---
_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: '60376'
abstract:
- lang: eng
text: AbstractA homeomorphism between two surfaces
not only defines a (continuous and bijective) geometric correspondence of points
but also (by implication) an identification of topological features, i.e. handles
and tunnels, and how the map twists around them. However, in practice, surface
maps are often encoded via sparse correspondences or fuzzy representations that
merely approximate a homeomorphism and are therefore inherently ambiguous about
map topology. In this work, we show a way to infer topological information from
an imperfect input map between two shapes. In particular, we compute a homology
map, a linear map that transports homology classes of cycles from one surface
to the other, subject to a global consistency constraint. Our inference robustly
handles imperfect (e.g., partial, sparse, fuzzy, noisy, outlier‐ridden, non‐injective)
input maps and is guaranteed to produce homology maps that are compatible with
true homeomorphisms between the input shapes. Homology maps inferred by our method
can be directly used to transfer homological information between shapes, or serve
as foundation for the construction of a proper homeomorphism guided by the input
map, e.g., via compatible surface decomposition.
author:
- first_name: Janis
full_name: Born, Janis
last_name: Born
- first_name: Patrick
full_name: Schmidt, Patrick
last_name: Schmidt
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Leif
full_name: Kobbelt, Leif
last_name: Kobbelt
citation:
ama: Born J, Schmidt P, Campen M, Kobbelt L. Surface Map Homology Inference. Computer
Graphics Forum. 2021;40(5):193-204. doi:10.1111/cgf.14367
apa: Born, J., Schmidt, P., Campen, M., & Kobbelt, L. (2021). Surface Map Homology
Inference. Computer Graphics Forum, 40(5), 193–204. https://doi.org/10.1111/cgf.14367
bibtex: '@article{Born_Schmidt_Campen_Kobbelt_2021, title={Surface Map Homology
Inference}, volume={40}, DOI={10.1111/cgf.14367},
number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Born,
Janis and Schmidt, Patrick and Campen, Marcel and Kobbelt, Leif}, year={2021},
pages={193–204} }'
chicago: 'Born, Janis, Patrick Schmidt, Marcel Campen, and Leif Kobbelt. “Surface
Map Homology Inference.” Computer Graphics Forum 40, no. 5 (2021): 193–204.
https://doi.org/10.1111/cgf.14367.'
ieee: 'J. Born, P. Schmidt, M. Campen, and L. Kobbelt, “Surface Map Homology Inference,”
Computer Graphics Forum, vol. 40, no. 5, pp. 193–204, 2021, doi: 10.1111/cgf.14367.'
mla: Born, Janis, et al. “Surface Map Homology Inference.” Computer Graphics
Forum, vol. 40, no. 5, Wiley, 2021, pp. 193–204, doi:10.1111/cgf.14367.
short: J. Born, P. Schmidt, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021)
193–204.
date_created: 2025-06-25T09:54:02Z
date_updated: 2025-07-14T12:47:40Z
department:
- _id: '969'
doi: 10.1111/cgf.14367
extern: '1'
intvolume: ' 40'
issue: '5'
language:
- iso: eng
page: 193-204
publication: Computer Graphics Forum
publication_identifier:
issn:
- 0167-7055
- 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Surface Map Homology Inference
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...
---
_id: '60374'
abstract:
- lang: eng
text: AbstractWe present a robust and fast method
for the creation of conforming quad layouts on surfaces. Our algorithm is based
on the quantization of a T‐mesh, i.e. an assignment of integer lengths to the
sides of a non‐conforming rectangular partition of the surface. This representation
has the benefit of being able to encode an infinite number of layout connectivity
options in a finite manner, which guarantees that a valid layout can always be
found. We carefully construct the T‐mesh from a given seamless parametrization
such that the algorithm can provide guarantees on the results' quality. In particular,
the user can specify a bound on the angular deviation of layout edges from prescribed
directions. We solve an integer linear program (ILP) to find a coarse quad layout
adhering to that maximal deviation. Our algorithm is guaranteed to yield a conforming
quad layout free of T‐junctions together with bounded angle distortion. Our results
show that the presented method is fast, reliable, and achieves high quality layouts.
author:
- first_name: Max
full_name: Lyon, Max
last_name: Lyon
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Leif
full_name: Kobbelt, Leif
last_name: Kobbelt
citation:
ama: Lyon M, Campen M, Kobbelt L. Quad Layouts via Constrained T‐Mesh Quantization.
