{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T17:16:09Z","timestamp":1783012569194,"version":"3.54.6"},"reference-count":50,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U25A20438"],"award-info":[{"award-number":["U25A20438"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62472258"],"award-info":[{"award-number":["62472258"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62595772"],"award-info":[{"award-number":["62595772"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computer-Aided Design"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cad.2026.104097","type":"journal-article","created":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T23:39:56Z","timestamp":1781048396000},"page":"104097","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Visual permeability-driven generation of support-free stochastic porous structures"],"prefix":"10.1016","volume":"199","author":[{"given":"Xiaokang","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaifeng","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lingxin","family":"Cao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Longdu","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lihao","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bingteng","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changhe","family":"Tu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5881-892X","authenticated-orcid":false,"given":"Lin","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baoquan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"7","key":"10.1016\/j.cad.2026.104097_b1","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1038\/nmat1421","article-title":"Porous scaffold design for tissue engineering","volume":"4","author":"Hollister","year":"2005","journal-title":"Nat Mater"},{"issue":"2","key":"10.1016\/j.cad.2026.104097_b2","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.addr.2007.08.041","article-title":"Biomimetic materials for tissue engineering","volume":"60","author":"Ma","year":"2008","journal-title":"Adv Drug Deliv Rev"},{"issue":"9","key":"10.1016\/j.cad.2026.104097_b3","doi-asserted-by":"crossref","first-page":"3876","DOI":"10.1039\/C2CS35378D","article-title":"Hierarchical porous materials: catalytic applications","volume":"42","author":"Parlett","year":"2013","journal-title":"Chem Soc Rev"},{"key":"10.1016\/j.cad.2026.104097_b4","series-title":"Proceedings of the special interest group on computer graphics and interactive techniques conference conference papers","article-title":"DualMS: Implicit dual-channel minimal surface optimization for heat exchanger design","author":"Zhang","year":"2025"},{"key":"10.1016\/j.cad.2026.104097_b5","series-title":"Proceedings of IASS annual symposia","first-page":"1","article-title":"Performative porosity\u2013adaptive infills for architectural elements","volume":"vol. 2020","author":"Bernhard","year":"2020"},{"key":"10.1016\/j.cad.2026.104097_b6","series-title":"The international conference on computational design and robotic fabrication","first-page":"117","article-title":"Environmental data-driven performance-based topological optimisation for morphology evolution of artificial Taihu stone","author":"Feng","year":"2021"},{"issue":"1","key":"10.1016\/j.cad.2026.104097_b7","first-page":"5","article-title":"Exploration of three-dimensional spatial learning approach based on machine learning\u2013taking Taihu stone as an example","volume":"2","author":"Deng","year":"2023","journal-title":"Archit Intell"},{"issue":"2","key":"10.1016\/j.cad.2026.104097_b8","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0045-7825(88)90086-2","article-title":"Generating optimal topologies in structural design using a homogenization method","volume":"71","author":"Bends\u00f8e","year":"1988","journal-title":"Comput Methods Appl Mech Engrg"},{"issue":"5","key":"10.1016\/j.cad.2026.104097_b9","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1007\/s00158-016-1551-x","article-title":"Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design","volume":"54","author":"Gaynor","year":"2016","journal-title":"Struct Multidiscip