---
OA_place: repository
OA_type: green
_id: '21737'
abstract:
- lang: eng
text: In calculus, l'Hopital's rule provides a simple way to evaluate the limits
of quotient functions when both the numerator and denominator vanish. But what
happens when we move beyond real functions on a real interval? In this article,
we study when the quotient of two complex-valued functions in higher dimension
can be defined continuously at the points where both functions vanish. Surprisingly,
the answer is far subtler than in the real-valued setting. We provide a complete
characterization for the continuity of the quotient function. We also point out
why extending this result to smoother quotients remains an intriguing challenge.
acknowledgement: "This project was funded in part by the European Research Council
(ERC Consolidator Grant 101045083 CoDiNA) and the National Science Foundation CAREER
Award 2239062.\r\n"
article_number: '2602.09958'
article_processing_charge: No
arxiv: 1
author:
- first_name: Albert
full_name: Chern, Albert
last_name: Chern
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
citation:
ama: Chern A, Ishida S. L’Hopital rules for complex-valued functions in higher dimensions.
arXiv. doi:10.48550/ARXIV.2602.09958
apa: Chern, A., & Ishida, S. (n.d.). L’Hopital rules for complex-valued functions
in higher dimensions. arXiv. https://doi.org/10.48550/ARXIV.2602.09958
chicago: Chern, Albert, and Sadashige Ishida. “L’Hopital Rules for Complex-Valued
Functions in Higher Dimensions.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2602.09958.
ieee: A. Chern and S. Ishida, “L’Hopital rules for complex-valued functions in higher
dimensions,” arXiv. .
ista: Chern A, Ishida S. L’Hopital rules for complex-valued functions in higher
dimensions. arXiv, 2602.09958.
mla: Chern, Albert, and Sadashige Ishida. “L’Hopital Rules for Complex-Valued Functions
in Higher Dimensions.” ArXiv, 2602.09958, doi:10.48550/ARXIV.2602.09958.
short: A. Chern, S. Ishida, ArXiv (n.d.).
corr_author: '1'
date_created: 2026-04-15T16:28:24Z
date_published: 2026-02-10T00:00:00Z
date_updated: 2026-04-28T10:56:30Z
day: '10'
ddc:
- '510'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/ARXIV.2602.09958
external_id:
arxiv:
- '2602.09958'
file:
- access_level: open_access
checksum: 6a76591c723d3e949ad5afa9f7dbb2ee
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creator: dernst
date_created: 2026-04-28T10:53:27Z
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file_size: 867109
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success: 1
file_date_updated: 2026-04-28T10:53:27Z
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keyword:
- l’Hopital theorem
- complex functions
language:
- iso: eng
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: arXiv
publication_status: submitted
status: public
title: L'Hopital rules for complex-valued functions in higher dimensions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21743'
abstract:
- lang: eng
text: We present symplectic structures on the shape space of unparameterized space
curves that generalize the classical Marsden–Weinstein structure. Our method integrates
the Liouville 1-form of the Marsden–Weinstein structure with Riemannian structures
that have been introduced in mathematical shape analysis. We also derive Hamiltonian
vector fields for several classical Hamiltonian functions with respect to these
new symplectic structures.
acknowledgement: The authors are grateful to Boris Khesin for valuable comments on
the MW symplectic structure and S. Ishida thanks Albert Chern for insightful discussions
on space curves and Chris Wojtan for his continuous support. M. Bauer was partially
supported by NSF grant DMS-1953244 and by the Binational Science Foundation (BSF).
S. Ishida was partially supported by ERC Consolidator Grant 101045083 “CoDiNA” funded
by the European Research Council. Some figures were generated by the software Houdini
and its education license was provided by SideFX. Open access funding provided by
University of Vienna.
article_number: '45'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Martin
full_name: Bauer, Martin
last_name: Bauer
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
- first_name: Peter W.
full_name: Michor, Peter W.
last_name: Michor
citation:
ama: Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves.
Journal of Nonlinear Science. 2026;36(2). doi:10.1007/s00332-026-10266-8
apa: Bauer, M., Ishida, S., & Michor, P. W. (2026). Symplectic structures on
the space of space curves. Journal of Nonlinear Science. Springer Nature.
https://doi.org/10.1007/s00332-026-10266-8
chicago: Bauer, Martin, Sadashige Ishida, and Peter W. Michor. “Symplectic Structures
on the Space of Space Curves.” Journal of Nonlinear Science. Springer Nature,
2026. https://doi.org/10.1007/s00332-026-10266-8.
ieee: M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space
of space curves,” Journal of Nonlinear Science, vol. 36, no. 2. Springer
Nature, 2026.
ista: Bauer M, Ishida S, Michor PW. 2026. Symplectic structures on the space of
space curves. Journal of Nonlinear Science. 36(2), 45.
mla: Bauer, Martin, et al. “Symplectic Structures on the Space of Space Curves.”
Journal of Nonlinear Science, vol. 36, no. 2, 45, Springer Nature, 2026,
doi:10.1007/s00332-026-10266-8.
short: M. Bauer, S. Ishida, P.W. Michor, Journal of Nonlinear Science 36 (2026).
date_created: 2026-04-16T07:29:17Z
date_published: 2026-04-15T00:00:00Z
date_updated: 2026-04-28T09:59:01Z
day: '15'
ddc:
- '510'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1007/s00332-026-10266-8
external_id:
arxiv:
- '2407.19908'
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oa: 1
oa_version: Published Version
project:
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grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Journal of Nonlinear Science
publication_identifier:
eissn:
- 1432-1467
issn:
- 0938-8974
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
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relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Symplectic structures on the space of space curves
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '21921'
abstract:
- lang: eng
text: "A variety of problems in geometry processing boil down to finding the most\r\nparallel
field relative to a connection. Instances of this prototypical problem\r\nshow
up in computing direction fields and stripe patterns, quadrilateral\r\nmeshing,
and visualization of fluid flows. When the class of allowed fields\r\nincludes
those with topological defects, a relaxation is required to make\r\nthe problem
well-posed. We observe that these problems can be viewed\r\nas synchronization
problems, which admit a natural semidefinite relaxation.\r\nWe propose a unified
method of solving all these problems via the efficient\r\nBurer-Monteiro factorization
method. Geometrically, this amounts to lifting the field values to a higher-dimensional
manifold, naturally resolving\r\nthe singular nature of defects. Practically,
we show that our convex relaxation method achieves better and more reliable optima
than previous work\r\nemploying alternative relaxations"
acknowledgement: "The authors thank Steven J. Gortler and Nicolas Boumal for interesting
discussions.\r\nDavid Palmer acknowledges the generous support of the NSF\r\nMSPRF
under award #2303403 during his time at Harvard University.\r\nNatalia Pacheco-Tallaj
was supported by the NSF DGE-2141064.\r\nMattéo Couplet was supported by Wallonie-Bruxelles
International"
article_processing_charge: No
author:
- first_name: Natalia
full_name: Pacheco-Tallaj, Natalia
last_name: Pacheco-Tallaj
- first_name: Matteo
full_name: Couplet, Matteo
last_name: Couplet
- first_name: Edward
full_name: Chien, Edward
last_name: Chien
- first_name: David
full_name: Palmer, David
id: 6574708f-2fd3-11f0-89e2-ae42ebc712a4
last_name: Palmer
orcid: 0000-0002-1931-5673
citation:
ama: 'Pacheco-Tallaj N, Couplet M, Chien E, Palmer D. Synchronizing fields with
singularities. In: SIGGRAPH Conference Papers. ACM. doi:10.1145/3799902.3811225'
apa: 'Pacheco-Tallaj, N., Couplet, M., Chien, E., & Palmer, D. (n.d.). Synchronizing
fields with singularities. In SIGGRAPH Conference Papers. Los Angeles,
CA, United States: ACM. https://doi.org/10.1145/3799902.3811225'
chicago: Pacheco-Tallaj, Natalia, Matteo Couplet, Edward Chien, and David Palmer.
“Synchronizing Fields with Singularities.” In SIGGRAPH Conference Papers.
ACM, n.d. https://doi.org/10.1145/3799902.3811225.
ieee: N. Pacheco-Tallaj, M. Couplet, E. Chien, and D. Palmer, “Synchronizing fields
with singularities,” in SIGGRAPH Conference Papers, Los Angeles, CA, United
States.
ista: 'Pacheco-Tallaj N, Couplet M, Chien E, Palmer D. Synchronizing fields with
singularities. SIGGRAPH Conference Papers. SIGGRAPH: International Conference
and Exhibition on Computer Graphics and Interactive Techniques.'
mla: Pacheco-Tallaj, Natalia, et al. “Synchronizing Fields with Singularities.”
