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Graph."],"published-print":{"date-parts":[[2025,8,1]]},"abstract":"<jats:p>\n                    This paper introduces a method to synthesize a 3D tensor field within a constrained geometric domain represented as a tetrahedral mesh. Whereas previous techniques optimize for\n                    <jats:italic toggle=\"yes\">isotropic<\/jats:italic>\n                    fields, we focus on\n                    <jats:italic toggle=\"yes\">anisotropic<\/jats:italic>\n                    tensor fields that are smooth and aligned with the domain boundary or user guidance. The key ingredient of our method is a novel computational design framework, built on top of the\n                    <jats:italic toggle=\"yes\">symmetric orthogonally decomposable<\/jats:italic>\n                    (odeco) tensor representation, to optimize the stretching ratios and orientations for each tensor in the domain. In contrast to past techniques designed only for\n                    <jats:italic toggle=\"yes\">isotropic<\/jats:italic>\n                    tensors, we demonstrate the efficacy of our approach in generating smooth volumetric tensor fields with high\n                    <jats:italic toggle=\"yes\">anisotropy<\/jats:italic>\n                    and shape conformity, especially for the domain with complex shapes. We apply these anisotropic tensor fields to various applications, such as anisotropic meshing, structural mechanics, and fabrication.\n                  <\/jats:p>","DOI":"10.1145\/3731181","type":"journal-article","created":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T04:02:22Z","timestamp":1753588942000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Designing 3D Anisotropic Frame Fields with Odeco Tensors"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5740-0599","authenticated-orcid":false,"given":"Haikuan","family":"Zhu","sequence":"first","affiliation":[{"name":"Wayne State University, Detroit, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-9072-1489","authenticated-orcid":false,"given":"Hongbo","family":"Li","sequence":"additional","affiliation":[{"name":"Wayne State University, Detroit, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-1753-4485","authenticated-orcid":false,"given":"Hsueh-Ti Derek","family":"Liu","sequence":"additional","affiliation":[{"name":"Roblox, Vancouver, Canada"},{"name":"University of British Columbia, Vancouver, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2284-3952","authenticated-orcid":false,"given":"Wenping","family":"Wang","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, College Station, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3981-2933","authenticated-orcid":false,"given":"Jing","family":"Hua","sequence":"additional","affiliation":[{"name":"Wayne State University, Detroit, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6489-6502","authenticated-orcid":false,"given":"Zichun","family":"Zhong","sequence":"additional","affiliation":[{"name":"Wayne State University, Detroit, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1201775.882296"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3328939.3328999"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12650-019-00555-8"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-017-1588-6"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601116"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323029"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611978001.5"},{"key":"e_1_2_2_8_1","volume-title":"The n-dimensional cotangent formula. 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