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Graph."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>\n                    Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the zero-level set of a neural signed distance function (SDF), with sparse geometric control is still a challenging task. Sparse input shape control typically includes 3D curve networks or, more generally, 3D curve sketches, which are unstructured and cannot be connected to form a curve network, and therefore more difficult to deal with. While 3D curve networks or curve sketches provide intuitive shape control, their sparsity and varied topology pose challenges in generating high-quality surfaces to meet such curve constraints. In this paper, we propose NeuVAS, a variational approach to shape modeling using neural implicit surfaces constrained under sparse input shape control, including unstructured 3D curve sketches as well as connected 3D curve networks. Specifically, we introduce a smoothness term based on a functional of surface curvatures to minimize shape variation of the zero-level set surface of a neural SDF. We also develop a new technique to faithfully model\n                    <jats:italic toggle=\"yes\">G<\/jats:italic>\n                    <jats:sup>0<\/jats:sup>\n                    sharp feature curves as specified in the input curve sketches. Comprehensive comparisons with the state-of-the-art methods demonstrate the significant advantages of our method.\n                  <\/jats:p>","DOI":"10.1145\/3763331","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T17:15:39Z","timestamp":1764868539000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["NeuVAS: Neural Implicit Surfaces for Variational Shape Modeling"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0938-267X","authenticated-orcid":false,"given":"Pengfei","family":"Wang","sequence":"first","affiliation":[{"name":"Shandong University, Jinan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6271-2546","authenticated-orcid":false,"given":"Qiujie","family":"Dong","sequence":"additional","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-8399-6853","authenticated-orcid":false,"given":"Fangtian","family":"Liang","sequence":"additional","affiliation":[{"name":"Shandong University, Jinan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3628-9777","authenticated-orcid":false,"given":"Hao","family":"Pan","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3284-4019","authenticated-orcid":false,"given":"Lei","family":"Yang","sequence":"additional","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4259-2863","authenticated-orcid":false,"given":"Congyi","family":"Zhang","sequence":"additional","affiliation":[{"name":"University of British Columbia, Vancouver, Canada"},{"name":"The University of Texas at Dallas, Richardson, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5233-3910","authenticated-orcid":false,"given":"Guying","family":"Lin","sequence":"additional","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0217-1543","authenticated-orcid":false,"given":"Caiming","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shandong University, Jinan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6950-3261","authenticated-orcid":false,"given":"Yuanfeng","family":"Zhou","sequence":"additional","affiliation":[{"name":"Shandong University, Jinan, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1231-3392","authenticated-orcid":false,"given":"Changhe","family":"Tu","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8452-8723","authenticated-orcid":false,"given":"Shiqing","family":"Xin","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9251-3716","authenticated-orcid":false,"given":"Alla","family":"Sheffer","sequence":"additional","affiliation":[{"name":"University of British Columbia, Vancouver, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2261250.2261314"},{"key":"e_1_2_1_2_1","volume-title":"Computer Graphics Forum","author":"Andrews James","year":"1850","unstructured":"James Andrews, Pushkar Joshi, and Nathan Carr. 2011. 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