---
_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. <i>ACM Transactions on Graphics</i>. 2023;42(5).
    doi:<a href="https://doi.org/10.1145/3605389">10.1145/3605389</a>'
  apa: 'Makatura, L., Wang, B., Chen, Y.-L., Deng, B., Wojtan, C., Bickel, B., &#38;
    Matusik, W. (2023). Procedural metamaterials: A unified procedural graph for metamaterial
    design. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery.
    <a href="https://doi.org/10.1145/3605389">https://doi.org/10.1145/3605389</a>'
  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.” <i>ACM Transactions on Graphics</i>. Association
    for Computing Machinery, 2023. <a href="https://doi.org/10.1145/3605389">https://doi.org/10.1145/3605389</a>.'
  ieee: 'L. Makatura <i>et al.</i>, “Procedural metamaterials: A unified procedural
    graph for metamaterial design,” <i>ACM Transactions on Graphics</i>, 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.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 5,
    168, Association for Computing Machinery, 2023, doi:<a href="https://doi.org/10.1145/3605389">10.1145/3605389</a>.'
  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:
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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: '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: <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium
    on Computer Animation</i>. Association for Computing Machinery; 2023. doi:<a href="https://doi.org/10.1145/3606037.3606836">10.1145/3606037.3606836</a>'
  apa: 'Chen, Y.-L., Ly, M., &#38; Wojtan, C. (2023). Unified treatment of contact,
    friction and shock-propagation in rigid body animation. In <i>Proceedings of the
    ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>. Los Angeles, CA,
    United States: Association for Computing Machinery. <a href="https://doi.org/10.1145/3606037.3606836">https://doi.org/10.1145/3606037.3606836</a>'
  chicago: Chen, Yi-Lu, Mickaël Ly, and Chris Wojtan. “Unified Treatment of Contact,
    Friction and Shock-Propagation in Rigid Body Animation.” In <i>Proceedings of
    the ACM SIGGRAPH/Eurographics Symposium on Computer Animation</i>. Association
    for Computing Machinery, 2023. <a href="https://doi.org/10.1145/3606037.3606836">https://doi.org/10.1145/3606037.3606836</a>.
  ieee: Y.-L. Chen, M. Ly, and C. Wojtan, “Unified treatment of contact, friction
    and shock-propagation in rigid body animation,” in <i>Proceedings of the ACM SIGGRAPH/Eurographics
    Symposium on Computer Animation</i>, 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.” <i>Proceedings of the ACM SIGGRAPH/Eurographics Symposium
    on Computer Animation</i>, 5, Association for Computing Machinery, 2023, doi:<a
    href="https://doi.org/10.1145/3606037.3606836">10.1145/3606037.3606836</a>.
  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'
...