Optim"},{"issue":"3","key":"10.1016\/j.cad.2026.104097_b10","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1007\/s00158-016-1522-2","article-title":"An additive manufacturing filter for topology optimization of print-ready designs","volume":"55","author":"Langelaar","year":"2017","journal-title":"Struct Multidiscip Optim"},{"issue":"10","key":"10.1016\/j.cad.2026.104097_b11","doi-asserted-by":"crossref","first-page":"3037","DOI":"10.1109\/TVCG.2019.2914044","article-title":"Strong 3D printing by TPMS injection","volume":"26","author":"Yan","year":"2019","journal-title":"IEEE Trans Vis Comput Graphics"},{"key":"10.1016\/j.cad.2026.104097_b12","doi-asserted-by":"crossref","unstructured":"Tian L, Lu L, Chen W, Xia Y, Wang CC, Wang W. Organic open-cell porous structure modeling. In: Proceedings of the 5th annual ACM symposium on computational fabrication. 2020, p. 1\u201312.","DOI":"10.1145\/3424630.3425414"},{"key":"10.1016\/j.cad.2026.104097_b13","article-title":"Fabricable stochastic periodic porous microstructures: A Wang cube and Gaussian kernel approach","volume":"103","author":"Tian","year":"2025","journal-title":"Addit Manuf"},{"issue":"10","key":"10.1016\/j.cad.2026.104097_b14","doi-asserted-by":"crossref","first-page":"2787","DOI":"10.1109\/TVCG.2017.2764462","article-title":"Support-free hollowing","volume":"24","author":"Wang","year":"2017","journal-title":"IEEE Trans Vis Comput Graphics"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b15","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01650949","article-title":"Optimal shape design as a material distribution problem","volume":"1","author":"Bends\u00f8e","year":"1989","journal-title":"Struct Optim"},{"issue":"2","key":"10.1016\/j.cad.2026.104097_b16","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1109\/TVCG.2017.2655523","article-title":"Infill optimization for additive manufacturing\u2014approaching bone-like porous structures","volume":"24","author":"Wu","year":"2017","journal-title":"IEEE Trans Vis Comput Graphics"},{"issue":"3","key":"10.1016\/j.cad.2026.104097_b17","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1002\/nme.5461","article-title":"Undercut and overhang angle control in topology optimization: a density gradient based integral approach","volume":"111","author":"Qian","year":"2017","journal-title":"Internat J Numer Methods Engrg"},{"issue":"5","key":"10.1016\/j.cad.2026.104097_b18","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1007\/s00158-018-2010-7","article-title":"A new overhang constraint for topology optimization of self-supporting structures in additive manufacturing","volume":"58","author":"Garaigordobil","year":"2018","journal-title":"Struct Multidiscip Optim"},{"issue":"5","key":"10.1016\/j.cad.2026.104097_b19","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1007\/s00158-017-1880-4","article-title":"Continuous front propagation-based overhang control for topology optimization with additive manufacturing","volume":"57","author":"van de Ven","year":"2018","journal-title":"Struct Multidiscip Optim"},{"issue":"2","key":"10.1016\/j.cad.2026.104097_b20","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1007\/s00158-021-02887-2","article-title":"Overhang control in topology optimization: a comparison of continuous front propagation-based and discrete layer-by-layer overhang control","volume":"64","author":"van de Ven","year":"2021","journal-title":"Struct Multidiscip Optim"},{"issue":"5","key":"10.1016\/j.cad.2026.104097_b21","doi-asserted-by":"crossref","first-page":"2289","DOI":"10.1007\/s00158-020-02805-y","article-title":"Topology optimization of self-supporting infill structures","volume":"63","author":"Liu","year":"2021","journal-title":"Struct Multidiscip Optim"},{"key":"10.1016\/j.cad.2026.104097_b22","series-title":"Computer graphics forum","first-page":"385","article-title":"Fast and Robust Stochastic structural optimization","volume":"vol. 39","author":"Cui","year":"2020"},{"key":"10.1016\/j.cad.2026.104097_b23","article-title":"Mechanical properties of additively-manufactured sheet-based gyroidal stochastic cellular materials","volume":"48","author":"Al-Ketan","year":"2021","journal-title":"Addit