Vector refinable splines and subdivision
Date
2008-12
Authors
Andriamaro, Miangaly Gaelle
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : Stellenbosch University
Abstract
In 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 ...
Description
Thesis (MSc (Mathematics))--Stellenbosch University, 2008.
Keywords
Vector refinable splines, B-spline functions, Lane-Riesenfeld subdivisions, Dissertations -- Mathematics, Theses -- Mathematics