C. T. Silva, and D. Zorin, “Bijective maps from simplicial foliations,”
ACM Transactions on Graphics, vol. 35, no. 4, pp. 1–15, 2016, doi: 10.1145/2897824.2925890.'
mla: Campen, Marcel, et al. “Bijective Maps from Simplicial Foliations.” ACM
Transactions on Graphics, vol. 35, no. 4, Association for Computing Machinery
(ACM), 2016, pp. 1–15, doi:10.1145/2897824.2925890.
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: '60442'
abstract:
- lang: eng
text: '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-calledseamlessparametrizations,
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.'
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. ACM Transactions
on Graphics. 2015;34(6):1-12. doi:10.1145/2816795.2818140
apa: Campen, M., Bommes, D., & Kobbelt, L. (2015). Quantized global parametrization.
ACM Transactions on Graphics, 34(6), 1–12. https://doi.org/10.1145/2816795.2818140
bibtex: '@article{Campen_Bommes_Kobbelt_2015, title={Quantized global parametrization},
volume={34}, DOI={10.1145/2816795.2818140},
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.”
ACM Transactions on Graphics 34, no. 6 (2015): 1–12. https://doi.org/10.1145/2816795.2818140.'
ieee: 'M. Campen, D. Bommes, and L. Kobbelt, “Quantized global parametrization,”
ACM Transactions on Graphics, vol. 34, no. 6, pp. 1–12, 2015, doi: 10.1145/2816795.2818140.'
mla: Campen, Marcel, et al. “Quantized Global Parametrization.” ACM Transactions
on Graphics, vol. 34, no. 6, Association for Computing Machinery (ACM), 2015,
pp. 1–12, doi:10.1145/2816795.2818140.
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'
...