Manuf"},{"key":"10.1016\/j.cad.2026.104097_b24","doi-asserted-by":"crossref","DOI":"10.1016\/j.cad.2023.103542","article-title":"Topology optimization of self-supporting porous structures based on triply periodic minimal surfaces","volume":"161","author":"Zheng","year":"2023","journal-title":"Comput-Aided Des"},{"key":"10.1016\/j.cad.2026.104097_b25","article-title":"Continuous transitions of triply periodic minimal surfaces","volume":"84","author":"Tian","year":"2024","journal-title":"Addit Manuf"},{"issue":"5","key":"10.1016\/j.cad.2026.104097_b26","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1111\/cgf.14610","article-title":"Fabricable multi-scale Wang tiles","volume":"41","author":"Liu","year":"2022","journal-title":"Comput Graph Forum"},{"key":"10.1016\/j.cad.2026.104097_b27","article-title":"New families of triply periodic minimal surface-like shell lattices","volume":"77","author":"Xu","year":"2023","journal-title":"Addit Manuf"},{"key":"10.1016\/j.cad.2026.104097_b28","doi-asserted-by":"crossref","unstructured":"Xue T, Liu L, Lu L, Henderson P, Tang P, Li H, Liu J, Zhao H, Peng H, Bickel B. MIND: Microstructure INverse Design with Generative Hybrid Neural Representation. In: Proceedings of the special interest group on computer graphics and interactive techniques conference conference papers. 2025, p. 1\u201312.","DOI":"10.1145\/3721238.3730682"},{"issue":"10","key":"10.1016\/j.cad.2026.104097_b29","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1016\/j.cad.2010.06.006","article-title":"A simple and effective geometric representation for irregular porous structure modeling","volume":"42","author":"Kou","year":"2010","journal-title":"Comput-Aided Des"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b30","first-page":"1","article-title":"Build-to-last: Strength to weight 3D printed objects","volume":"33","author":"Lu","year":"2014","journal-title":"ACM Trans Graph (ToG)"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2897824.2925922","article-title":"Procedural voronoi foams for additive manufacturing","volume":"35","author":"Mart\u00ednez","year":"2016","journal-title":"ACM Trans Graph"},{"issue":"1","key":"10.1016\/j.cad.2026.104097_b32","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0022-5096(01)00056-4","article-title":"Elastic properties of model random three-dimensional open-cell solids","volume":"50","author":"Roberts","year":"2002","journal-title":"J Mech Phys Solids"},{"key":"10.1016\/j.cad.2026.104097_b33","article-title":"Five simple tools for stochastic lattice creation","volume":"49","author":"Groth","year":"2022","journal-title":"Addit Manuf"},{"issue":"2","key":"10.1016\/j.cad.2026.104097_b34","doi-asserted-by":"crossref","first-page":"40","DOI":"10.3390\/fractalfract5020040","article-title":"Utilizing fractals for modeling and 3D printing of porous structures","volume":"5","author":"Ullah","year":"2021","journal-title":"Fractal Fract"},{"issue":"1","key":"10.1016\/j.cad.2026.104097_b35","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1080\/16864360.2017.1353747","article-title":"Design for additive manufacturing of porous structures using stochastic point-cloud: a pragmatic approach","volume":"15","author":"Sharif Ullah","year":"2018","journal-title":"Comput-Aided Des Appl"},{"issue":"1","key":"10.1016\/j.cad.2026.104097_b36","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.cirp.2020.04.088","article-title":"A system for designing and 3D printing of porous structures","volume":"69","author":"Ullah","year":"2020","journal-title":"CIRP Ann"},{"issue":"12","key":"10.1016\/j.cad.2026.104097_b37","doi-asserted-by":"crossref","first-page":"2329","DOI":"10.1007\/s13202-023-01683-6","article-title":"3D-porous-GAN: a high-performance 3D GAN for digital core reconstruction from a single 3D image","volume":"13","author":"Shi","year":"2023","journal-title":"J Pet Explor Prod Technol"},{"issue":"2","key":"10.1016\/j.cad.2026.104097_b38","doi-asserted-by":"crossref","DOI":"10.1115\/1.4066095","article-title":"Reconstruction and generation of porous metamaterial units via variational graph autoencoder and large language model","volume":"25","author":"Naghavi Khanghah","year":"2025","journal-title":"J Comput Inf Sci