{"paper":{"title":"Constructing Trivariate B-splines with Positive Jacobian by Pillow Operation and Geometric Iterative Fitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Chuanfeng Hu, Hao Huang, Hongwei Lin","submitted_at":"2018-11-30T03:21:19Z","abstract_excerpt":"The advent of isogeometric analysis has prompted a need for methods to generate Trivariate B-spline Solids (TBS) with positive Jacobian. However, it is difficult to guarantee a positive Jacobian of a TBS since the geometric pre-condition for ensuring the positive Jacobian is very complicated. In this paper, we propose a method for generating TBSs with guaranteed positive Jacobian. For the study, we used a tetrahedral (tet) mesh model and segmented it into sub-volumes using the pillow operation. Then, to reduce the difficulty in ensuring a positive Jacobian, we separately fitted the boundary cu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12597","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}