Ternary interpolatory subdivision

Description

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Subdivision is an important and e cient tool for rendering smooth curves and
surfaces in computer graphics, by repeatedly applying a subdivision (re ning)
scheme to a given set of points. In the literature, attention has been mostly
restricted to developing binary subdivision schemes. The primary emphasis of
this thesis is on ternary subdivision, and in particular on the interpolatory case.
We will derive a symmetric ternary interpolatory subdivision scheme for the
rendering of curves, satisfying analogous properties to the Dubuc-Deslauriers
binary scheme. Explicit construction methods, as well as a corresponding
convergence analysis, will be presented. Graphical illustrations of the results
will also be provided. / AFRIKAANSE OPSOMMING: Subdivisie bied 'n belangrike en doeltre ende metode om gladde krommes
en oppervlakke in rekenaargra ka te genereer. Hierdie metode behels dat 'n
subdivisieskema (of verfyningskema) herhaaldelik toegepas word op 'n gegewe
versameling punte. In die literatuur word daar hoofsaaklik gefokus op die ont-
wikkeling van bin^ere subdivisieskemas. In hierdie tesis word die klem gel^e op
tern^ere subdivisieskemas, en in die besonder op interpolerende skemas. Ons sal
'n simmetriese tern^ere interpolerende subdivisieskema, wat analo e eienskappe
as di e van die Dubuc-Deslauriers bin^ere skema bevredig, ontwikkel, om krom-
mes te lewer. Eksplisiete konstruksiemetodes en ooreenkomstige konvergensie-
analise, asook gra ese illustrasies van die resultate, sal getoon word.

Links & Downloads

1. http://hdl.handle.net/10019.1/71652

Tags

Dissertations -- Mathematics

Theses -- Mathematics

Computer graphics

Curves on surfaces

Subdivision surfaces (Geometry)

Additional Fields

Identifer	oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/71652
Date	12 1900
Creators	Van der Walt, Maria Dorothea
Contributors	De Villiers, J. M., Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
Publisher	Stellenbosch : Stellenbosch University
Source Sets	South African National ETD Portal
Detected Language	English
Type	Thesis
Format	104 p. : ill.
Rights	Stellenbosch University