SIGGRAPH Conference Papers, ACM, doi:10.1145/3799902.3811225.
short: N. Pacheco-Tallaj, M. Couplet, E. Chien, D. Palmer, in:, SIGGRAPH Conference
Papers, ACM, n.d.
conference:
end_date: 2026-07-23
location: Los Angeles, CA, United States
name: 'SIGGRAPH: International Conference and Exhibition on Computer Graphics and
Interactive Techniques'
start_date: 2026-07-19
corr_author: '1'
date_created: 2026-05-29T12:53:59Z
date_published: 2026-06-01T00:00:00Z
date_updated: 2026-06-02T06:26:52Z
day: '01'
ddc:
- '000'
department:
- _id: ChWo
doi: 10.1145/3799902.3811225
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month: '06'
oa: 1
oa_version: Accepted Version
publication: SIGGRAPH Conference Papers
publication_identifier:
eisbn:
- '9798400725548'
publication_status: accepted
publisher: ACM
quality_controlled: '1'
status: public
title: Synchronizing fields with singularities
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '21923'
abstract:
- lang: eng
text: "The appearance of simulated natural phenomena heavily depends on the way
surfaces are textured. However, applying texture maps to dynamic deformable surfaces
presents a significant challenge, due to ever-shifting differences in length scales
involved. When these surfaces move and advect the texture along with them, their
final appearance degrades as deformed regions dramatically distort their texture
map. Modifications to the texture directly at the pixel level in response to the
deformation may introduce ghosting artifacts and look unnatural. In the real world,
the appearance of surface details on a deforming material changes through the
interplay of physical processes such as rupturing, exposure of internal structure,
or wrinkling. Motivated by these behaviors, in this work we explore how physical
principles can guide the texturing methods based on the measure of surface deformation.\r\nWe
present two novel wave-based procedural texturing algorithms which reproduce common
physical properties like advection and self-similarity, enabling the plausible
animation of deforming objects with extreme texture map distortions. Our algorithms
are fully procedural, require no actual physics simulation, and store no state
or history of deformation besides the input UV map, making them highly parallelizable
on the GPU and efficient enough for real-time applications. We show the versatility
of the method by animating physical phenomena with extreme deformations such as
flowing lava, stretching putty and outpouring sludge."
acknowledged_ssus:
- _id: ScienComp
acknowledgement: "We thank the anonymous reviewers for their helpful comments, the
members of the Visual Computing Group at ISTA for their feedback. We also thank
Jonathan Gagnon for their help with running the Lapped Textures codes and SideFX
for the Houdini Education software licenses.\r\nImages in Fig. 2 by Kisoulou and
Vultured on Unsplash, Michal Jarmoluk and Public Domain Pictures from Pixabay and
Hawai‘i Volcanoes NPS on flickr. This research was supported by the Scientific Service
Units (SSU) of ISTA through resources provided by Scientific Computing and was funded
in part by the European Union (ERC-2021-COG 101045083 CoDiNA)."
article_number: '154'
article_processing_charge: Yes
article_type: original
author:
- first_name: Aleksei
full_name: Kalinov, Aleksei
id: 44b7120e-eb97-11eb-a6c2-e1557aa81d02
last_name: Kalinov
orcid: 0000-0003-2189-3904
- first_name: Mickaël
full_name: Ly, Mickaël
id: 6340d7f0-b48d-11eb-b10d-b7487e71d9f1
last_name: Ly
- first_name: Christian
full_name: Hafner, Christian
id: 400429CC-F248-11E8-B48F-1D18A9856A87
last_name: Hafner
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: Kalinov A, Ly M, Hafner C, Wojtan C. Physics-inspired procedural texturing
of extremely deformable surfaces. ACM Transactions on Graphics. 45(4).
doi:10.1145/3811353
apa: 'Kalinov, A., Ly, M., Hafner, C., & Wojtan, C. (n.d.). Physics-inspired
procedural texturing of extremely deformable surfaces. ACM Transactions on
Graphics. Los Angeles, CA, United States: ACM. https://doi.org/10.1145/3811353'
chicago: Kalinov, Aleksei, Mickaël Ly, Christian Hafner, and Chris Wojtan. “Physics-Inspired
Procedural Texturing of Extremely Deformable Surfaces.” ACM Transactions on
Graphics. ACM, n.d. https://doi.org/10.1145/3811353.
ieee: A. Kalinov, M. Ly, C. Hafner, and C. Wojtan, “Physics-inspired procedural
texturing of extremely deformable surfaces,” ACM Transactions on Graphics,
vol. 45, no. 4. ACM.
ista: Kalinov A, Ly M, Hafner C, Wojtan C. Physics-inspired procedural texturing
of extremely deformable surfaces. ACM Transactions on Graphics. 45(4), 154.
mla: Kalinov, Aleksei, et al. “Physics-Inspired Procedural Texturing of Extremely
Deformable Surfaces.” ACM Transactions on Graphics, vol. 45, no. 4, 154,
ACM, doi:10.1145/3811353.
short: A. Kalinov, M. Ly, C. Hafner, C. Wojtan, ACM Transactions on Graphics 45
(n.d.).
conference:
end_date: 2026-07-23
location: Los Angeles, CA, United States
name: 'SIGGRAPH: International Conference and Exhibition on Computer Graphics and
Interactive Techniques'
start_date: 2026-07-19
corr_author: '1'
date_created: 2026-05-29T13:25:16Z
date_published: 2026-07-01T00:00:00Z
date_updated: 2026-06-02T08:56:50Z
day: '01'
ddc:
- '006'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1145/3811353
file:
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checksum: ea165bf731ddd3045f83878dcb833672
content_type: video/mp4
creator: akalinov
date_created: 2026-05-29T13:19:33Z
date_updated: 2026-05-29T13:19:33Z
file_id: '21924'
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content_type: video/mp4
creator: akalinov
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has_accepted_license: '1'
intvolume: ' 45'
issue: '4'
keyword:
- Procedural animation
language:
- iso: eng
month: '07'
oa: 1
oa_version: Accepted Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: ACM Transactions on Graphics
publication_identifier:
issn:
- 0730-0301
publication_status: inpress
publisher: ACM
quality_controlled: '1'
status: public
title: Physics-inspired procedural texturing of extremely deformable surfaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2026'
...
---
OA_place: publisher
_id: '19630'
abstract:
- lang: eng
text: "This thesis consists of three chapters, each corresponding to one publication.
While each of these projects tackles a topic in a different area of research,
they all share a common thread in the type of topological structure they handle
- a partition of space into volumes separated by interfaces that meet in non-manifold
junctions.\r\n\r\nIn Chapter 2, we study clusters of soap bubbles from a simulation
perspective. In particular, we develop a surface-only algorithm that couples large
scale motion and shape deformation of soap bubble clusters with the small scale
evolution of the thin film's thickness, which is responsible for visual phenomena
like surface vortices, Newton's interference patterns, capillary waves, and deformation-dependent
rupturing of films in a foam. We model film thickness as a reduced degree of freedom
in the Navier-Stokes equations and from them derive three sets of equations governing
normal and tangential motion of the soap film surface, as well as the evolution
of the thin film thickness. We discretize these equations on a non-manifold triangle
mesh, extending and adapting operators to handle complex topology. We also present
an incompressible fluid solver for 2.5D films and an advection algorithm for convecting
fields across non-manifold surface junctions. Our simulations enhance bubble solvers
with additional effects caused by convection, rippling, draining, and evaporation
of the thin film.\r\n\r\nIn Chapter 3, we introduce a multi-material non-manifold
mesh-based surface tracking algorithm that converts mesh defects, such as overlaps,
self-intersections, and inversions into topological changes. Our algorithm generalizes
prior work on manifold surface tracking with topological changes: it preserves
surface features like mesh-based methods, and it robustly handles topological
changes like level set methods. Our method also offers improved efficiency and
robustness over the state of the art. We demonstrate the effectiveness of the
approach on a range of examples, including complex soap film simulations, such
as those presented in Chapter 2, but with an order of magnitude more interacting
bubbles than what we could achieve before, and Boolean unions of non-manifold
meshes consisting of millions of triangles.\r\n\r\nLastly, in Chapter 4, we utilize
developments in the theory of random geometric complexes facilitated by observations
from Discrete Morse theory. We survey the methods and results obtained with this
new approach, and discuss some of its shortcomings. We use simulations to illustrate
the results and to form conjectures, getting numerical estimates for combinatorial,
topological, and geometric properties of weighted and unweighted Delaunay mosaics,
their dual Voronoi tessellations, and the Alpha and Wrap complexes contained in
the mosaics."
acknowledged_ssus:
- _id: ScienComp
acknowledgement: The project in Chapter 2 has received funding from the European Research
Council (ERC) under the European Union's Horizon 2020 research and innovation programme
under grant agreement No. 638176. The project in Chapter 3 was funded in part by
the European Union (ERC-2021-COG 101045083 CoDiNA). The project in Chapter 4 has
received funding from the European Research Council (ERC) under the European Union's
Horizon 2020 research and innovation programme (grant agreements No 78818 Alpha
and No 638176). It was also partially supported by the DFG Collaborative Research
Center TRR 109, 'Discretization in Geometry and Dynamics', through grant no. I02979-N35
of the Austrian Science Fund (FWF). Thank you for providing funds to support my
work.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Peter
full_name: Synak, Peter
id: 331776E2-F248-11E8-B48F-1D18A9856A87
last_name: Synak
citation:
ama: Synak P. Methods for fluid simulation, surface tracking, and statistics of
non-manifold structures. 2025. doi:10.15479/AT-ISTA-19630
apa: Synak, P. (2025). Methods for fluid simulation, surface tracking, and statistics
of non-manifold structures. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-19630
chicago: Synak, Peter. “Methods for Fluid Simulation, Surface Tracking, and Statistics
of Non-Manifold Structures.” Institute of Science and Technology Austria, 2025.
https://doi.org/10.15479/AT-ISTA-19630.
ieee: P. Synak, “Methods for fluid simulation, surface tracking, and statistics
of non-manifold structures,” Institute of Science and Technology Austria, 2025.
ista: Synak P. 2025. Methods for fluid simulation, surface tracking, and statistics
of non-manifold structures. Institute of Science and Technology Austria.
mla: Synak, Peter. Methods for Fluid Simulation, Surface Tracking, and Statistics
of Non-Manifold Structures. Institute of Science and Technology Austria, 2025,
doi:10.15479/AT-ISTA-19630.
short: P. Synak, Methods for Fluid Simulation, Surface Tracking, and Statistics
of Non-Manifold Structures, Institute of Science and Technology Austria, 2025.
corr_author: '1'
date_created: 2025-04-29T09:39:34Z
date_published: 2025-04-29T00:00:00Z
date_updated: 2026-04-16T08:29:34Z
day: '29'
ddc:
- '519'
- '006'
degree_awarded: PhD
department:
- _id: ChWo
- _id: GradSch
doi: 10.15479/AT-ISTA-19630
ec_funded: 1
file:
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call_identifier: H2020
grant_number: '638176'
name: 'Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large
Scales'
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
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call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
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publisher: Institute of Science and Technology Austria
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orcid: 0000-0001-6646-5546
title: Methods for fluid simulation, surface tracking, and statistics of non-manifold
structures
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...