Computer Graphics Forum. 2021;40(2):305-314. doi:10.1111/cgf.142634
apa: Lyon, M., Campen, M., & Kobbelt, L. (2021). Quad Layouts via Constrained
T‐Mesh Quantization. Computer Graphics Forum, 40(2), 305–314. https://doi.org/10.1111/cgf.142634
bibtex: '@article{Lyon_Campen_Kobbelt_2021, title={Quad Layouts via Constrained
T‐Mesh Quantization}, volume={40}, DOI={10.1111/cgf.142634},
number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Lyon,
Max and Campen, Marcel and Kobbelt, Leif}, year={2021}, pages={305–314} }'
chicago: 'Lyon, Max, Marcel Campen, and Leif Kobbelt. “Quad Layouts via Constrained
T‐Mesh Quantization.” Computer Graphics Forum 40, no. 2 (2021): 305–14.
https://doi.org/10.1111/cgf.142634.'
ieee: 'M. Lyon, M. Campen, and L. Kobbelt, “Quad Layouts via Constrained T‐Mesh
Quantization,” Computer Graphics Forum, vol. 40, no. 2, pp. 305–314, 2021,
doi: 10.1111/cgf.142634.'
mla: Lyon, Max, et al. “Quad Layouts via Constrained T‐Mesh Quantization.” Computer
Graphics Forum, vol. 40, no. 2, Wiley, 2021, pp. 305–14, doi:10.1111/cgf.142634.
short: M. Lyon, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021) 305–314.
date_created: 2025-06-25T09:17:15Z
date_updated: 2025-07-14T12:47:35Z
department:
- _id: '969'
doi: 10.1111/cgf.142634
extern: '1'
intvolume: ' 40'
issue: '2'
language:
- iso: eng
page: 305-314
publication: Computer Graphics Forum
publication_identifier:
issn:
- 0167-7055
- 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Quad Layouts via Constrained T‐Mesh Quantization
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...
---
_id: '60375'
abstract:
- lang: eng
text: AbstractA common approach to automatic quad
layout generation on surfaces is to, in a first stage, decide on the positioning
of irregular layout vertices, followed by finding sensible layout edges connecting
these vertices and partitioning the surface into quadrilateral patches in a second
stage. While this two‐step approach reduces the problem's complexity, this separation
also limits the result quality. In the worst case, the set of layout vertices
fixed in the first stage without consideration of the second may not even permit
a valid quad layout. We propose an algorithm for the creation of quad layouts
in which the initial layout vertices can be adjusted in the second stage. Whenever
beneficial for layout quality or even validity, these vertices may be moved within
a prescribed radius or even be removed. Our algorithm is based on a robust quantization
strategy, turning a continuous T‐mesh structure into a discrete layout. We show
the effectiveness of our algorithm on a variety of inputs.
author:
- first_name: Max
full_name: Lyon, Max
last_name: Lyon
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
- first_name: Leif
full_name: Kobbelt, Leif
last_name: Kobbelt
citation:
ama: Lyon M, Campen M, Kobbelt L. Simpler Quad Layouts using Relaxed Singularities.
Computer Graphics Forum. 2021;40(5):169-180. doi:10.1111/cgf.14365
apa: Lyon, M., Campen, M., & Kobbelt, L. (2021). Simpler Quad Layouts using
Relaxed Singularities. Computer Graphics Forum, 40(5), 169–180.
https://doi.org/10.1111/cgf.14365
bibtex: '@article{Lyon_Campen_Kobbelt_2021, title={Simpler Quad Layouts using Relaxed
Singularities}, volume={40}, DOI={10.1111/cgf.14365},
number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Lyon,
Max and Campen, Marcel and Kobbelt, Leif}, year={2021}, pages={169–180} }'
chicago: 'Lyon, Max, Marcel Campen, and Leif Kobbelt. “Simpler Quad Layouts Using
Relaxed Singularities.” Computer Graphics Forum 40, no. 5 (2021): 169–80.
https://doi.org/10.1111/cgf.14365.'
