---
_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: The authors acknowledge Chris Wojtan for his continuous support to
the present work through discussions and advice. The second author thanks Anna Sisak
for a fruitful discussion on prequantum bundles. This project was funded in part
by the European Research Council (ERC Consolidator Grant 101045083 CoDiNA).
article_number: '2303.14555'
article_processing_charge: No
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
citation:
ama: Chern A, Ishida S. Area formula for spherical polygons via prequantization.
arXiv. doi:10.48550/arXiv.2303.14555
apa: Chern, A., & Ishida, S. (n.d.). Area formula for spherical polygons via
prequantization. arXiv. https://doi.org/10.48550/arXiv.2303.14555
chicago: Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons
via Prequantization.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2303.14555.
ieee: A. Chern and S. Ishida, “Area formula for spherical polygons via prequantization,”
arXiv. .
ista: Chern A, Ishida S. Area formula for spherical polygons via prequantization.
arXiv, 2303.14555.
mla: Chern, Albert, and Sadashige Ishida. “Area Formula for Spherical Polygons via
Prequantization.” ArXiv, 2303.14555, doi:10.48550/arXiv.2303.14555.
short: A. Chern, S. Ishida, ArXiv (n.d.).
date_created: 2023-04-18T19:16:06Z
date_published: 2023-03-25T00:00:00Z
date_updated: 2023-04-25T06:51:21Z
day: '25'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/arXiv.2303.14555
external_id:
arxiv:
- '2303.14555'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2303.14555
month: '03'
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: Area formula for spherical polygons via prequantization
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_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: 2023-12-04T08:09:05Z
day: '01'
ddc:
- '531'
- '006'
department:
- _id: GradSch
- _id: ChWo
- _id: BeBi
doi: 10.1145/3605389
file:
- access_level: open_access
checksum: 0192f597d7a2ceaf89baddfd6190d4c8
content_type: application/zip
creator: yichen
date_created: 2023-11-29T15:16:01Z
date_updated: 2023-11-29T15:16:01Z
file_id: '14630'
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file_size: 95467870
relation: main_file
success: 1
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checksum: 7fb024963be81933494f38de191e4710
content_type: application/zip
creator: yichen
date_created: 2023-11-29T15:16:01Z
date_updated: 2023-11-29T15:16:01Z
file_id: '14631'
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content_type: application/pdf
creator: dernst
date_created: 2023-12-04T08:04:14Z
date_updated: 2023-12-04T08:04:14Z
file_id: '14638'
file_name: 2023_ACMToG_Makatura.pdf
file_size: 57067476
relation: main_file
success: 1
file_date_updated: 2023-12-04T08:04:14Z
has_accepted_license: '1'
intvolume: ' 42'
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:
issn:
- 0730-0301
- 1557-7368
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
status: public
title: 'Procedural metamaterials: A unified procedural graph for metamaterial design'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 42
year: '2023'
...
---
_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 hospital-\r\nity. 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_number: '2312.12213'
article_processing_charge: No
author:
- first_name: Sadashige
full_name: Ishida, Sadashige
id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
last_name: Ishida
- 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. arXiv. doi:10.48550/arXiv.2312.12213
apa: Ishida, S., & Lavenant, H. (n.d.). Quantitative convergence of a discretization
of dynamic optimal transport using the dual formulation. arXiv. https://doi.org/10.48550/arXiv.2312.12213
chicago: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2312.12213.
ieee: S. Ishida and H. Lavenant, “Quantitative convergence of a discretization of
dynamic optimal transport using the dual formulation,” arXiv. .
ista: Ishida S, Lavenant H. Quantitative convergence of a discretization of dynamic
optimal transport using the dual formulation. arXiv, 2312.12213.
mla: Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization
of Dynamic Optimal Transport Using the Dual Formulation.” ArXiv, 2312.12213,
doi:10.48550/arXiv.2312.12213.
short: S. Ishida, H. Lavenant, ArXiv (n.d.).
date_created: 2023-12-21T10:14:37Z
date_published: 2023-12-19T00:00:00Z
date_updated: 2023-12-27T13:44:33Z
day: '19'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/arXiv.2312.12213
external_id:
arxiv:
- '2312.12213'
keyword:
- Optimal transport
- Hamilton-Jacobi equation
- convex optimization
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2312.12213
month: '12'
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: Quantitative convergence of a discretization of dynamic optimal transport using
the dual formulation
type: preprint
user_id: 3E5EF7F0-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).
date_created: 2023-08-27T22:01:17Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2024-01-02T09:35:55Z
day: '01'
ddc:
- '000'
department:
- _id: ChWo
doi: 10.1145/3592098
external_id:
isi:
- '001044671300049'
file:
- access_level: open_access
checksum: 1d178bb2f8011d9f5aedda6427e18c7a
content_type: video/mp4
creator: sjeschke
date_created: 2023-12-21T12:26:40Z
date_updated: 2023-12-21T12:26:40Z
file_id: '14704'
file_name: PaperVideo_final.mp4
file_size: 511572575
relation: main_file
success: 1
- access_level: open_access
checksum: a49b2e744d5cd1276bb8b2e0ce6dc638
content_type: application/pdf
creator: dernst
date_created: 2024-01-02T09:34:27Z
date_updated: 2024-01-02T09:34:27Z
file_id: '14725'
file_name: 2023_ACMToG_Jeschke.pdf
file_size: 7469177
relation: main_file
success: 1
file_date_updated: 2024-01-02T09:34:27Z
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: '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
date_created: 2024-01-08T13:00:24Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2024-02-28T12:51:40Z
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'
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'
...