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abstract:
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text: "The space of codimension-2 shapes, such as curves in 3D and surfaces in 4D,
is an infinite-dimensional manifold. This thesis explores geometric structures
and dynamics on this space, with emphasis on their implications for physics, particularly
hydrodynamics.\r\n\r\nOur investigation ranges from theoretical studies of infinite-dimensional
symplectic and prequantum geometry to numerical computation of the time evolution
of shapes. The thesis presents four main contributions.\r\n\r\nIn the first part,
we introduce implicit representations of codimension-2 shapes using a class of
complex-valued functions, and prove that the space of these implicit representations
forms a prequantum bundle over the codimension-2 shape space. This reveals a new
geometric interpretation of the canonical symplectic structure on the codimension-2
shape space.\r\n\r\nIn the second part, we use implicit representations to develop
a simulation method for the dynamics of space curves. To handle chaotic systems
such as vortex filaments in hydrodynamics, we exploit the infinite degrees of
freedom, hidden in both the configuration and dynamics of implicit representations.\r\n\r\nIn
the third part, we introduce new symplectic structures on the space of space curves,
which generalize the only previously known symplectic structure on this space,
allowing for new Hamiltonian dynamics of space curves.\r\n\r\nIn the fourth part,
we apply a symplectic viewpoint to a differential geometric problem with practical
applications. We derive a new area formula for spherical polygons via prequantization. "
acknowledged_ssus:
- _id: CampIT
acknowledgement: "Projects contained in this thesis were financially supported in
part by the\r\nEuropean Research Council with grants 1. ERC Consolidator Grant 101045083
CoDiNA,\r\nand 2. the European Union’s Horizon 2020 research and innovation programme
under grant\r\nagreement No. 638176."
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id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
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orcid: 0000-0002-3121-3100
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ama: Ishida S. Symplectic-prequantum structures and dynamics on the codimension-2
shape space. 2025. doi:10.15479/AT-ISTA-20551
apa: Ishida, S. (2025). Symplectic-prequantum structures and dynamics on the
codimension-2 shape space. Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-20551
chicago: Ishida, Sadashige. “Symplectic-Prequantum Structures and Dynamics on the
Codimension-2 Shape Space.” Institute of Science and Technology Austria, 2025.
https://doi.org/10.15479/AT-ISTA-20551.
ieee: S. Ishida, “Symplectic-prequantum structures and dynamics on the codimension-2
shape space,” Institute of Science and Technology Austria, 2025.
ista: Ishida S. 2025. Symplectic-prequantum structures and dynamics on the codimension-2
shape space. Institute of Science and Technology Austria.
mla: Ishida, Sadashige. Symplectic-Prequantum Structures and Dynamics on the
Codimension-2 Shape Space. Institute of Science and Technology Austria, 2025,
doi:10.15479/AT-ISTA-20551.
short: S. Ishida, Symplectic-Prequantum Structures and Dynamics on the Codimension-2
Shape Space, Institute of Science and Technology Austria, 2025.
corr_author: '1'
date_created: 2025-10-27T10:28:52Z
date_published: 2025-10-31T00:00:00Z
date_updated: 2026-04-07T12:02:23Z
day: '31'
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degree_awarded: PhD
department:
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- _id: ChWo
doi: 10.15479/AT-ISTA-20551
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call_identifier: H2020
grant_number: '638176'
name: 'Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large
Scales'
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication_identifier:
isbn:
- 978-3-99078-070-1
issn:
- 2663-337X
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publisher: Institute of Science and Technology Austria
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full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
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- first_name: Albert
full_name: Chern, Albert
last_name: Chern
title: Symplectic-prequantum structures and dynamics on the codimension-2 shape space
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abstract:
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text: This paper explores the geometry of the space of codimension-2 submanifolds.
We implicitly represent these submanifolds by a class of complex-valued functions.
This reveals a prequantum bundle structure over the space of submanifolds, equipped
with the well-known Marsden-Weinstein symplectic structure. This bundle allows
a new physical interpretation of the Marsden-Weinstein structure as the curvature
of a connection form, which measures the average of volumes swept by the deformation
of the S^1-family of hypersurfaces, defined as the phases of a complex function
implicitly representing a submanifold.
article_processing_charge: No
arxiv: 1
author:
- first_name: Albert
full_name: Chern, Albert
last_name: Chern
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
citation:
ama: Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and
their prequantum structure. arXiv. doi:10.48550/ARXIV.2507.11727
apa: Chern, A., & Ishida, S. (n.d.). Implicit representations of codimension-2
submanifolds and their prequantum structure. arXiv. https://doi.org/10.48550/ARXIV.2507.11727
chicago: Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2
Submanifolds and Their Prequantum Structure.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2507.11727.
ieee: A. Chern and S. Ishida, “Implicit representations of codimension-2 submanifolds
and their prequantum structure,” arXiv. .
ista: Chern A, Ishida S. Implicit representations of codimension-2 submanifolds
and their prequantum structure. arXiv, 10.48550/ARXIV.2507.11727.
mla: Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2
Submanifolds and Their Prequantum Structure.” ArXiv, doi:10.48550/ARXIV.2507.11727.
short: A. Chern, S. Ishida, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-30T18:36:56Z
date_published: 2025-07-15T00:00:00Z
date_updated: 2026-04-07T12:02:23Z
day: '15'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/ARXIV.2507.11727
external_id:
arxiv:
- '2507.11727'
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month: '07'
oa: 1
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publication: arXiv
publication_status: draft
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status: public
title: Implicit representations of codimension-2 submanifolds and their prequantum
structure
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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short: CC BY (4.0)
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '20628'
abstract:
- lang: eng
text: "The realistic simulation of sand, soil, powders, rubble piles, and large
collections of rigid bodies is a common and important problem in the fields of
computer graphics, computational physics, and engineering. Direct simulation of
these individual bodies quickly becomes expensive, so we often approximate the
entire group as a continuum material that can be more easily computed using tools
for solving partial differential equations, like the material point method (MPM).
In this paper, we present a method for automatically extracting continuum material
properties from a collection of rigid\r\nbodies. We use numerical homogenization
with periodic boundary conditions to simulate an effectively infinite number of
rigid bodies in contact. We then record the effective stress-strain relationships
from these simulations and convert them into elastic properties and yield criteria
for the continuum simulations. Our experiments validate existing theoretical models
like the Mohr-Coulomb yield surface by extracting material behaviors from a collection
of spheres in contact. We further generalize these existing models to more exotic
materials derived from diverse and non-convex shapes. We\r\nobserve complicated
jamming behaviors from non-convex grains, and we introduce a new material model
for materials with extremely high levels of internal friction and cohesion. We
simulate these new continuum models using MPM with an improved return mapping
technique. The end result is a complete system for turning an input rigid body
simulation into an efficient continuum simulation with the same effective mechanical
properties."
acknowledgement: 'We thank the anonymous reviewers for their helpful comments, the
members of the Visual Computing Group at ISTA for their feedback and Gauthier Rousseau
for the insightful discussions. This research was supported by the Scientific Service
Units (SSU) of ISTA through resources provided by Scientific Computing and was funded
in part by the European Union (ERC-2021-COG 101045083 CoDiNA). '
article_number: '220'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Yi-Lu
full_name: Chen, Yi-Lu
id: 0b467602-dbcd-11ea-9d1d-ed480aa46b70
last_name: Chen
orcid: 0009-0005-0723-0655
- first_name: Mickaël
full_name: Ly, Mickaël
id: 6340d7f0-b48d-11eb-b10d-b7487e71d9f1
last_name: Ly
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: Chen Y-L, Ly M, Wojtan C. Numerical homogenization of sand from grain-level
simulations. ACM Transactions on Graphics. 2025;44(6). doi:10.1145/3763344
apa: 'Chen, Y.-L., Ly, M., & Wojtan, C. (2025). Numerical homogenization of
sand from grain-level simulations. ACM Transactions on Graphics. Hong Kong,
China: Association for Computing Machinery. https://doi.org/10.1145/3763344'
chicago: Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Numerical Homogenization of
Sand from Grain-Level Simulations.” ACM Transactions on Graphics. Association
for Computing Machinery, 2025. https://doi.org/10.1145/3763344.
ieee: Y.-L. Chen, M. Ly, and C. Wojtan, “Numerical homogenization of sand from grain-level
simulations,” ACM Transactions on Graphics, vol. 44, no. 6. Association
for Computing Machinery, 2025.
ista: Chen Y-L, Ly M, Wojtan C. 2025. Numerical homogenization of sand from grain-level
simulations. ACM Transactions on Graphics. 44(6), 220.
mla: Chen, Yi-Lu, et al. “Numerical Homogenization of Sand from Grain-Level Simulations.”