ieee: 'M. Lyon, M. Campen, and L. Kobbelt, “Simpler Quad Layouts using Relaxed Singularities,”
Computer Graphics Forum, vol. 40, no. 5, pp. 169–180, 2021, doi: 10.1111/cgf.14365.'
mla: Lyon, Max, et al. “Simpler Quad Layouts Using Relaxed Singularities.” Computer
Graphics Forum, vol. 40, no. 5, Wiley, 2021, pp. 169–80, doi:10.1111/cgf.14365.
short: M. Lyon, M. Campen, L. Kobbelt, Computer Graphics Forum 40 (2021) 169–180.
date_created: 2025-06-25T09:39:31Z
date_updated: 2025-07-14T12:47:37Z
department:
- _id: '969'
doi: 10.1111/cgf.14365
extern: '1'
intvolume: ' 40'
issue: '5'
language:
- iso: eng
page: 169-180
publication: Computer Graphics Forum
publication_identifier:
issn:
- 0167-7055
- 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Simpler Quad Layouts using Relaxed Singularities
type: journal_article
user_id: '117512'
volume: 40
year: '2021'
...
---
_id: '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: '60383'
abstract:
- lang: eng
text: AbstractThe problem of seamless parametrization
of surfaces is of interest in the context of structured quadrilateral mesh generation
and spline‐based surface approximation. It has been tackled by a variety of approaches,
commonly relying on continuous numerical optimization to ultimately obtain suitable
parameter domains. We present a general combinatorial seamless parameter domain
construction, free from the potential numerical issues inherent to continuous
optimization techniques in practice. The domains are constructed as abstract polygonal
complexes which can be embedded in a discrete planar grid space, as unions of
unit squares. We ensure that the domain structure matches any prescribed parametrization
singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary
genus are supported. Once a domain suitable for a given surface is constructed,
a seamless and locally injective parametrization over this domain can be obtained
using existing planar disk mapping techniques, making recourse to Tutte's classical
embedding theorem.
author:
- first_name: Jiaran
full_name: Zhou, Jiaran
last_name: Zhou
- first_name: Changhe
full_name: Tu, Changhe
last_name: Tu
- first_name: Denis
full_name: Zorin, Denis
last_name: Zorin
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: Zhou J, Tu C, Zorin D, Campen M. Combinatorial Construction of Seamless Parameter
Domains. Computer Graphics Forum. 2020;39(2):179-190. doi:10.1111/cgf.13922
apa: Zhou, J., Tu, C., Zorin, D., & Campen, M. (2020). Combinatorial Construction
of Seamless Parameter Domains. Computer Graphics Forum, 39(2), 179–190.
https://doi.org/10.1111/cgf.13922
bibtex: '@article{Zhou_Tu_Zorin_Campen_2020, title={Combinatorial Construction of
Seamless Parameter Domains}, volume={39}, DOI={10.1111/cgf.13922},
number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Zhou,
Jiaran and Tu, Changhe and Zorin, Denis and Campen, Marcel}, year={2020}, pages={179–190}
}'
chicago: 'Zhou, Jiaran, Changhe Tu, Denis Zorin, and Marcel Campen. “Combinatorial
Construction of Seamless Parameter Domains.” Computer Graphics Forum 39,
no. 2 (2020): 179–90. https://doi.org/10.1111/cgf.13922.'
ieee: 'J. Zhou, C. Tu, D. Zorin, and M. Campen, “Combinatorial Construction of Seamless
Parameter Domains,” Computer Graphics Forum, vol. 39, no. 2, pp. 179–190,
2020, doi: 10.1111/cgf.13922.'
mla: Zhou, Jiaran, et al. “Combinatorial Construction of Seamless Parameter Domains.”
Computer Graphics Forum, vol. 39, no. 2, Wiley, 2020, pp. 179–90, doi:10.1111/cgf.13922.
short: J. Zhou, C. Tu, D. Zorin, M. Campen, Computer Graphics Forum 39 (2020) 179–190.
date_created: 2025-06-26T06:52:07Z
date_updated: 2025-07-14T12:48:19Z
department:
- _id: '969'
doi: 10.1111/cgf.13922
extern: '1'
intvolume: ' 39'
issue: '2'
language:
- iso: eng
page: 179-190
publication: Computer Graphics Forum
publication_identifier:
issn:
- 0167-7055
- 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Combinatorial Construction of Seamless Parameter Domains
type: journal_article
user_id: '117512'
volume: 39
year: '2020'
...