Eng"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3197517.3201343","article-title":"Polyhedral Voronoi diagrams for additive manufacturing","volume":"37","author":"Mart\u00ednez","year":"2018","journal-title":"ACM Trans Graph"},{"key":"10.1016\/j.cad.2026.104097_b40","doi-asserted-by":"crossref","DOI":"10.1016\/j.cag.2015.05.009","article-title":"Orientation analysis of 3D objects toward minimal support volume in 3D-printing","author":"Ezair","year":"2015","journal-title":"Comput Graph"},{"key":"10.1016\/j.cad.2026.104097_b41","series-title":"SIGGRAPH Asia technical briefs","article-title":"Cross-sectional structural analysis for 3D printing optimization","author":"Umetani","year":"2013"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2461912.2461957","article-title":"Make it stand: balancing shapes for 3D fabrication","volume":"32","author":"Pr\u00e9vost","year":"2013","journal-title":"ACM Trans Graph (ToG)"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b43","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1007\/s41095-024-0402-8","article-title":"Shell stand: Stable thin shell models for 3D fabrication","volume":"10","author":"Xing","year":"2024","journal-title":"Comput Vis Media"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3306346.3323022","article-title":"CurviSlicer: Slightly curved slicing for 3-axis printers","volume":"38","author":"Etienne","year":"2019","journal-title":"ACM Trans Graph"},{"issue":"4","key":"10.1016\/j.cad.2026.104097_b45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3197517.3201342","article-title":"Support-free volume printing by multi-axis motion","volume":"37","author":"Dai","year":"2018","journal-title":"ACM Trans Graph"},{"issue":"6","key":"10.1016\/j.cad.2026.104097_b46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2816795.2818121","article-title":"Perceptual models of preference in 3D printing direction","volume":"34","author":"Zhang","year":"2015","journal-title":"ACM Trans Graph"},{"issue":"1","key":"10.1016\/j.cad.2026.104097_b47","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1145\/505241.505243","article-title":"An optimal minimum spanning tree algorithm","volume":"49","author":"Pettie","year":"2002","journal-title":"J ACM"},{"key":"10.1016\/j.cad.2026.104097_b48","doi-asserted-by":"crossref","unstructured":"Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Morse-Smale complexes for piecewise linear 3-manifolds. In: Proceedings of the nineteenth annual symposium on computational geometry. 2003, p. 361\u201370.","DOI":"10.1145\/777792.777846"},{"issue":"1","key":"10.1016\/j.cad.2026.104097_b49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2629366","article-title":"Approximating minimum bounded degree spanning trees to within one of optimal","volume":"62","author":"Singh","year":"2015","journal-title":"J ACM"},{"issue":"2","key":"10.1016\/j.cad.2026.104097_b50","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1002\/nme.1620240207","article-title":"The method of moving asymptotes\u2014a new method for structural optimization","volume":"24","author":"Svanberg","year":"1987","journal-title":"Internat J Numer Methods Engrg"}],"container-title":["Computer-Aided Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010448526000679?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010448526000679?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T16:20:48Z","timestamp":1783009248000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0010448526000679"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":50,"alternative-id":["S0010448526000679"],"URL":"https:\/\/doi.org\/10.1016\/j.cad.2026.104097","relation":{"is-supplemented-by":[{"id-type":"uri","id":"https:\/\/github.com\/llliuxk\/taihustone.git","asserted-by":"subject"}]},"ISSN":["0010-4485"],"issn-type":[{"value":"0010-4485","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Visual permeability-driven generation of support-free stochastic porous structures","name":"articletitle","label":"Article Title"},{"value":"Computer-Aided Design","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cad.2026.104097","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"104097"}}