ACM Transactions on Graphics, vol. 44, no. 6, 220, Association for Computing
Machinery, 2025, doi:10.1145/3763344.
short: Y.-L. Chen, M. Ly, C. Wojtan, ACM Transactions on Graphics 44 (2025).
conference:
end_date: 2025-12-18
location: Hong Kong, China
name: 'SIGGRAPH Asia: Conference and Exhibition on Computer Graphics and Interactive
Techniques in Asia'
start_date: 2025-12-15
corr_author: '1'
date_created: 2025-11-10T14:12:06Z
date_published: 2025-12-04T00:00:00Z
date_updated: 2025-12-09T14:53:32Z
day: '04'
ddc:
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- '006'
- '621'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1145/3763344
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issue: '6'
language:
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month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Numerical homogenization of sand from grain-level simulations
tmp:
image: /image/cc_by_nd.png
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name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
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...
---
OA_place: publisher
_id: '18301'
abstract:
- lang: eng
text: Physics simulation in computer graphics can bring triangle meshes into topologically
invalid states. The method in this thesis contributed to Heiss-Synak* and Kalinov*
et al. [2024] who devised a non-manifold hybrid surface tracker—a surface tracker
that repairs explicit non-manifold triangle meshes with the help of the implicit
domain. Specifically, this thesis provides an algorithm for filling the holes
that are left after removing problematic parts of the mesh.
alternative_title:
- ISTA Master's Thesis
article_processing_charge: No
author:
- first_name: Arian
full_name: Etemadihaghighi, Arian
id: 36cea3aa-f38e-11ec-8ae0-c65ae6f6098f
last_name: Etemadihaghighi
citation:
ama: Etemadi A. Filling the holes of non-manifold self-intersecting meshes for implicit
topology changes in surface tracking. 2024. doi:10.15479/at:ista:18301
apa: Etemadi, A. (2024). Filling the holes of non-manifold self-intersecting
meshes for implicit topology changes in surface tracking. Institute of Science
and Technology Austria. https://doi.org/10.15479/at:ista:18301
chicago: Etemadi, Arian. “Filling the Holes of Non-Manifold Self-Intersecting Meshes
for Implicit Topology Changes in Surface Tracking.” Institute of Science and Technology
Austria, 2024. https://doi.org/10.15479/at:ista:18301.
ieee: A. Etemadi, “Filling the holes of non-manifold self-intersecting meshes for
implicit topology changes in surface tracking,” Institute of Science and Technology
Austria, 2024.
ista: Etemadi A. 2024. Filling the holes of non-manifold self-intersecting meshes
for implicit topology changes in surface tracking. Institute of Science and Technology
Austria.
mla: Etemadi, Arian. Filling the Holes of Non-Manifold Self-Intersecting Meshes
for Implicit Topology Changes in Surface Tracking. Institute of Science and
Technology Austria, 2024, doi:10.15479/at:ista:18301.
short: A. Etemadi, Filling the Holes of Non-Manifold Self-Intersecting Meshes for
Implicit Topology Changes in Surface Tracking, Institute of Science and Technology
Austria, 2024.
corr_author: '1'
date_created: 2024-10-11T19:52:20Z
date_published: 2024-10-15T00:00:00Z
date_updated: 2026-04-07T13:02:36Z
day: '15'
ddc:
- '000'
degree_awarded: MS
department:
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doi: 10.15479/at:ista:18301
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relation: source_file
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keyword:
- surface tracking
- non-manifold
- hole-filling
- topology change
- multi-material
- solid-modeling
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: '39'
publication_identifier:
issn:
- 2791-4585
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '17219'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
title: Filling the holes of non-manifold self-intersecting meshes for implicit topology
changes in surface tracking
tmp:
image: /images/cc_by_sa.png
legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode
name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC
BY-SA 4.0)
short: CC BY-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14703'
abstract:
- lang: eng
text: We present a discretization of the dynamic optimal transport problem for which
we can obtain the convergence rate for the value of the transport cost to its
continuous value when the temporal and spatial stepsize vanish. This convergence
result does not require any regularity assumption on the measures, though experiments
suggest that the rate is not sharp. Via an analysis of the duality gap we also
obtain the convergence rates for the gradient of the optimal potentials and the
velocity field under mild regularity assumptions. To obtain such rates we discretize
the dual formulation of the dynamic optimal transport problem and use the mature
literature related to the error due to discretizing the Hamilton-Jacobi equation.
acknowledgement: 'The authors would like to thank Chris Wojtan for his continuous
support and several interesting discussions. Part of this research was performed
during two visits: one of SI to the BIDSA research center at Bocconi University,
and one of HL to the Institute of Science and Technology Austria. Both host institutions
are warmly acknowledged for the hospitality. HL is partially supported by the MUR-Prin
2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with Applications
to Optimization and Machine Learning”, funded by the European Union - Next Generation
EU. SI is supported in part by ERC Consolidator Grant 101045083 “CoDiNA” funded
by the European Research Council.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
- first_name: Hugo
full_name: Lavenant, Hugo
last_name: Lavenant
citation:
ama: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. Foundations of Computational
Mathematics. 2024. doi:10.1007/s10208-024-09686-3
apa: Ishida, S., & Lavenant, H. (2024). Quantitative convergence of a discretization
of dynamic optimal transport using the dual formulation. Foundations of Computational
Mathematics. Springer Nature. https://doi.org/10.1007/s10208-024-09686-3
chicago: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” Foundations of Computational
Mathematics. Springer Nature, 2024. https://doi.org/10.1007/s10208-024-09686-3.
ieee: S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation,” Foundations of Computational
Mathematics. Springer Nature, 2024.
ista: Ishida S, Lavenant H. 2024. Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation. Foundations of Computational
Mathematics.
mla: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” Foundations of Computational
Mathematics, Springer Nature, 2024, doi:10.1007/s10208-024-09686-3.
short: S. Ishida, H. Lavenant, Foundations of Computational Mathematics (2024).
corr_author: '1'
date_created: 2023-12-21T10:14:37Z
date_published: 2024-11-11T00:00:00Z
date_updated: 2026-06-18T17:37:10Z
day: '11'
ddc:
- '000'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1007/s10208-024-09686-3
external_id:
arxiv:
- '2312.12213'
isi:
- '001352503300001'
isi: 1
keyword:
- Optimal transport
- Hamilton-Jacobi equation
- convex optimization
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10208-024-09686-3
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative convergence of a discretization of dynamic optimal transport using
the dual formulation
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '12846'
abstract:
- lang: eng
text: We present a formula for the signed area of a spherical polygon via prequantization.
In contrast to the traditional formula based on the Gauss-Bonnet theorem that
requires measuring angles, the new formula mimics Green's theorem and is applicable
to a wider range of degenerate spherical curves and polygons.
acknowledgement: This work was funded by European Research Council Consolidator grant
101045083 CoDiNA and National Science Foundation CAREER award 2239062. Some figures
in the article were generated by the software Houdini and its education license
was provided by SideFX. The authors acknowledge anonymous referees for their reviews
and insightful suggestions, and Chris Wojtan for his continuous support through
discussions. The second author thanks Anna Sisak for a fruitful discussion on prequantum
bundles.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Albert
full_name: Chern, Albert
last_name: Chern
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
citation:
ama: Chern A, Ishida S. Area formula for spherical polygons via prequantization.
SIAM Journal on Applied Algebra and Geometry. 2024;8(3):782-796. doi:10.1137/23M1565255
apa: Chern, A., & Ishida, S. (2024). Area formula for spherical polygons via
prequantization. SIAM Journal on Applied Algebra and Geometry. Society
for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1565255
chicago: Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons
via Prequantization.” SIAM Journal on Applied Algebra and Geometry. Society
for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1565255.
ieee: A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,”
SIAM Journal on Applied Algebra and Geometry, vol. 8, no. 3. Society for
Industrial and Applied Mathematics, pp. 782–796, 2024.
ista: Chern A, Ishida S. 2024. Area formula for spherical polygons via prequantization.
SIAM Journal on Applied Algebra and Geometry. 8(3), 782–796.
mla: Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via
Prequantization.” SIAM Journal on Applied Algebra and Geometry, vol. 8,
no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 782–96, doi:10.1137/23M1565255.
short: A. Chern, S. Ishida, SIAM Journal on Applied Algebra and Geometry 8 (2024)
782–796.
corr_author: '1'
date_created: 2023-04-18T19:16:06Z
date_published: 2024-09-23T00:00:00Z
date_updated: 2026-04-07T12:02:22Z
day: '23'
ddc:
- '516'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1137/23M1565255
external_id:
arxiv:
- '2303.14555'
isi:
- '001342265800009'
has_accepted_license: '1'
intvolume: ' 8'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2303.14555
month: '09'
oa: 1
oa_version: Preprint
page: 782-796
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: SIAM Journal on Applied Algebra and Geometry
publication_identifier:
eissn:
- 2470-6566
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
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relation: dissertation_contains
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scopus_import: '1'
status: public
title: Area formula for spherical polygons via prequantization
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2024'
...