---
_id: '60382'
article_number: '102862'
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. Efficient piecewise higher-order parametrization of discrete
surfaces with local and global injectivity. Computer-Aided Design. 2020;127.
doi:10.1016/j.cad.2020.102862
apa: Mandad, M., & Campen, M. (2020). Efficient piecewise higher-order parametrization
of discrete surfaces with local and global injectivity. Computer-Aided Design,
127, Article 102862. https://doi.org/10.1016/j.cad.2020.102862
bibtex: '@article{Mandad_Campen_2020, title={Efficient piecewise higher-order parametrization
of discrete surfaces with local and global injectivity}, volume={127}, DOI={10.1016/j.cad.2020.102862},
number={102862}, journal={Computer-Aided Design}, publisher={Elsevier BV}, author={Mandad,
Manish and Campen, Marcel}, year={2020} }'
chicago: Mandad, Manish, and Marcel Campen. “Efficient Piecewise Higher-Order Parametrization
of Discrete Surfaces with Local and Global Injectivity.” Computer-Aided Design
127 (2020). https://doi.org/10.1016/j.cad.2020.102862.
ieee: 'M. Mandad and M. Campen, “Efficient piecewise higher-order parametrization
of discrete surfaces with local and global injectivity,” Computer-Aided Design,
vol. 127, Art. no. 102862, 2020, doi: 10.1016/j.cad.2020.102862.'
mla: Mandad, Manish, and Marcel Campen. “Efficient Piecewise Higher-Order Parametrization
of Discrete Surfaces with Local and Global Injectivity.” Computer-Aided Design,
vol. 127, 102862, Elsevier BV, 2020, doi:10.1016/j.cad.2020.102862.
short: M. Mandad, M. Campen, Computer-Aided Design 127 (2020).
date_created: 2025-06-26T06:50:22Z
date_updated: 2025-07-14T12:48:16Z
department:
- _id: '969'
doi: 10.1016/j.cad.2020.102862
extern: '1'
intvolume: ' 127'
language:
- iso: eng
publication: Computer-Aided Design
publication_identifier:
issn:
- 0010-4485
publication_status: published
publisher: Elsevier BV
status: public
title: Efficient piecewise higher-order parametrization of discrete surfaces with
local and global injectivity
type: journal_article
user_id: '117512'
volume: 127
year: '2020'
...
---
_id: '60388'
abstract:
- lang: eng
text: AbstractIn the field of global surface parametrization
a recent focus has been on so‐called seamless parametrization. This term refers
to parametrization approaches which, while using an atlas of charts to enable
the handling of surfaces of arbitrary topology, relate the parametrization across
the cuts between charts via transition functions from special classes of transformations.
This effectively makes the cuts invisible to applications which are invariant
to these specific transformations in some sense. In actual implementations of
these parametrization approaches, however, these restrictions are obeyed only
approximately; errors stem from the tolerances of numerical solvers employed and,
ultimately, from the limited accuracy of floating point arithmetic. In practice,
robustness issues arise from these flaws in the seamlessness of a parametrization,
no matter how small. We present a robust global algorithm that turns a given approximately
seamless parametrization into an exactly seamless one ‐ that still is representable
by standard floating point numbers. It supports common practically relevant additional
constraints regarding boundary and feature curve alignment or isocurve connectivity,
and ensures that these are likewise fulfilled exactly. This allows subsequent
algorithms to operate robustly on the resulting truly seamless parametrization.
We believe that the core of our method will furthermore be of benefit in a broader
range of applications involving linearly constrained numerical optimization.
author:
- first_name: Manish
full_name: Mandad, Manish
last_name: Mandad
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: Mandad M, Campen M. Exact Constraint Satisfaction for Truly Seamless Parametrization.
