Vector refinable splines and subdivision

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dc.contributor.advisorDe Villiers, J. M.
dc.contributor.authorAndriamaro, Miangaly Gaelle
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Mathematics.
dc.date.accessioned2009-03-02T08:31:23Zen_ZA
dc.date.accessioned2010-06-01T08:32:16Z
dc.date.available2009-03-02T08:31:23Zen_ZA
dc.date.available2010-06-01T08:32:16Z
dc.date.issued2008-12
dc.descriptionThesis (MSc (Mathematics))--Stellenbosch University, 2008.
dc.description.abstractIn this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove some of its properties, thereby building a basis for a later extension to the vector setting. Defining a subdivision scheme associated to the B-spline refinement mask, we then present the proof of a well-known convergence result. Subdivision is a powerful tool used in computer-aided geometric design (CAGD) for the generation of curves and surfaces. The basic step of a subdivision algorithm consists of starting with a given set of points, called the initial control points, and creating new points as a linear combination of the previous ones, thereby generating new control points. Under certain conditions, repeated applications of this procedure yields a continuous limit curve. One important goal of this thesis is to study a particular extension of scalar subdivision to matrix subdivision ...en
dc.identifier.urihttp://hdl.handle.net/10019.1/1747
dc.language.isoen
dc.publisherStellenbosch : Stellenbosch University
dc.rights.holderStellenbosch University
dc.subjectVector refinable splinesen
dc.subjectB-spline functionsen
dc.subjectLane-Riesenfeld subdivisionsen_ZA
dc.subjectDissertations -- Mathematicsen
dc.subjectTheses -- Mathematicsen
dc.subject.lcshRefinable functionsen_ZA
dc.subject.lcshSplinesen
dc.titleVector refinable splines and subdivisionen
dc.typeThesis
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