---
_id: '17203'
abstract:
- lang: eng
text: "The behavior of a rigid body primarily depends on its mass moments, which
consist of the mass, center of mass, and moments of inertia. It is possible to
manipulate these quantities without altering the geometric appearance of an object
by introducing cavities in its interior. Algorithms that find cavities of suitable
shapes and sizes have enabled the computational design of spinning tops, yo-yos,
wheels, buoys, and statically balanced objects. Previous work is based, for example,
on topology optimization on voxel grids, which introduces a large number of optimization
variables and box constraints, or offset surface computation, which cannot guarantee
that solutions to a feasible problem will always be found.\r\n\r\nIn this work,
we provide a mathematical analysis of constrained topology optimization problems
that depend only on mass moments. This class of problems covers, among others,
all applications mentioned above. Our main result is to show that no matter the
outer shape of the rigid body to be optimized or the optimization objective and
constraints considered, the optimal solution always features a quadric-shaped
interface between material and cavities. This proves that optimal interfaces are
always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases,
such as planes.\r\n\r\nThis insight lets us replace a difficult topology optimization
problem with a provably equivalent non-linear equation system in a small number
(<10) of variables, which represent the coefficients of the quadric. This system
can be solved in a few seconds for most examples, provides insights into the geometric
structure of many specific applications, and lets us describe their solution properties.
Finally, our method integrates seamlessly into modern fabrication workflows because
our solutions are analytical surfaces that are native to the CAD domain."
acknowledgement: We thank Gianmarco Cherchi for his help in tailoring the Mesh Booleans
code for this project, Stefan Jeschke for his help with the photographs, Malina
Strugaru and Aleksei Kalinov for their help with the samples, and the anonymous
reviewers as well as the members of the ISTA Visual Computing Group for their feedback.
This project was funded in part by the European Research Council (ERC Consolidator
Grant 101045083 CoDiNA).
article_number: '78'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Christian
full_name: Hafner, Christian
id: 400429CC-F248-11E8-B48F-1D18A9856A87
last_name: Hafner
- first_name: Mickaël
full_name: Ly, Mickaël
id: 6340d7f0-b48d-11eb-b10d-b7487e71d9f1
last_name: Ly
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: 'Hafner C, Ly M, Wojtan C. Spin-it faster: Quadrics solve all topology optimization
problems that depend only on mass moments. Transactions on Graphics. 2024;43(4).
doi:10.1145/3658194'
apa: 'Hafner, C., Ly, M., & Wojtan, C. (2024). Spin-it faster: Quadrics solve
all topology optimization problems that depend only on mass moments. Transactions
on Graphics. Denver, Colorado: Association for Computing Machinery. https://doi.org/10.1145/3658194'
chicago: 'Hafner, Christian, Mickaël Ly, and Chris Wojtan. “Spin-It Faster: Quadrics
Solve All Topology Optimization Problems That Depend Only on Mass Moments.” Transactions
on Graphics. Association for Computing Machinery, 2024. https://doi.org/10.1145/3658194.'
ieee: 'C. Hafner, M. Ly, and C. Wojtan, “Spin-it faster: Quadrics solve all topology
optimization problems that depend only on mass moments,” Transactions on Graphics,
vol. 43, no. 4. Association for Computing Machinery, 2024.'
ista: 'Hafner C, Ly M, Wojtan C. 2024. Spin-it faster: Quadrics solve all topology
optimization problems that depend only on mass moments. Transactions on Graphics.
43(4), 78.'
mla: 'Hafner, Christian, et al. “Spin-It Faster: Quadrics Solve All Topology Optimization
Problems That Depend Only on Mass Moments.” Transactions on Graphics, vol.
43, no. 4, 78, Association for Computing Machinery, 2024, doi:10.1145/3658194.'
short: C. Hafner, M. Ly, C. Wojtan, Transactions on Graphics 43 (2024).
conference:
end_date: 2024-08-01
location: Denver, Colorado
start_date: 2024-07-28
corr_author: '1'
date_created: 2024-07-05T12:08:57Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-08T08:29:09Z
day: '01'
ddc:
- '516'
department:
- _id: ChWo
doi: 10.1145/3658194
external_id:
isi:
- '001289270900045'
file:
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checksum: 0dc9f5a6422b8a49a79026900f349ee5
content_type: application/pdf
creator: chafner
date_created: 2024-07-05T12:05:17Z
date_updated: 2024-07-05T12:05:17Z
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file_size: 7225150
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file_id: '17205'
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content_type: video/mp4
creator: chafner
date_created: 2024-07-17T09:29:13Z
date_updated: 2024-07-17T09:29:13Z
file_id: '17276'
file_name: sif-video-final.mp4
file_size: 170001305
relation: supplementary_material
title: Submission Video
file_date_updated: 2024-07-17T09:29:13Z
has_accepted_license: '1'
intvolume: ' 43'
isi: 1
issue: '4'
keyword:
- Topology Optimization
- Mass Moments
- Computational Geometry
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Spin-it faster: Quadrics solve all topology optimization problems that depend
only on mass moments'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 43
year: '2024'
...
---
_id: '17214'
abstract:
- lang: eng
text: 'Current numerical algorithms for simulating friction fall in one of two camps:
smooth solvers sacrifice the stable treatment of static friction in exchange for
fast convergence, and non-smooth solvers accurately compute friction at convergence
rates that are often prohibitive for large graphics applications. We introduce
a novel bridge between these two ideas that computes static and dynamic friction
stably and efficiently. Our key idea is to convert the highly constrained non-smooth
problem into an unconstrained smooth problem using logarithmic barriers that converges
to the exact solution as accuracy increases. We phrase the problem as an interior
point primal-dual problem that can be solved efficiently with Newton iteration.
We observe quadratic convergence despite the non-smooth nature of the original
problem, and our method is well-suited for large systems of tightly packed objects
with many contact points. We demonstrate the efficacy of our method with stable
piles of grains and stacks of objects, complex granular flows, and robust interlocking
assemblies of rigid bodies.'
acknowledgement: We thank Vincent Acary for his help with Siconos, as well as the
anonymous reviewers and the members of the Visual Computing Group at ISTA for their
helpful comments. This research was funded in part by the European Union (ERC-2021-COG
101045083 CoDiNA).
article_processing_charge: Yes (via OA deal)
author:
- first_name: Yi-Lu
full_name: Chen, Yi-Lu
id: 0b467602-dbcd-11ea-9d1d-ed480aa46b70
last_name: Chen
- first_name: Mickaël
full_name: Ly, Mickaël
id: 6340d7f0-b48d-11eb-b10d-b7487e71d9f1
last_name: Ly
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: 'Chen Y-L, Ly M, Wojtan C. Primal-dual non-smooth friction for rigid body animation.
In: Special Interest Group on Computer Graphics and Interactive Techniques
Conference Conference Papers ’24. Association for Computing Machinery; 2024.
doi:10.1145/3641519.3657485'
apa: 'Chen, Y.-L., Ly, M., & Wojtan, C. (2024). Primal-dual non-smooth friction
for rigid body animation. In Special Interest Group on Computer Graphics and
Interactive Techniques Conference Conference Papers ’24. Denver, United States:
Association for Computing Machinery. https://doi.org/10.1145/3641519.3657485'
chicago: Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Primal-Dual Non-Smooth Friction
for Rigid Body Animation.” In Special Interest Group on Computer Graphics and
Interactive Techniques Conference Conference Papers ’24. Association for Computing
Machinery, 2024. https://doi.org/10.1145/3641519.3657485.
ieee: Y.-L. Chen, M. Ly, and C. Wojtan, “Primal-dual non-smooth friction for rigid
body animation,” in Special Interest Group on Computer Graphics and Interactive
Techniques Conference Conference Papers ’24, Denver, United States, 2024.
ista: 'Chen Y-L, Ly M, Wojtan C. 2024. Primal-dual non-smooth friction for rigid
body animation. Special Interest Group on Computer Graphics and Interactive Techniques
Conference Conference Papers ’24. SIGGRAPH: Computer Graphics and Interactive
Techniques Conference.'
mla: Chen, Yi-Lu, et al. “Primal-Dual Non-Smooth Friction for Rigid Body Animation.”