Computer Graphics Forum. 2019;38(2):135-145. doi:10.1111/cgf.13625
apa: Mandad, M., & Campen, M. (2019). Exact Constraint Satisfaction for Truly
Seamless Parametrization. Computer Graphics Forum, 38(2), 135–145.
https://doi.org/10.1111/cgf.13625
bibtex: '@article{Mandad_Campen_2019, title={Exact Constraint Satisfaction for Truly
Seamless Parametrization}, volume={38}, DOI={10.1111/cgf.13625},
number={2}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Mandad,
Manish and Campen, Marcel}, year={2019}, pages={135–145} }'
chicago: 'Mandad, Manish, and Marcel Campen. “Exact Constraint Satisfaction for
Truly Seamless Parametrization.” Computer Graphics Forum 38, no. 2 (2019):
135–45. https://doi.org/10.1111/cgf.13625.'
ieee: 'M. Mandad and M. Campen, “Exact Constraint Satisfaction for Truly Seamless
Parametrization,” Computer Graphics Forum, vol. 38, no. 2, pp. 135–145,
2019, doi: 10.1111/cgf.13625.'
mla: Mandad, Manish, and Marcel Campen. “Exact Constraint Satisfaction for Truly
Seamless Parametrization.” Computer Graphics Forum, vol. 38, no. 2, Wiley,
2019, pp. 135–45, doi:10.1111/cgf.13625.
short: M. Mandad, M. Campen, Computer Graphics Forum 38 (2019) 135–145.
date_created: 2025-06-26T07:35:31Z
date_updated: 2025-07-14T12:44:26Z
department:
- _id: '969'
doi: 10.1111/cgf.13625
extern: '1'
intvolume: ' 38'
issue: '2'
language:
- iso: eng
page: 135-145
publication: Computer Graphics Forum
publication_identifier:
issn:
- 0167-7055
- 1467-8659
publication_status: published
publisher: Wiley
status: public
title: Exact Constraint Satisfaction for Truly Seamless Parametrization
type: journal_article
user_id: '117512'
volume: 38
year: '2019'
...
---
_id: '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: '60448'
author:
- first_name: Isaak
full_name: Lim, Isaak
last_name: Lim
- first_name: Alexander
full_name: Dielen, Alexander
last_name: Dielen
- 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: 'Lim I, Dielen A, Campen M, Kobbelt L. A Simple Approach to Intrinsic Correspondence
Learning on Unstructured 3D Meshes. In: Leal-Taixé L, Roth S, eds. Computer
Vision - ECCV 2018 Workshops - Munich, Germany, September 8-14, 2018, Proceedings,
Part III. Vol 11131. Lecture Notes in Computer Science. Springer; 2018:349–362.
doi:10.1007/978-3-030-11015-4_26'
apa: Lim, I., Dielen, A., Campen, M., & Kobbelt, L. (2018). A Simple Approach
to Intrinsic Correspondence Learning on Unstructured 3D Meshes. In L. Leal-Taixé
& S. Roth (Eds.), Computer Vision - ECCV 2018 Workshops - Munich, Germany,
September 8-14, 2018, Proceedings, Part III (Vol. 11131, pp. 349–362). Springer.
https://doi.org/10.1007/978-3-030-11015-4_26
bibtex: '@inproceedings{Lim_Dielen_Campen_Kobbelt_2018, series={Lecture Notes in
Computer Science}, title={A Simple Approach to Intrinsic Correspondence Learning
on Unstructured 3D Meshes}, volume={11131}, DOI={10.1007/978-3-030-11015-4_26},
booktitle={Computer Vision - ECCV 2018 Workshops - Munich, Germany, September
8-14, 2018, Proceedings, Part III}, publisher={Springer}, author={Lim, Isaak and
Dielen, Alexander and Campen, Marcel and Kobbelt, Leif}, editor={Leal-Taixé, Laura
and Roth, Stefan}, year={2018}, pages={349–362}, collection={Lecture Notes in
Computer Science} }'
chicago: Lim, Isaak, Alexander Dielen, Marcel Campen, and Leif Kobbelt. “A Simple
Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes.” In Computer
Vision - ECCV 2018 Workshops - Munich, Germany, September 8-14, 2018, Proceedings,
Part III, edited by Laura Leal-Taixé and Stefan Roth, 11131:349–362. Lecture
Notes in Computer Science. Springer, 2018. https://doi.org/10.1007/978-3-030-11015-4_26.
