dc.contributor.author Lybekk, Espen Christian dc.date.accessioned 2017-09-04T22:28:02Z dc.date.issued 2017 dc.identifier.citation Lybekk, Espen Christian. Nonlinear interpolatory curve subdivision schemes. Master thesis, University of Oslo, 2017 dc.identifier.uri http://hdl.handle.net/10852/57799 dc.description.abstract The aim of this thesis is to study the convergence and smoothness of certain nonlinear interpolatory curve subdivision schemes. The emphasis will be on the iterated geometric schemes, which are extensions of the nonlinear four-point scheme by Dyn, Floater and Hormann, based on iterated chordal and centripetal parameterizations. Dyn et al. show convergence of the scheme for uniform, centripetal and chordal parameterizations, i.e. alpha=0,1/2,1, but we here consider the entire interval [0,1] of alpha, and derive new results concerning convergence. In particular, we show that the scheme by Dyn et al. is C^0 for all alpha in [1/2,1], but that there always exist control points such that the limit curve is not well defined for all alpha in (0,1/2). We also show that a scheme based on the iterated geometric schemes and the six-point scheme with tension parameter, is C^0 for a range of parameters. The aforementioned schemes are then shown to fit into a recent framework by Ewald et al., for studying smoothness criteria, and we propose modified refinement rules based on the circle preserving scheme by Sabin and Dodgson to better fit this framework. Lastly, numerical experiments are carried out to measure the smoothness of the schemes, and a new way to generate the multilevel grid based on the geometry of the points, is proposed. eng dc.language.iso eng dc.subject subdivision dc.subject interpolation dc.subject curve dc.subject nonlinear dc.title Nonlinear interpolatory curve subdivision schemes eng dc.type Master thesis dc.date.updated 2017-09-04T22:28:02Z dc.creator.author Lybekk, Espen Christian dc.date.embargoenddate 2022-06-30 dc.rights.terms Utsatt tilgjengeliggjøring: Kun forskere og studenter kan få innsyn i dokumentet. Tilgangskode/Access code B dc.identifier.urn URN:NBN:no-60500 dc.type.document Masteroppgave dc.rights.accessrights embargoedaccess dc.identifier.fulltext Fulltext https://www.duo.uio.no/bitstream/handle/10852/57799/11/Espen_Lybekk_Thesis.pdf
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