{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T15:02:38Z","timestamp":1784559758529,"version":"3.55.0"},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:00:00Z","timestamp":1777334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Grants Council (Hong Kong)\u2019s General Research Fund"},{"name":"Innovating Timber Roofs: Algorithmic Expansion of Light-Weight Glulam Solutions for Low-Tech Construction Contexts","award":["17\u2009608\u2009221"],"award-info":[{"award-number":["17\u2009608\u2009221"]}]},{"name":"University of Hong Kong Department of Architecture Special Projects","award":["FY2022-2023"],"award-info":[{"award-number":["FY2022-2023"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,6,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This paper presents a deterministic computational workflow for the rationalization of curved glue-laminated beam assemblies through tolerance-based clustering and mold optimization. The method computes equilibrium catenary geometries, evaluates directed Hausdorff deviation, groups beams under a user-defined tolerance threshold, and optimizes shared mold families to reduce formwork requirements. It outputs the number of input curves, the cluster count, the maximum deviation per family, and a tolerance\u2013cluster relationship that supports early-stage design-to-fabrication decision-making. Applied to a curved glulam roof case study, the workflow shows how tolerance governs mold reduction, with three- and eight-cluster scenarios demonstrating the trade-off between geometric fidelity and fabrication complexity, while keeping deviations below 1%. A full-scale prototype fabricated from a single optimized jig further demonstrates practical feasibility and controlled as-built accuracy in a low-resource fabrication setting.<\/jats:p>","DOI":"10.1093\/jcde\/qwag042","type":"journal-article","created":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T11:22:59Z","timestamp":1777288979000},"page":"1-29","source":"Crossref","is-referenced-by-count":0,"title":["Deterministic \u03c4-based clustering and mould optimization for reusable formwork in curved glulam construction"],"prefix":"10.1093","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1921-395X","authenticated-orcid":false,"given":"Kristof","family":"Crolla","sequence":"first","affiliation":[{"name":"Department of Architecture, The University of Hong Kong , 3\/F, Knowles Building, Pokfulam Road ,\u00a0","place":["Hong Kong SAR"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8613-4177","authenticated-orcid":false,"given":"Yilun","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Architecture, The University of Hong Kong , 3\/F, Knowles Building, Pokfulam Road ,\u00a0","place":["Hong Kong SAR"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1289-9159","authenticated-orcid":false,"given":"Pei-Hsien","family":"Hsu","sequence":"additional","affiliation":[{"name":"Graduate Institute of Architecture, National Yang Ming Chiao Tung University , No. 1001, Daxue Rd, East District, Hsinchu City 300093 ,","place":["Taiwan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8362-7719","authenticated-orcid":false,"given":"June-Hao","family":"Hou","sequence":"additional","affiliation":[{"name":"Graduate Institute of Architecture, National Yang Ming Chiao Tung University , No. 1001, Daxue Rd, East District, Hsinchu City 300093 ,","place":["Taiwan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6505-3097","authenticated-orcid":false,"given":"Nichol Long Hin","family":"Wong","sequence":"additional","affiliation":[{"name":"Department of Architecture, The University of Hong Kong , 3\/F, Knowles Building, Pokfulam Road ,\u00a0","place":["Hong Kong SAR"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9030-9573","authenticated-orcid":false,"given":"Yu-Tung","family":"Cheng","sequence":"additional","affiliation":[{"name":"Graduate Institute of Architecture, National Yang Ming Chiao Tung University , No. 1001, Daxue Rd, East District, Hsinchu City 300093 ,","place":["Taiwan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,4,28]]},"reference":[{"key":"2026072010154543600_bib1","volume-title":"Exact and Heuristic Solution Approaches for the Cluster Deletion Problem, Networks","author":"Ambrosio","year":"2025"},{"key":"2026072010154543600_bib2","doi-asserted-by":"publisher","first-page":"737","DOI":"10.5169\/seals-59969","volume-title":"Nagano Olympic Memorial Arena: Design and Construction, Long-Span and High-Rise Structures: Proceedings of the IABSE Symposium Kobe 1998","author":"Ban","year":"1998"},{"key":"2026072010154543600_bib3","doi-asserted-by":"publisher","first-page":"103710","DOI":"10.1016\/j.autcon.2021.103710","article-title":"Developing a mold-free approach for complex glulam production with the assist of computer vision technologies","volume":"127","author":"Chai","year":"2021","journal-title":"Automation in Construction"},{"key":"2026072010154543600_bib4","doi-asserted-by":"publisher","first-page":"103571","DOI":"10.1016\/j.autcon.2021.103571","article-title":"Manufacturing