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Graph."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>\n                    Cross fields play a critical role in various geometry processing tasks, especially for quad mesh generation. Existing methods for cross field generation often struggle to balance computational efficiency with generation quality, using slow per-shape optimization. We introduce\n                    <jats:italic toggle=\"yes\">CrossGen<\/jats:italic>\n                    , a novel framework that supports both feed-forward prediction and latent generative modeling of cross fields for quad meshing by unifying geometry and cross field representations within a joint latent space. Our method enables extremely fast computation of high-quality cross fields of general input shapes, typically within one second without per-shape optimization. Our method assumes a point-sampled surface, also called a\n                    <jats:italic toggle=\"yes\">point-cloud surface<\/jats:italic>\n                    , as input, so we can accommodate various surface representations by a straightforward point sampling process. Using an auto-encoder network architecture, we encode input point-cloud surfaces into a sparse voxel grid with fine-grained latent spaces, which are decoded into both SDF-based surface geometry and cross fields (see the teaser figure). We also contribute a dataset of models with both high-quality signed distance fields (SDFs) representations and their corresponding cross fields, and use it to train our network. Once trained, the network is capable of computing a cross field of an input surface in a feed-forward manner, ensuring high geometric fidelity, noise resilience, and rapid inference. Furthermore, leveraging the same unified latent representation, we incorporate a diffusion model for computing cross fields of new shapes generated from partial input, such as sketches. To demonstrate its practical applications, we validate\n                    <jats:italic toggle=\"yes\">CrossGen<\/jats:italic>\n                    on the quad mesh generation task for a large variety of surface shapes. Experimental results demonstrate that\n                    <jats:italic toggle=\"yes\">CrossGen<\/jats:italic>\n                    generalizes well across diverse shapes and consistently yields high-fidelity cross fields, thus facilitating the generation of high-quality quad meshes.\n                  <\/jats:p>","DOI":"10.1145\/3763299","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T17:15:39Z","timestamp":1764868539000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["CrossGen: Learning and Generating Cross Fields for Quad Meshing"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6271-2546","authenticated-orcid":false,"given":"Qiujie","family":"Dong","sequence":"first","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"},{"name":"Shandong University, Qingdao, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6049-4458","authenticated-orcid":false,"given":"Jiepeng","family":"Wang","sequence":"additional","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8273-1808","authenticated-orcid":false,"given":"Rui","family":"Xu","sequence":"additional","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3335-6623","authenticated-orcid":false,"given":"Cheng","family":"Lin","sequence":"additional","affiliation":[{"name":"Macau University of Science and Technology, Macau, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2933-5667","authenticated-orcid":false,"given":"Yuan","family":"Liu","sequence":"additional","affiliation":[{"name":"Hong Kong University of Science and Technology, Hong Kong, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8452-8723","authenticated-orcid":false,"given":"Shiqing","family":"Xin","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6489-6502","authenticated-orcid":false,"given":"Zichun","family":"Zhong","sequence":"additional","affiliation":[{"name":"Wayne State University, Detroit, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0144-9489","authenticated-orcid":false,"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, Texas, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1231-3392","authenticated-orcid":false,"given":"Changhe","family":"Tu","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2729-5860","authenticated-orcid":false,"given":"Taku","family":"Komura","sequence":"additional","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7880-9470","authenticated-orcid":false,"given":"Leif","family":"Kobbelt","sequence":"additional","affiliation":[{"name":"RWTH Aachen University, Aachen, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0988-1452","authenticated-orcid":false,"given":"Scott","family":"Schaefer","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, Texas, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2284-3952","authenticated-orcid":false,"given":"Wenping","family":"Wang","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, Texas, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Computing cross fields A PDE approach based on the Ginzburg-Landau theory. 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