dc.date.accessioned | 2020-06-08T17:53:53Z | |
dc.date.available | 2020-06-08T17:53:53Z | |
dc.date.created | 2020-02-06T18:27:02Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Lyche, Tom Muntingh, Georg . B-spline-like bases for C2 cubics on the Powell–Sabin 12-split. SMAI Journal of Computational Mathematics (SMAI j. comput. math.). 2019, S5, 129-159 | |
dc.identifier.uri | http://hdl.handle.net/10852/76790 | |
dc.description.abstract | For spaces of constant, linear, and quadratic splines of maximal smoothness on the Powell–Sabin 12-split of a triangle, the so-called S-bases were recently introduced. These are simplex spline bases with B-spline-like properties on the 12-split of a single triangle, which are tied together across triangles in a Bézier-like manner.
In this paper we give a formal definition of an S-basis in terms of certain basic properties. We proceed to investigate the existence of S-bases for the aforementioned spaces and additionally the cubic case, resulting in an exhaustive list. From their nature as simplex splines, we derive simple differentiation and recurrence formulas to other S-bases. We establish a Marsden identity that gives rise to various quasi-interpolants and domain points forming an intuitive control net, in terms of which conditions for C0-, C1-, and C2-smoothness are derived. | |
dc.language | EN | |
dc.publisher | Paris: Société de mathématiques appliquées et industrielles | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.title | B-spline-like bases for C2 cubics on the Powell–Sabin 12-split | |
dc.type | Journal article | |
dc.creator.author | Lyche, Tom | |
dc.creator.author | Muntingh, Georg | |
cristin.unitcode | 185,15,13,45 | |
cristin.unitname | Differensiallikninger og beregningsorientert matematikk | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.cristin | 1791791 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SMAI Journal of Computational Mathematics (SMAI j. comput. math.)&rft.volume=S5&rft.spage=129&rft.date=2019 | |
dc.identifier.jtitle | SMAI Journal of Computational Mathematics (SMAI j. comput. math.) | |
dc.identifier.volume | S5 | |
dc.identifier.startpage | 129 | |
dc.identifier.endpage | 159 | |
dc.identifier.urn | URN:NBN:no-79892 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 2426-8399 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/76790/1/2019SMAI-JCM_2019__S5__129_0.pdf | |
dc.type.version | PublishedVersion | |