Special Interest Group on Computer Graphics and Interactive Techniques Conference
Conference Papers ’24, Association for Computing Machinery, 2024, doi:10.1145/3641519.3657485.
short: Y.-L. Chen, M. Ly, C. Wojtan, in:, Special Interest Group on Computer Graphics
and Interactive Techniques Conference Conference Papers ’24, Association for Computing
Machinery, 2024.
conference:
end_date: 2024-08-01
location: Denver, United States
name: 'SIGGRAPH: Computer Graphics and Interactive Techniques Conference'
start_date: 2024-07-28
corr_author: '1'
date_created: 2024-07-10T11:06:20Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-08T08:54:38Z
day: '01'
ddc:
- '621'
- '531'
- '006'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1145/3641519.3657485
external_id:
isi:
- '001282218200091'
file:
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creator: yichen
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date_updated: 2024-07-10T11:03:14Z
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creator: yichen
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date_updated: 2024-07-10T11:03:12Z
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file_size: 10518286
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content_type: video/mp4
creator: yichen
date_created: 2024-07-10T11:03:51Z
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file_size: 280610763
relation: main_file
success: 1
file_date_updated: 2024-07-10T11:03:58Z
has_accepted_license: '1'
isi: 1
keyword:
- physical simulation
- frictional contact
- rigid body mechanics
- non-smooth dynamics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Special Interest Group on Computer Graphics and Interactive Techniques
Conference Conference Papers '24
publication_identifier:
isbn:
- '9798400705250'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Primal-dual non-smooth friction for rigid body animation
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '17219'
abstract:
- lang: eng
text: 'We introduce a multi-material non-manifold mesh-based surface tracking algorithm
that converts self-intersections into topological changes. Our algorithm generalizes
prior work on manifold surface tracking with topological changes: it preserves
surface features like mesh-based methods, and it robustly handles topological
changes like level set methods. Our method also offers improved efficiency and
robustness over the state of the art. We demonstrate the effectiveness of the
approach on a range of examples, including complex soap film simulations with
thousands of interacting bubbles, and boolean unions of non-manifold meshes consisting
of millions of triangles.'
acknowledgement: Peter Heiss-Synak helped conceive the project, helped formulate the
algorithm structure, contributed ideas and code to Sections 6 & 8, the mesh data
structure, algorithm robustness and benchmarks, helped write the paper, and provided
supervision and conceptual solutions throughout the project. Aleksei Kalinov contributed
ideas and code to Sections 7, 8.5, and 5, the sparse grid data structure, algorithm
robustness and benchmarks, optimized the performance, produced all results, most
figures, and the supplementary video, helped write the text, and provided conceptual
solutions throughout the project. Malina Strugaru helped implement the mesh data
structure and designed re-meshing operations for non-manifold triangle meshes. Arian
Etemadi developed early prototypes for ideas in Sections 8.1 and 8.3 and helped
write the paper. Huidong Yang developed early prototypes for isosurface extraction
and visualization. Chris Wojtan helped conceive the project, helped write the paper,
and provided supervision, prototype grid data structure code, and conceptual solutions
throughout the project. We thank the anonymous reviewers for their helpful comments,
the members of the Visual Computing Group at ISTA for their feedback, Christopher
Batty for discussions about LosTopos, and SideFX for the Houdini Education software
licenses. This research was funded in part by the European Union (ERC-2021-COG
101045083 CoDiNA).
article_number: '54'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Peter
full_name: Synak, Peter
id: 331776E2-F248-11E8-B48F-1D18A9856A87
last_name: Synak
- first_name: Aleksei
full_name: Kalinov, Aleksei
id: 44b7120e-eb97-11eb-a6c2-e1557aa81d02
last_name: Kalinov
orcid: 0000-0003-2189-3904
- first_name: Irina-Malina
full_name: Strugaru, Irina-Malina
id: 2afc607f-f128-11eb-9611-8f2a0dfcf074
last_name: Strugaru
- first_name: Arian
full_name: Etemadihaghighi, Arian
id: 36cea3aa-f38e-11ec-8ae0-c65ae6f6098f
last_name: Etemadihaghighi
- first_name: Huidong
full_name: Yang, Huidong
last_name: Yang
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: Synak P, Kalinov A, Strugaru I-M, Etemadi A, Yang H, Wojtan C. Multi-material
mesh-based surface tracking with implicit topology changes. ACM Transactions
on Graphics. 2024;43(4). doi:10.1145/3658223
apa: Synak, P., Kalinov, A., Strugaru, I.-M., Etemadi, A., Yang, H., & Wojtan,
C. (2024). Multi-material mesh-based surface tracking with implicit topology changes.
ACM Transactions on Graphics. Association for Computing Machinery. https://doi.org/10.1145/3658223
chicago: Synak, Peter, Aleksei Kalinov, Irina-Malina Strugaru, Arian Etemadi, Huidong
Yang, and Chris Wojtan. “Multi-Material Mesh-Based Surface Tracking with Implicit
Topology Changes.” ACM Transactions on Graphics. Association for Computing
Machinery, 2024. https://doi.org/10.1145/3658223.
ieee: P. Synak, A. Kalinov, I.-M. Strugaru, A. Etemadi, H. Yang, and C. Wojtan,
“Multi-material mesh-based surface tracking with implicit topology changes,” ACM
Transactions on Graphics, vol. 43, no. 4. Association for Computing Machinery,
2024.
ista: Synak P, Kalinov A, Strugaru I-M, Etemadi A, Yang H, Wojtan C. 2024. Multi-material
mesh-based surface tracking with implicit topology changes. ACM Transactions on
Graphics. 43(4), 54.
mla: Synak, Peter, et al. “Multi-Material Mesh-Based Surface Tracking with Implicit
Topology Changes.” ACM Transactions on Graphics, vol. 43, no. 4, 54, Association
for Computing Machinery, 2024, doi:10.1145/3658223.
short: P. Synak, A. Kalinov, I.-M. Strugaru, A. Etemadi, H. Yang, C. Wojtan, ACM
Transactions on Graphics 43 (2024).
corr_author: '1'
date_created: 2024-07-10T12:24:00Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2026-04-07T13:02:36Z
day: '01'
ddc:
- '004'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1145/3658223
external_id:
isi:
- '001289270900021'
file:
- access_level: open_access
checksum: 1917067d4b52d7729019b03560004e43
content_type: application/pdf
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has_accepted_license: '1'
intvolume: ' 43'
isi: 1
issue: '4'
keyword:
- surface tracking
- topology change
- non- manifold meshes
- multi-material flows
- solid modeling
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
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publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
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relation: dissertation_contains
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- id: '18301'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Multi-material mesh-based surface tracking with implicit topology changes
tmp:
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legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
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year: '2024'
...
---
OA_place: repository
_id: '17361'
abstract:
- lang: eng
text: We present symplectic structures on the shape space of unparameterized space
curves that generalize the classical Marsden-Weinstein structure. Our method integrates
the Liouville 1-form of the Marsden-Weinstein structure with Riemannian structures
that have been introduced in mathematical shape analysis. We also derive Hamiltonian
vector fields for several classical Hamiltonian functions with respect to these
new symplectic structures.
acknowledgement: The authors are grateful to Boris Khesin for valuable comments on
the MW symplectic structure and S. Ishida thanks Albert Chern for insightful discussions
on space curves and Chris Wojtan for his continuous support. M. Bauer was partially
supported by NSF grant DMS-1953244 and by the Binational Science Foundation (BSF).
S. Ishida was partially supported by ERC Consolidator Grant 101045083 “CoDiNA” funded
by the European Research Council. Some figures were generated by the software Houdini
and its education license was provided by SideFX.
article_processing_charge: No
arxiv: 1
author:
- first_name: Martin
full_name: Bauer, Martin
last_name: Bauer
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
orcid: 0000-0002-3121-3100
- first_name: Peter W.
full_name: Michor, Peter W.
last_name: Michor
citation:
ama: Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves.
arXiv. doi:10.48550/arXiv.2407.19908
apa: Bauer, M., Ishida, S., & Michor, P. W. (n.d.). Symplectic structures on
the space of space curves. arXiv. https://doi.org/10.48550/arXiv.2407.19908
chicago: Bauer, Martin, Sadashige Ishida, and Peter W. Michor. “Symplectic Structures
on the Space of Space Curves.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2407.19908.
ieee: M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space
of space curves,” arXiv. .
ista: Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space
curves. arXiv, 10.48550/arXiv.2407.19908.
mla: Bauer, Martin, et al. “Symplectic Structures on the Space of Space Curves.”
ArXiv, doi:10.48550/arXiv.2407.19908.
short: M. Bauer, S. Ishida, P.W. Michor, ArXiv (n.d.).
date_created: 2024-08-01T06:34:08Z
date_published: 2024-07-29T00:00:00Z
date_updated: 2026-04-28T09:59:01Z
day: '29'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/arXiv.2407.19908
external_id:
arxiv:
- '2407.19908'
keyword:
- space of space curves
- symplectic stuctures
language:
- iso: eng
main_file_link:
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oa: 1
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grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: arXiv
publication_status: draft
related_material:
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title: Symplectic structures on the space of space curves
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
_id: '14628'
abstract:
- lang: eng
text: We introduce a compact, intuitive procedural graph representation for cellular
metamaterials, which are small-scale, tileable structures that can be architected
to exhibit many useful material properties. Because the structures’ “architectures”
vary widely—with elements such as beams, thin shells, and solid bulks—it is difficult
to explore them using existing representations. Generic approaches like voxel
grids are versatile, but it is cumbersome to represent and edit individual structures;
architecture-specific approaches address these issues, but are incompatible with
one another. By contrast, our procedural graph succinctly represents the construction
process for any structure using a simple skeleton annotated with spatially varying
thickness. To express the highly constrained triply periodic minimal surfaces
(TPMS) in this manner, we present the first fully automated version of the conjugate
surface construction method, which allows novices to create complex TPMS from
intuitive input. We demonstrate our representation’s expressiveness, accuracy,
and compactness by constructing a wide range of established structures and hundreds
of novel structures with diverse architectures and material properties. We also
conduct a user study to verify our representation’s ease-of-use and ability to
expand engineers’ capacity for exploration.