double-curved glulam with robotic band saw cutting technique","volume":"124","author":"Chai","year":"2021","journal-title":"Automation in Construction"},{"key":"2026072010154543600_bib5","author":"Chavan","year":"2025"},{"key":"2026072010154543600_bib6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-03676-8_2","article-title":"Beyond form definition: material informed digital fabrication in timber construction","volume-title":"Digital Wood Design. Lecture Notes in Civil Engineering","author":"Correa","year":"2019"},{"key":"2026072010154543600_bib7","doi-asserted-by":"publisher","first-page":"611","DOI":"10.52842\/conf.ecaade.2023.1.611","article-title":"Catenary wooden roof structures: Precedent knowledge for future algorithmic design and construction optimization","volume-title":"Digital Design Reconsidered: Proceedings of the 41st Conference on Education and Research in Computer Aided Architectural Design in Europe (eCAADe 2023)","author":"Crolla","year":"2023"},{"key":"2026072010154543600_bib8","doi-asserted-by":"publisher","first-page":"000004","DOI":"10.54113\/j.sust.2021.000004","article-title":"A review of mechanical behavior of structural laminated bamboo lumber","volume":"1","author":"Dauletbek","year":"2021","journal-title":"Sustainable Structures"},{"key":"2026072010154543600_bib9","doi-asserted-by":"publisher","first-page":"3522","DOI":"10.15376\/biores.18.2.3522-3539","article-title":"Physical and mechanical properties of glued laminated bamboo","volume":"18","author":"de\u00a0Lima","year":"2023","journal-title":"BioResources"},{"key":"2026072010154543600_bib10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1778765.1778782","article-title":"Paneling architectural freeform surfaces","volume":"29","author":"Eigensatz","year":"2010","journal-title":"ACM Transactions on Graphics"},{"key":"2026072010154543600_bib11","first-page":"12","author":"Fast","year":"2017"},{"key":"2026072010154543600_bib12","first-page":"2171","article-title":"DEAP: Evolutionary algorithms made easy","volume":"13","author":"Fortin","year":"2012","journal-title":"Journal of Machine Learning Research"},{"key":"2026072010154543600_bib13","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1007\/978-3-030-03676-8_25","article-title":"Computational mechanical modelling of wood\u2014From microstructural characteristics over wood-based products to advanced timber structures, digital wood design","volume":"24","author":"F\u00fcssl","year":"2019","journal-title":"Lecture Notes in Civil Engineering"},{"key":"2026072010154543600_bib14","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/B978-0-12-803581-8.10748-9","article-title":"Bamboo: The emerging renewable material for sustainable construction","volume":"2","author":"Goh","year":"2020","journal-title":"Encyclopedia of Renewable and Sustainable Materials"},{"key":"2026072010154543600_bib15","doi-asserted-by":"publisher","first-page":"11","DOI":"10.25080\/TCWV9851","article-title":"Exploring network structure, dynamics, and function using NetworkX","volume-title":"Proceedings of the 7th Python in Science Conference (SciPy 2008)","author":"Hagberg","year":"2008"},{"key":"2026072010154543600_bib16","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","article-title":"Array programming with NumPy","volume":"585","author":"Harris","year":"2020","journal-title":"Nature"},{"key":"2026072010154543600_bib17","doi-asserted-by":"publisher","DOI":"10.11129\/detail.9783034614634","volume-title":"Timber Construction Manual","author":"Herzog","year":"2004"},{"key":"2026072010154543600_bib18","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1093\/jcde\/qwae048","article-title":"Toward reciprocal feedback between computational design, engineering, and fabrication to co-design coreless filament-wound structures","volume":"11","author":"Kannenberg","year":"2024","journal-title":"Journal of Computational Design and Engineering"},{"key":"2026072010154543600_bib19","doi-asserted-by":"publisher","first-page":"56","DOI":"10.25080\/Majora-92bf1922-00a","article-title":"Data structures for statistical computing in Python","volume-title":"Proceedings of the 9th Python in Science Conference","author":"McKinney","year":"2010"},{"key":"2026072010154543600_bib20","volume-title":"Rhinoceros 3D and Grasshopper (Version 8)","author":"McNeel","year":"2024"},{"key":"2026072010154543600_bib21","doi-asserted-by":"publisher","DOI":"10.4324\/9781315678825","volume-title":"Advancing Wood Architecture: a Computational Approach","author":"Menges","year":"2016"},{"key":"2026072010154543600_bib22","doi-asserted-by":"publisher","first-page":"47","DOI":"10.31586\/wjcea.2022.449","article-title":"A comparison of life cycle impact of mass timber and concrete in building construction","volume":"1","author":"Mofolasayo","year":"2022","journal-title":"Trends Journal of Sciences Research"},{"key":"2026072010154543600_bib23","volume-title":"Laminated Timber Construction: Development, Aesthetics, and Building Practice of