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Graph."],"published-print":{"date-parts":[[2026,10,31]]},"abstract":"<jats:p>\n                    Effectively representing and generating 3D roof structures remains a challenging task in urban modeling. This article introduces a loop-based roof representation (LFR) and\n                    <jats:italic toggle=\"yes\">Loops2Roofs<\/jats:italic>\n                    algorithm, a novel diffusion-based generative approach that directly outputs 3D polygonal roof meshes using the LFR. Our key novelty lies in representing the roofs as a set of polygonal faces bounded by loops. This flexible representation improves generalization to complex roof structures across different architectural styles and can be effectively learned and generated by machine learning models. Roof generation proceeds in two stages. First, a Transformer-based diffusion model directly denoises the 3D coordinates of roof face vertices. This model is conditioned on structural priors, specifically the number of roof faces and vertices per face, which are pre-generated using an auto-regressive model. Second, a neural stitching module enforces roof topology and recovers the geometric incident relationships between edges of different 3D loops. Optionally, our algorithm can incorporate 2D building footprints as input for image-conditioned roof generation. The final output is a compact, structured roof mesh encoded in the LFR format. We demonstrate the effectiveness and efficiency of our approach by generating diverse, realistic roof models, ranging from synthetic to real-world buildings. Experiments show that\n                    <jats:italic toggle=\"yes\">Loops2Roofs<\/jats:italic>\n                    significantly advances structured roof generation, outperforming existing methods on three benchmarks.\n                  <\/jats:p>","DOI":"10.1145\/3807955","type":"journal-article","created":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T10:56:02Z","timestamp":1775818562000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Loops2Roofs: Diffusion-based 3D Roof Generation using a Loop Representation"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3376-1725","authenticated-orcid":false,"given":"Jianwei","family":"Guo","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Beijing Normal University","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-1060-689X","authenticated-orcid":false,"given":"Pu","family":"Li","sequence":"additional","affiliation":[{"name":"MAIS, Institute of Automation, CAS and School of Artificial Intelligence","place":["UCAS, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6965-2969","authenticated-orcid":false,"given":"Qi","family":"Zeng","sequence":"additional","affiliation":[{"name":"MAIS, Institute of Automation, CAS and School of Artificial Intelligence","place":["UCAS, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1654-3462","authenticated-orcid":false,"given":"Wenhao","family":"Zhang","sequence":"additional","affiliation":[{"name":"MAIS, Institute of Automation","place":["CAS, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8605-8321","authenticated-orcid":false,"given":"Pengxu","family":"Li","sequence":"additional","affiliation":[{"name":"MAIS, Institute of Automation, CAS and School of Artificial Intelligence","place":["UCAS, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5629-9975","authenticated-orcid":false,"given":"Liangliang","family":"Nan","sequence":"additional","affiliation":[{"name":"Delft University of Technology","place":["Delft, Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5293-2112","authenticated-orcid":false,"given":"Bedrich","family":"Benes","sequence":"additional","affiliation":[{"name":"Purdue University","place":["West Lafayette, USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2209-2404","authenticated-orcid":false,"given":"Dongming","family":"Yan","sequence":"additional","affiliation":[{"name":"MAIS, Institute of Automation, CAS and School of Artificial Intelligence","place":["UCAS, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,6,29]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-61332-3_144"},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-80350-5_65"},{"key":"e_1_3_2_4_1","doi-asserted-by":"crossref","unstructured":"Fatemeh Alidoost Hossein Arefi and Michael Hahn. 2020. 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