acknowledgement: "The authors thank Mina Konaković Luković and Michael Foshey for
their early contributions to this project, David Palmer and Paul Zhang for their
insightful discussions about minimal surfaces and the CSCM, Julian Panetta for providing
the Elastic Textures code, and Hannes Hergeth for his feedback and support. We also
thank our user study participants and anonymous reviewers.\r\nThis material is based
upon work supported by the National Science Foundation\r\n(NSF) Graduate Research
Fellowship under Grant No. 2141064; the MIT Morningside\r\nAcademy for Design Fellowship;
the Defense Advanced Research Projects Agency\r\n(DARPA) Grant No. FA8750-20-C-0075;
the ERC Consolidator Grant No. 101045083,\r\n“CoDiNA: Computational Discovery of
Numerical Algorithms for Animation and Simulation of Natural Phenomena”; and the
NewSat project, which is co-funded by the Operational Program for Competitiveness
and Internationalisation (COMPETE2020), Portugal 2020, the European Regional Development
Fund (ERDF), and the Portuguese Foundation for Science and Technology (FTC) under
the MIT Portugal program."
article_number: '168'
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Liane
full_name: Makatura, Liane
last_name: Makatura
- first_name: Bohan
full_name: Wang, Bohan
last_name: Wang
- first_name: Yi-Lu
full_name: Chen, Yi-Lu
id: 0b467602-dbcd-11ea-9d1d-ed480aa46b70
last_name: Chen
- first_name: Bolei
full_name: Deng, Bolei
last_name: Deng
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
- first_name: Bernd
full_name: Bickel, Bernd
id: 49876194-F248-11E8-B48F-1D18A9856A87
last_name: Bickel
orcid: 0000-0001-6511-9385
- first_name: Wojciech
full_name: Matusik, Wojciech
last_name: Matusik
citation:
ama: 'Makatura L, Wang B, Chen Y-L, et al. Procedural metamaterials: A unified procedural
graph for metamaterial design. ACM Transactions on Graphics. 2023;42(5).
doi:10.1145/3605389'
apa: 'Makatura, L., Wang, B., Chen, Y.-L., Deng, B., Wojtan, C., Bickel, B., &
Matusik, W. (2023). Procedural metamaterials: A unified procedural graph for metamaterial
design. ACM Transactions on Graphics. Association for Computing Machinery.
https://doi.org/10.1145/3605389'
chicago: 'Makatura, Liane, Bohan Wang, Yi-Lu Chen, Bolei Deng, Chris Wojtan, Bernd
Bickel, and Wojciech Matusik. “Procedural Metamaterials: A Unified Procedural
Graph for Metamaterial Design.” ACM Transactions on Graphics. Association
for Computing Machinery, 2023. https://doi.org/10.1145/3605389.'
ieee: 'L. Makatura et al., “Procedural metamaterials: A unified procedural
graph for metamaterial design,” ACM Transactions on Graphics, vol. 42,
no. 5. Association for Computing Machinery, 2023.'
ista: 'Makatura L, Wang B, Chen Y-L, Deng B, Wojtan C, Bickel B, Matusik W. 2023.
Procedural metamaterials: A unified procedural graph for metamaterial design.
ACM Transactions on Graphics. 42(5), 168.'
mla: 'Makatura, Liane, et al. “Procedural Metamaterials: A Unified Procedural Graph
for Metamaterial Design.” ACM Transactions on Graphics, vol. 42, no. 5,
168, Association for Computing Machinery, 2023, doi:10.1145/3605389.'
short: L. Makatura, B. Wang, Y.-L. Chen, B. Deng, C. Wojtan, B. Bickel, W. Matusik,
ACM Transactions on Graphics 42 (2023).
date_created: 2023-11-29T15:02:03Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2025-09-09T13:33:58Z
day: '01'
ddc:
- '531'
- '006'
department:
- _id: GradSch
- _id: ChWo
- _id: BeBi
doi: 10.1145/3605389
external_id:
isi:
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creator: yichen
date_created: 2023-11-29T15:16:01Z
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issue: '5'
keyword:
- Computer Graphics and Computer-Aided Design
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
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title: 'Procedural metamaterials: A unified procedural graph for metamaterial design'
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year: '2023'
...
---
_id: '14748'
acknowledged_ssus:
- _id: ScienComp
acknowledgement: We thank the anonymous reviewers and the members of the Visual Computing
Group at ISTA for their helpful comments. This research was supported by the Scientific
Service Units (SSU) of ISTA through resources provided by Scientific Computing,
and was funded in part by the European Union (ERC-2021-COG 101045083 CoDiNA).
article_number: '5'
article_processing_charge: No
author:
- first_name: Yi-Lu
full_name: Chen, Yi-Lu
id: 0b467602-dbcd-11ea-9d1d-ed480aa46b70
last_name: Chen
- first_name: Mickaël
full_name: Ly, Mickaël
id: 6340d7f0-b48d-11eb-b10d-b7487e71d9f1
last_name: Ly
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: 'Chen Y-L, Ly M, Wojtan C. Unified treatment of contact, friction and shock-propagation
in rigid body animation. In: Proceedings of the ACM SIGGRAPH/Eurographics Symposium
on Computer Animation. Association for Computing Machinery; 2023. doi:10.1145/3606037.3606836'
apa: 'Chen, Y.-L., Ly, M., & Wojtan, C. (2023). Unified treatment of contact,
friction and shock-propagation in rigid body animation. In Proceedings of the
ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Los Angeles, CA,
United States: Association for Computing Machinery. https://doi.org/10.1145/3606037.3606836'
chicago: Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Unified Treatment of Contact,
Friction and Shock-Propagation in Rigid Body Animation.” In Proceedings of
the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Association
for Computing Machinery, 2023. https://doi.org/10.1145/3606037.3606836.
ieee: Y.-L. Chen, M. Ly, and C. Wojtan, “Unified treatment of contact, friction
and shock-propagation in rigid body animation,” in Proceedings of the ACM SIGGRAPH/Eurographics
Symposium on Computer Animation, Los Angeles, CA, United States, 2023.
ista: 'Chen Y-L, Ly M, Wojtan C. 2023. Unified treatment of contact, friction and
shock-propagation in rigid body animation. Proceedings of the ACM SIGGRAPH/Eurographics
Symposium on Computer Animation. SCA: Symposium on Computer Animation, 5.'
mla: Chen, Yi-Lu, et al. “Unified Treatment of Contact, Friction and Shock-Propagation
in Rigid Body Animation.” Proceedings of the ACM SIGGRAPH/Eurographics Symposium
on Computer Animation, 5, Association for Computing Machinery, 2023, doi:10.1145/3606037.3606836.
short: Y.-L. Chen, M. Ly, C. Wojtan, in:, Proceedings of the ACM SIGGRAPH/Eurographics
Symposium on Computer Animation, Association for Computing Machinery, 2023.
conference:
end_date: 2023-08-06
location: Los Angeles, CA, United States
name: 'SCA: Symposium on Computer Animation'
start_date: 2023-08-04
corr_author: '1'
date_created: 2024-01-08T13:00:24Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2025-04-14T12:58:27Z
day: '01'
department:
- _id: ChWo
doi: 10.1145/3606037.3606836
language:
- iso: eng
month: '08'
oa_version: None
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
publication_identifier:
isbn:
- '9798400702686'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
related_material:
record:
- id: '15292'
relation: other
status: public
status: public
title: Unified treatment of contact, friction and shock-propagation in rigid body
animation
type: conference_abstract
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '15292'
abstract:
- lang: eng
text: We present a rigid body animation technique which prevents solids from interpenetrating,
dissipates energy through friction, and propagates shocks through contacts. We
employ the Alternating Direction Method of Multipliers (ADMM) to couple non-smooth
Coulomb friction with impact propagation, allowing efficient and accurate non-smooth
dynamics along with a correct transmission of impacts through assemblies of rigid
bodies. We further extend our method to model adhesion, dynamic friction and lubricated
contact.
acknowledgement: We thank the anonymous reviewers and the members of the Visual Computing
Group at ISTA for their helpful comments. This research was supported by the Scientific
Service Units (SSU) of ISTA through resources provided by Scientific Computing,
and was funded in part by the European Union (ERC-2021-COG 101045083 CoDiNA)
article_processing_charge: No
author:
- first_name: Yi-Lu
full_name: Chen, Yi-Lu
id: 0b467602-dbcd-11ea-9d1d-ed480aa46b70
last_name: Chen
- first_name: Mickaël
full_name: Ly, Mickaël
id: 6340d7f0-b48d-11eb-b10d-b7487e71d9f1
last_name: Ly
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: Chen Y-L, Ly M, Wojtan C. Unified Treatment of Contact, Friction and Shock-Propagation
in Rigid Body Animation. ACM; 2023. doi:10.1145/3606037.3606836
apa: 'Chen, Y.-L., Ly, M., & Wojtan, C. (2023). Unified treatment of contact,
friction and shock-propagation in rigid body animation. Proceedings of
the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Los Angeles,
CA, United States: ACM. https://doi.org/10.1145/3606037.3606836'
chicago: Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. Unified Treatment of Contact,
Friction and Shock-Propagation in Rigid Body Animation. Proceedings of
the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. ACM, 2023.
https://doi.org/10.1145/3606037.3606836.
ieee: Y.-L. Chen, M. Ly, and C. Wojtan, Unified treatment of contact, friction
and shock-propagation in rigid body animation. ACM, 2023.