ieee: 'I. Lim, A. Dielen, M. Campen, and L. Kobbelt, “A Simple Approach to Intrinsic
Correspondence Learning on Unstructured 3D Meshes,” in Computer Vision - ECCV
2018 Workshops - Munich, Germany, September 8-14, 2018, Proceedings, Part III,
2018, vol. 11131, pp. 349–362, doi: 10.1007/978-3-030-11015-4_26.'
mla: Lim, Isaak, et al. “A Simple Approach to Intrinsic Correspondence Learning
on Unstructured 3D Meshes.” Computer Vision - ECCV 2018 Workshops - Munich,
Germany, September 8-14, 2018, Proceedings, Part III, edited by Laura Leal-Taixé
and Stefan Roth, vol. 11131, Springer, 2018, pp. 349–362, doi:10.1007/978-3-030-11015-4_26.
short: 'I. Lim, A. Dielen, M. Campen, L. Kobbelt, in: L. Leal-Taixé, S. Roth (Eds.),
Computer Vision - ECCV 2018 Workshops - Munich, Germany, September 8-14, 2018,
Proceedings, Part III, Springer, 2018, pp. 349–362.'
date_created: 2025-06-27T10:30:34Z
date_updated: 2025-07-14T12:40:32Z
department:
- _id: '969'
doi: 10.1007/978-3-030-11015-4_26
editor:
- first_name: Laura
full_name: Leal-Taixé, Laura
last_name: Leal-Taixé
- first_name: Stefan
full_name: Roth, Stefan
last_name: Roth
extern: '1'
intvolume: ' 11131'
language:
- iso: eng
page: 349–362
publication: Computer Vision - ECCV 2018 Workshops - Munich, Germany, September 8-14,
2018, Proceedings, Part III
publisher: Springer
series_title: Lecture Notes in Computer Science
status: public
title: A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes
type: conference
user_id: '117512'
volume: 11131
year: '2018'
...
---
_id: '60391'
author:
- first_name: Jiaran
full_name: Zhou, Jiaran
last_name: Zhou
- 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
- first_name: Changhe
full_name: Tu, Changhe
last_name: Tu
- first_name: Claudio T.
full_name: Silva, Claudio T.
last_name: Silva
citation:
ama: Zhou J, Campen M, Zorin D, Tu C, Silva CT. Quadrangulation of non-rigid objects
using deformation metrics. Computer Aided Geometric Design. 2018;62:3-15.
doi:10.1016/j.cagd.2018.03.003
apa: Zhou, J., Campen, M., Zorin, D., Tu, C., & Silva, C. T. (2018). Quadrangulation
of non-rigid objects using deformation metrics. Computer Aided Geometric Design,
62, 3–15. https://doi.org/10.1016/j.cagd.2018.03.003
bibtex: '@article{Zhou_Campen_Zorin_Tu_Silva_2018, title={Quadrangulation of non-rigid
objects using deformation metrics}, volume={62}, DOI={10.1016/j.cagd.2018.03.003},
journal={Computer Aided Geometric Design}, publisher={Elsevier BV}, author={Zhou,
Jiaran and Campen, Marcel and Zorin, Denis and Tu, Changhe and Silva, Claudio
T.}, year={2018}, pages={3–15} }'
chicago: 'Zhou, Jiaran, Marcel Campen, Denis Zorin, Changhe Tu, and Claudio T. Silva.
“Quadrangulation of Non-Rigid Objects Using Deformation Metrics.” Computer
Aided Geometric Design 62 (2018): 3–15. https://doi.org/10.1016/j.cagd.2018.03.003.'
ieee: 'J. Zhou, M. Campen, D. Zorin, C. Tu, and C. T. Silva, “Quadrangulation of
non-rigid objects using deformation metrics,” Computer Aided Geometric Design,
vol. 62, pp. 3–15, 2018, doi: 10.1016/j.cagd.2018.03.003.'
mla: Zhou, Jiaran, et al. “Quadrangulation of Non-Rigid Objects Using Deformation
Metrics.” Computer Aided Geometric Design, vol. 62, Elsevier BV, 2018,
pp. 3–15, doi:10.1016/j.cagd.2018.03.003.