a Modern Technology","author":"M\u00fcller","year":"2000"},{"key":"2026072010154543600_bib24","volume-title":"Frei Otto. Complete Works: Lightweight Construction, Natural Design","author":"Nerdinger","year":"2005"},{"key":"2026072010154543600_bib25","first-page":"1","article-title":"Multi-scalar modelling for free-form timber structures","volume-title":"Proceedings of the IASS Annual Symposium 2016: Spatial Structures in the 21st Century","author":"Poinet","year":"2016"},{"key":"2026072010154543600_bib26","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1002\/ad.1564","article-title":"Linking structure and parametric geometry","volume":"83","author":"Preisinger","year":"2013","journal-title":"Architectural Design"},{"key":"2026072010154543600_bib27","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1177\/07349041211034460","article-title":"Review of large-scale fire tests on cross-laminated timber","volume":"39","author":"Ronquillo","year":"2021","journal-title":"Journal of Fire Sciences"},{"key":"2026072010154543600_bib28","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1002\/ad.1111","article-title":"Materialising complexity","volume":"80","author":"Scheurer","year":"2010","journal-title":"Architectural Design"},{"key":"2026072010154543600_bib29","article-title":"Constructive algorithms for graph coloring","volume-title":"Baeldung on Computer Science","author":"Sryheni","year":"2024"},{"key":"2026072010154543600_bib30","doi-asserted-by":"publisher","first-page":"258","DOI":"10.2307\/j.ctt1n7qkg7.39","article-title":"From lamination to assembly modelling the seine musicale","volume-title":"Fabricate 2017","author":"Stehling","year":"2017"},{"key":"2026072010154543600_bib31","unstructured":"The pandas development team . (2020). \u201cpandas-dev\/pandas: Pandas.\u201d Zenodo. 10.5281\/zenodo.3509134."},{"key":"2026072010154543600_bib32","first-page":"283","author":"Tkachenko","year":"2025"},{"key":"2026072010154543600_bib33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4230\/LIPIcs.ISAAC.2020.13","article-title":"Between shapes, using the Hausdorff distance","volume-title":"31st International Symposium on Algorithms and Computation (ISAAC 2020)","author":"van\u00a0Kreveld","year":"2020"},{"key":"2026072010154543600_bib34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-92294-2_31","article-title":"Altered behavior: The performative nature of manufacture chainsaw choreographies + bandsaw manoeuvres","volume-title":"Robotic Fabrication in Architecture, Art and Design 2018","author":"Vercruysse","year":"2019"},{"key":"2026072010154543600_bib35","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.autcon.2015.09.011","article-title":"Robotic timber construction\u2014Expanding additive fabrication to new dimensions","volume":"61","author":"Willmann","year":"2016","journal-title":"Automation in Construction"},{"key":"2026072010154543600_bib36","first-page":"150","article-title":"Simplifying catenary wood structures: Post-digital expansion of glulam\u2019s construction solution space","volume-title":"ACADIA 19: Ubiquity and Autonomy, Proceedings of the 39th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA)","author":"Wong","year":"2019"},{"key":"2026072010154543600_bib37","doi-asserted-by":"publisher","first-page":"181","DOI":"10.52842\/conf.caadria.2024.3.181","article-title":"Curved glulam architecture design optimization for low-tech construction: The fabrication and construction of KATENARA","volume-title":"Accelerated Design: Proceedings of the 29th CAADRIA Conference","author":"Wong","year":"2024"},{"key":"2026072010154543600_bib38","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/978-3-030-03676-8_9","article-title":"Reinterpretation of traditional wood structures with digital design and fabrication technologies","volume-title":"Digital Wood Design. Lecture Notes in Civil Engineering","author":"Yuan","year":"2019"},{"key":"2026072010154543600_bib39","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.enbuild.2019.06.047","article-title":"Comparing the embodied carbon and energy of a mass timber structure system to typical steel and concrete alternatives for parking garages","volume":"199","author":"Zeitz","year":"2019","journal-title":"Energy and Buildings"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jcde\/advance-article-pdf\/doi\/10.1093\/jcde\/qwag042\/68181509\/qwag042.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/13\/6\/1\/68181509\/qwag042.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jcde\/article-pdf\/13\/6\/1\/68181509\/qwag042.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T14:16:05Z","timestamp":1784556965000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/13\/6\/1\/8664326"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,28]]},"references-count":39,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,6,4]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwag042","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,6]]},"published":{"date-parts":[[2026,4,28]]}}}