ista: Chen Y-L, Ly M, Wojtan C. 2023. Unified treatment of contact, friction and
shock-propagation in rigid body animation, ACM,p.
mla: Chen, Yi-Lu, et al. “Unified Treatment of Contact, Friction and Shock-Propagation
in Rigid Body Animation.” Proceedings of the ACM SIGGRAPH/Eurographics Symposium
on Computer Animation, ACM, 2023, doi:10.1145/3606037.3606836.
short: Y.-L. Chen, M. Ly, C. Wojtan, Unified Treatment of Contact, Friction and
Shock-Propagation in Rigid Body Animation, ACM, 2023.
conference:
end_date: 2023-08-06
location: Los Angeles, CA, United States
name: 'SCA: Symposium on Computer Animation'
start_date: 2023-08-04
corr_author: '1'
date_created: 2024-04-03T14:57:23Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2025-04-14T12:58:27Z
day: '01'
ddc:
- '005'
- '531'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1145/3606037.3606836
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creator: yichen
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creator: yichen
date_created: 2024-04-03T14:58:23Z
date_updated: 2024-04-03T14:58:23Z
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language:
- iso: eng
month: '08'
oa: 1
oa_version: None
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
publication_status: published
publisher: ACM
related_material:
record:
- id: '14748'
relation: other
status: public
status: public
title: Unified treatment of contact, friction and shock-propagation in rigid body
animation
type: conference_poster
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14240'
abstract:
- lang: eng
text: This paper introduces a novel method for simulating large bodies of water
as a height field. At the start of each time step, we partition the waves into
a bulk flow (which approximately satisfies the assumptions of the shallow water
equations) and surface waves (which approximately satisfy the assumptions of Airy
wave theory). We then solve the two wave regimes separately using appropriate
state-of-the-art techniques, and re-combine the resulting wave velocities at the
end of each step. This strategy leads to the first heightfield wave model capable
of simulating complex interactions between both deep and shallow water effects,
like the waves from a boat wake sloshing up onto a beach, or a dam break producing
wave interference patterns and eddies. We also analyze the numerical dispersion
created by our method and derive an exact correction factor for waves at a constant
water depth, giving us a numerically perfect re-creation of theoretical water
wave dispersion patterns.
acknowledged_ssus:
- _id: ScienComp
acknowledgement: "We thank Georg Sperl for helping with early research for this paper,
Mickael Ly and Yi-Lu Chen for proofreading, and members of the ISTA Visual Computing
Group for general feedback. This project was funded in part by the European Research
Council (ERC Consolidator Grant 101045083 CoDiNA).\r\nThe motorboat and sailboat
were modeled by Sergei and the palmtrees by YadroGames. The environment map was
created by Emil Persson."
article_number: '83'
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Stefan
full_name: Jeschke, Stefan
id: 44D6411A-F248-11E8-B48F-1D18A9856A87
last_name: Jeschke
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: Jeschke S, Wojtan C. Generalizing shallow water simulations with dispersive
surface waves. ACM Transactions on Graphics. 2023;42(4). doi:10.1145/3592098
apa: Jeschke, S., & Wojtan, C. (2023). Generalizing shallow water simulations
with dispersive surface waves. ACM Transactions on Graphics. Association
for Computing Machinery. https://doi.org/10.1145/3592098
chicago: Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations
with Dispersive Surface Waves.” ACM Transactions on Graphics. Association
for Computing Machinery, 2023. https://doi.org/10.1145/3592098.
ieee: S. Jeschke and C. Wojtan, “Generalizing shallow water simulations with dispersive
surface waves,” ACM Transactions on Graphics, vol. 42, no. 4. Association
for Computing Machinery, 2023.
ista: Jeschke S, Wojtan C. 2023. Generalizing shallow water simulations with dispersive
surface waves. ACM Transactions on Graphics. 42(4), 83.
mla: Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations
with Dispersive Surface Waves.” ACM Transactions on Graphics, vol. 42,
no. 4, 83, Association for Computing Machinery, 2023, doi:10.1145/3592098.
short: S. Jeschke, C. Wojtan, ACM Transactions on Graphics 42 (2023).
corr_author: '1'
date_created: 2023-08-27T22:01:17Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2025-04-14T08:01:13Z
day: '01'
ddc:
- '000'
department:
- _id: ChWo
doi: 10.1145/3592098
external_id:
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- '001044671300049'
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has_accepted_license: '1'
intvolume: ' 42'
isi: 1
issue: '4'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
grant_number: '101045083'
name: Computational Discovery of Numerical Algorithms for Animation and Simulation
of Natural Phenomena
publication: ACM Transactions on Graphics
publication_identifier:
eissn:
- 1557-7368
issn:
- 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Generalizing shallow water simulations with dispersive surface waves
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 42
year: '2023'
...
---
_id: '11432'
abstract:
- lang: eng
text: "This paper proposes a method for simulating liquids in large bodies of water
by coupling together a water surface wave simulator with a 3D Navier-Stokes simulator.
The surface wave simulation uses the equivalent sources method (ESM) to efficiently
animate large bodies of water with precisely controllable wave propagation behavior.
The 3D liquid simulator animates complex non-linear fluid behaviors like splashes
and breaking waves using off-the-shelf simulators using FLIP or the level set
method with semi-Lagrangian advection.\r\nWe combine the two approaches by using
the 3D solver to animate localized non-linear behaviors, and the 2D wave solver
to animate larger regions with linear surface physics. We use the surface motion
from the 3D solver as boundary conditions for 2D surface wave simulator, and we
use the velocity and surface heights from the 2D surface wave simulator as boundary
conditions for the 3D fluid simulation. We also introduce a novel technique for
removing visual artifacts caused by numerical errors in 3D fluid solvers: we use
experimental data to estimate the artificial dispersion caused by the 3D solver
and we then carefully tune the wave speeds of the 2D solver to match it, effectively
eliminating any differences in wave behavior across the boundary. To the best
of our knowledge, this is the first time such a empirically driven error compensation
approach has been used to remove coupling errors from a physics simulator.\r\nOur
coupled simulation approach leverages the strengths of each simulation technique,
animating large environments with seamless transitions between 2D and 3D physics."
acknowledged_ssus:
- _id: ScienComp
acknowledgement: We wish to thank the anonymous reviewers and the members of the Visual
Computing Group at IST Austria and MFX Team at INRIA for their valuable feedback.
This research was supported by the Scientific Service Units (SSU) of IST Austria
through resources provided by Scientific Computing. This project has received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme under grant agreement No. 638176.
article_processing_charge: No
article_type: original
author:
- first_name: Camille
full_name: Schreck, Camille
id: 2B14B676-F248-11E8-B48F-1D18A9856A87
last_name: Schreck
- first_name: Christopher J
full_name: Wojtan, Christopher J
id: 3C61F1D2-F248-11E8-B48F-1D18A9856A87
last_name: Wojtan
orcid: 0000-0001-6646-5546
citation:
ama: Schreck C, Wojtan C. Coupling 3D liquid simulation with 2D wave propagation
for large scale water surface animation using the equivalent sources method. Computer
Graphics Forum. 2022;41(2):343-353. doi:10.1111/cgf.14478
apa: Schreck, C., & Wojtan, C. (2022). Coupling 3D liquid simulation with 2D
wave propagation for large scale water surface animation using the equivalent
sources method. Computer Graphics Forum. Wiley. https://doi.org/10.1111/cgf.14478
chicago: Schreck, Camille, and Chris Wojtan. “Coupling 3D Liquid Simulation with
2D Wave Propagation for Large Scale Water Surface Animation Using the Equivalent
Sources Method.” Computer Graphics Forum. Wiley, 2022. https://doi.org/10.1111/cgf.14478.
ieee: C. Schreck and C. Wojtan, “Coupling 3D liquid simulation with 2D wave propagation
for large scale water surface animation using the equivalent sources method,”
Computer Graphics Forum, vol. 41, no. 2. Wiley, pp. 343–353, 2022.
ista: Schreck C, Wojtan C. 2022. Coupling 3D liquid simulation with 2D wave propagation
for large scale water surface animation using the equivalent sources method. Computer
Graphics Forum. 41(2), 343–353.
mla: Schreck, Camille, and Chris Wojtan. “Coupling 3D Liquid Simulation with 2D
Wave Propagation for Large Scale Water Surface Animation Using the Equivalent
Sources Method.” Computer Graphics Forum, vol. 41, no. 2, Wiley, 2022,
pp. 343–53, doi:10.1111/cgf.14478.
short: C. Schreck, C. Wojtan, Computer Graphics Forum 41 (2022) 343–353.
corr_author: '1'
date_created: 2022-06-05T22:01:49Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2024-10-22T09:58:19Z
day: '01'
department:
- _id: ChWo
doi: 10.1111/cgf.14478
ec_funded: 1
external_id:
isi:
- '000802723900027'
intvolume: ' 41'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.archives-ouvertes.fr/hal-03641349/
month: '05'
oa: 1
oa_version: Submitted Version
page: 343-353
project:
- _id: 2533E772-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '638176'
name: 'Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large
Scales'
publication: Computer Graphics Forum
publication_identifier:
eissn:
- 1467-8659
issn:
- 0167-7055
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coupling 3D liquid simulation with 2D wave propagation for large scale water
surface animation using the equivalent sources method
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 41
year: '2022'
...