Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Vector refinable splines and subdivision
Thesis (MSc (Mathematics))--Stellenbosch University, 2008.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Stellenbosch : Stellenbosch University
2009
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613904126869504 |
|---|---|
| access_status_str | Open Access |
| author | Andriamaro, Miangaly Gaelle |
| author2 | De Villiers, J. M. |
| author_browse | Andriamaro, Miangaly Gaelle De Villiers, J. M. |
| author_facet | De Villiers, J. M. Andriamaro, Miangaly Gaelle |
| author_sort | Andriamaro, Miangaly Gaelle |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc (Mathematics))--Stellenbosch University, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/1747 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:33.016Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2009 |
| publishDateRange | 2009 |
| publishDateSort | 2009 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/1747 Vector refinable splines and subdivision Andriamaro, Miangaly Gaelle De Villiers, J. M. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Mathematics. Vector refinable splines B-spline functions Dissertations -- Mathematics Theses -- Mathematics Lane-Riesenfeld subdivisions Refinable functions Splines Thesis (MSc (Mathematics))--Stellenbosch University, 2008. 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 ... 2009-03-02T08:31:23Z 2010-06-01T08:32:16Z 2009-03-02T08:31:23Z 2010-06-01T08:32:16Z 2008-12 Thesis http://hdl.handle.net/10019.1/1747 en Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Vector refinable splines B-spline functions Dissertations -- Mathematics Theses -- Mathematics Lane-Riesenfeld subdivisions Refinable functions Splines Andriamaro, Miangaly Gaelle Vector refinable splines and subdivision |
| title | Vector refinable splines and subdivision |
| title_full | Vector refinable splines and subdivision |
| title_fullStr | Vector refinable splines and subdivision |
| title_full_unstemmed | Vector refinable splines and subdivision |
| title_short | Vector refinable splines and subdivision |
| title_sort | vector refinable splines and subdivision |
| topic | Vector refinable splines B-spline functions Dissertations -- Mathematics Theses -- Mathematics Lane-Riesenfeld subdivisions Refinable functions Splines |
| url | http://hdl.handle.net/10019.1/1747 |
| work_keys_str_mv | AT andriamaromiangalygaelle vectorrefinablesplinesandsubdivision |