short: J. Zhou, M. Campen, D. Zorin, C. Tu, C.T. Silva, Computer Aided Geometric
Design 62 (2018) 3–15.
date_created: 2025-06-26T07:59:11Z
date_updated: 2025-07-14T12:44:44Z
department:
- _id: '969'
doi: 10.1016/j.cagd.2018.03.003
extern: '1'
intvolume: ' 62'
language:
- iso: eng
page: 3-15
publication: Computer Aided Geometric Design
publication_identifier:
issn:
- 0167-8396
publication_status: published
publisher: Elsevier BV
status: public
title: Quadrangulation of non-rigid objects using deformation metrics
type: journal_article
user_id: '117512'
volume: 62
year: '2018'
...
---
_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: '60398'
abstract:
- lang: eng
text: AbstractThe efficient and practical representation
and processing of geometrically or topologically complex shapes often demands
a partitioning into simpler patches. Possibilities range from unstructured arrangements
of arbitrarily shaped patches on the one end, to highly structured conforming
networks of all‐quadrilateral patches on the other end of the spectrum. Due to
its regularity, this latter extreme of conforming partitions with quadrilateral
patches, called quad layouts, is most beneficial in many application scenarios,
for instance enabling the use of tensor‐product representations based on splines
or Bézier patches, grid‐based multi‐resolution techniques and discrete pixel‐based
map representations. However, this type of partition is also most complicated
to create due to the strict inherent structural restrictions. Traditionally often
performed manually in a tedious and demanding process, research in computer graphics
and geometry processing has led to a number of computer‐assisted, semi‐automatic,
as well as fully automatic approaches to address this problem more efficiently.
This survey provides a detailed discussion of this range of methods, treats their
strengths and weaknesses and outlines open problems in this field of research.
author:
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: 'Campen M. Partitioning Surfaces Into Quadrilateral Patches: A Survey. Computer
Graphics Forum. 2017;36(8):567-588. doi:10.1111/cgf.13153'
apa: 'Campen, M. (2017). Partitioning Surfaces Into Quadrilateral Patches: A Survey.
Computer Graphics Forum, 36(8), 567–588. https://doi.org/10.1111/cgf.13153'
bibtex: '@article{Campen_2017, title={Partitioning Surfaces Into Quadrilateral Patches:
A Survey}, volume={36}, DOI={10.1111/cgf.13153},
number={8}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Campen,
Marcel}, year={2017}, pages={567–588} }'
chicago: 'Campen, Marcel. “Partitioning Surfaces Into Quadrilateral Patches: A Survey.”
Computer Graphics Forum 36, no. 8 (2017): 567–88. https://doi.org/10.1111/cgf.13153.'
ieee: 'M. Campen, “Partitioning Surfaces Into Quadrilateral Patches: A Survey,”
Computer Graphics Forum, vol. 36, no. 8, pp. 567–588, 2017, doi: 10.1111/cgf.13153.'
mla: 'Campen, Marcel. “Partitioning Surfaces Into Quadrilateral Patches: A Survey.”
Computer Graphics Forum, vol. 36, no. 8, Wiley, 2017, pp. 567–88, doi:10.1111/cgf.13153.'
short: M. Campen, Computer Graphics Forum 36 (2017) 567–588.
date_created: 2025-06-26T08:14:22Z
date_updated: 2025-07-14T12:42:33Z
department:
- _id: '969'
doi: 10.1111/cgf.13153
extern: '1'
intvolume: ' 36'
issue: '8'
language:
- iso: eng
page: 567-588
publication: Computer Graphics Forum
publication_identifier:
issn:
- 0167-7055
- 1467-8659
publication_status: published
publisher: Wiley
status: public
title: 'Partitioning Surfaces Into Quadrilateral Patches: A Survey'
type: journal_article
user_id: '117512'
volume: 36
year: '2017'
...
---
_id: '60406'
abstract:
- lang: eng
text: "An algorithm for the computation of global discrete conformal\r\nparametrizations
with prescribed global holonomy signatures for triangle meshes\r\nwas recently
described in [Campen and Zorin 2017]. In this paper we provide a\r\ndetailed analysis
of convergence and correctness of this algorithm. We\r\ngeneralize and extend
ideas of [Springborn et al. 2008] to show a connection of\r\nthe algorithm to
Newton's algorithm applied to solving the system of\r\nconstraints on angles in
the parametric domain, and demonstrate that this\r\nsystem can be obtained as
a gradient of a convex energy."
