{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T21:03:01Z","timestamp":1780606981198,"version":"3.54.1"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,9]],"date-time":"2024-06-09T00:00:00Z","timestamp":1717891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Informatics Institute, University of Florida, and UF Graduate School Preeminence Awards","award":["123F259"],"award-info":[{"award-number":["123F259"]}]},{"name":"The Scientific and Technological Research Council of Turkey","award":["123F259"],"award-info":[{"award-number":["123F259"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Merging parallel quad strips facilitates narrowing surface passages, and allows a design to transition to a simpler shape. While a number of spline surface constructions exist for the isotropic case where n pieces join, few existing spline constructions deliver a good shape for control nets that merge parameter lines. Additionally, untilrecently, none provided a good shape for fast-contracting polyhedral control nets. This work improves the state-of-the-art of piecewise polynomial spline surfaces accommodating fast-contracting control nets. The new fast-contracting (FC) surface algorithm yields the industry-preferred uniform degree bi-3 (bi-cubic). The surfaces are by default differentiable, have an improved shape, measured empirically as to highlight the line distribution, and require fewer pieces compared to existing methods.<\/jats:p>","DOI":"10.3390\/axioms13060390","type":"journal-article","created":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T08:59:06Z","timestamp":1718009946000},"page":"390","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Bicubic Splines for Fast-Contracting Control Nets"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9398-6424","authenticated-orcid":false,"given":"K\u0229stutis","family":"Kar\u010diauskas","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Vilnius University, LT-03225 Vilnius, Lithuania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0338-6469","authenticated-orcid":false,"given":"Kyle Shih-Huang","family":"Lo","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences and Engineering, University of Florida, Gainesville, FL 32611, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0266-5546","authenticated-orcid":false,"given":"Erkan","family":"Gunpinar","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Istanbul Technical University, 34437 Istanbul, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2499-1529","authenticated-orcid":false,"given":"J\u00f6rg","family":"Peters","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences and Engineering, University of Florida, Gainesville, FL 32611, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77:1","DOI":"10.1145\/3072959.3073635","article-title":"Field-Aligned Online Surface Reconstruction","volume":"36","author":"Schertler","year":"2017","journal-title":"ACM Trans. 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