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However, the formula\u2019s isotropy limits its capacity to leverage the directional features of point clouds. In this study, we introduce a convection augmentation term to extend the classic Gauss formula. This new term allows our method to leverage point clouds\u2019 directional characteristics effectively. With the proper choice of the velocity field, this method could construct more equations to calculate a more precise indicator function. Furthermore, an adaptive selection strategy of the velocity field is proposed. For large-scale point clouds, we propose a CUDA-and-octree-based acceleration algorithm with\n            <jats:italic toggle=\"yes\">O(N)<\/jats:italic>\n            space complexity and\n            <jats:italic toggle=\"yes\">O(N<\/jats:italic>\n            log\n            <jats:italic toggle=\"yes\">N)<\/jats:italic>\n            time complexity. Our method can complete the orientation and reconstruction tasks of point clouds with up to 500K within a few seconds. Extensive experiments demonstrate that our method achieves state-of-the-art performance and manages various challenging situations, especially for models with thin structures or small holes. The source code is publicly available at\n            <jats:italic toggle=\"yes\">https:\/\/github.com\/mayueji\/CAGR<\/jats:italic>\n            .\n          <\/jats:p>","DOI":"10.1145\/3750723","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T11:14:38Z","timestamp":1753269278000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Convection Augmented Gauss Reconstruction for Unoriented Point Clouds"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4307-9867","authenticated-orcid":false,"given":"Yueji","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University","place":["Beijing, China"]},{"name":"Yau Mathematical Sciences Center, Tsinghua University","place":["Beijing, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7873-5977","authenticated-orcid":false,"given":"Dong","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China","place":["Hefei, China"]},{"name":"School of Software, Tsinghua University","place":["Hefei, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9122-0302","authenticated-orcid":false,"given":"Zuoqiang","family":"Shi","sequence":"additional","affiliation":[{"name":"Yau Mathematical Sciences Center, Tsinghua University","place":["Beijing, China"]},{"name":"Yanqi Lake Beijing Institute of Mathematical Sciences and Applications","place":["Beijing, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5176-9202","authenticated-orcid":false,"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Software, Tsinghua University","place":["Beijing, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,9,10]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/wics.101"},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52688.2022.01872"},{"key":"e_1_3_3_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00642580"},{"key":"e_1_3_3_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.02058.x"},{"key":"e_1_3_3_6_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6451"},{"key":"e_1_3_3_7_1","doi-asserted-by":"publisher","DOI":"10.5555\/1281920.1281928"},{"key":"e_1_3_3_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-58558-7_7"},{"key":"e_1_3_3_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657429"},{"key":"e_1_3_3_10_1","doi-asserted-by":"publisher","unstructured":"Amos Gropp Lior Yariv Niv Haim Matan Atzmon and Yaron Lipman. 2020. 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