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. On Discrete Conformal Seamless Similarity Maps. arXiv:170502422.
Published online 2017.
apa: Campen, M., & Zorin, D. (2017). On Discrete Conformal Seamless Similarity
Maps. In arXiv:1705.02422.
bibtex: '@article{Campen_Zorin_2017, title={On Discrete Conformal Seamless Similarity
Maps}, journal={arXiv:1705.02422}, author={Campen, Marcel and Zorin, Denis}, year={2017}
}'
chicago: Campen, Marcel, and Denis Zorin. “On Discrete Conformal Seamless Similarity
Maps.” ArXiv:1705.02422, 2017.
ieee: M. Campen and D. Zorin, “On Discrete Conformal Seamless Similarity Maps,”
arXiv:1705.02422. 2017.
mla: Campen, Marcel, and Denis Zorin. “On Discrete Conformal Seamless Similarity
Maps.” ArXiv:1705.02422, 2017.
short: M. Campen, D. Zorin, ArXiv:1705.02422 (2017).
date_created: 2025-06-26T08:37:34Z
date_updated: 2025-07-14T12:42:13Z
department:
- _id: '969'
extern: '1'
external_id:
arxiv:
- '1705.02422'
language:
- iso: eng
publication: arXiv:1705.02422
status: public
title: On Discrete Conformal Seamless Similarity Maps
type: preprint
user_id: '117512'
year: '2017'
...
---
_id: '60397'
author:
- first_name: Marcel
full_name: Campen, Marcel
id: '114904'
last_name: Campen
orcid: 0000-0003-2340-3462
citation:
ama: 'Campen M. Tiling the Bunny: Quad Layouts for Efficient 3D Geometry Representation.
IEEE Computer Graphics and Applications. 2017;37(3):88-95. doi:10.1109/mcg.2017.35'
apa: 'Campen, M. (2017). Tiling the Bunny: Quad Layouts for Efficient 3D Geometry
Representation. IEEE Computer Graphics and Applications, 37(3),
88–95. https://doi.org/10.1109/mcg.2017.35'
bibtex: '@article{Campen_2017, title={Tiling the Bunny: Quad Layouts for Efficient
3D Geometry Representation}, volume={37}, DOI={10.1109/mcg.2017.35},
number={3}, journal={IEEE Computer Graphics and Applications}, publisher={Institute
of Electrical and Electronics Engineers (IEEE)}, author={Campen, Marcel}, year={2017},
pages={88–95} }'
chicago: 'Campen, Marcel. “Tiling the Bunny: Quad Layouts for Efficient 3D Geometry
Representation.” IEEE Computer Graphics and Applications 37, no. 3 (2017):
88–95. https://doi.org/10.1109/mcg.2017.35.'
ieee: 'M. Campen, “Tiling the Bunny: Quad Layouts for Efficient 3D Geometry Representation,”
IEEE Computer Graphics and Applications, vol. 37, no. 3, pp. 88–95, 2017,
doi: 10.1109/mcg.2017.35.'
mla: 'Campen, Marcel. “Tiling the Bunny: Quad Layouts for Efficient 3D Geometry
Representation.” IEEE Computer Graphics and Applications, vol. 37, no.
3, Institute of Electrical and Electronics Engineers (IEEE), 2017, pp. 88–95,
doi:10.1109/mcg.2017.35.'
short: M. Campen, IEEE Computer Graphics and Applications 37 (2017) 88–95.
date_created: 2025-06-26T08:12:08Z
date_updated: 2025-07-14T12:45:26Z
department:
- _id: '969'
doi: 10.1109/mcg.2017.35
extern: '1'
intvolume: ' 37'
issue: '3'
language:
- iso: eng
page: 88-95
publication: IEEE Computer Graphics and Applications
publication_identifier:
issn:
- 0272-1716
- 1558-1756
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: 'Tiling the Bunny: Quad Layouts for Efficient 3D Geometry Representation'
type: journal_article
user_id: '117512'
volume: 37
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'
...