eprintid: 13011
rev_number: 6
eprint_status: archive
userid: 1
dir: disk0/00/01/30/11
datestamp: 2012-01-18 15:37:31
lastmod: 2014-04-03 23:19:56
status_changed: 2012-08-15 09:03:59
type: masterThesis
metadata_visibility: show
creators_name: Rieck, Bastian
title: Smoothness analysis of subdivision algorithms
ispublished: pub
subjects: 510
divisions: 708000
keywords: Numerische GeometrieSubdivision Algorithms , Smoothness , Differential Topology , Numerical Analysis
cterms_swd: Unterteilungsalgorithmus
cterms_swd: Glattheit <Mathematik>
cterms_swd: Differentialtopologie
cterms_swd: Algorithmische Geometrie
abstract: In computer graphics, subdivision algorithms are common tools for smoothing down irregularly shaped meshes. Of special interest, due to their simple formulations, are algorithms that generalize B-spline subdivision. Their conceptual simplicity is in stark contrast to the complexity of analysing their results. A complete formal examination of smoothness properties for subdivision schemes was only recently performed by Jörg Peters and Ulrich Reif. This thesis presents a precise and detailed introduction to the analysis of subdivision algorithms. For this purpose, first of all, the necessary background in B-spline theory is established. Building on this, two of the most common subdivision algorithms, the Doo-Sabin and the Catmull-Clark scheme, are motivated. Their treatment is followed by an in-depth description of methods for analysing smoothness properties of subdivision schemes, as developed by Peters and Reif. Afterwards, these methods are applied to the two aforementioned algorithms, thereby establishing smoothness for both algorithms in their original form. Last, in order to demonstrate the effects of choosing unsuitable weights, a number of degenerate weights, which produce irregular shapes in almost all cases, are derived for both schemes—these have hitherto not been published.
abstract_translated_lang: ger
class_scheme: msc
class_labels: 57R10, 65D10, 65D18, 68U05
date: 2010
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00013011
ppn_swb: 1651257426
own_urn: urn:nbn:de:bsz:16-opus-130111
language: eng
bibsort: RIECKBASTISMOOTHNESS2010
full_text_status: public
citation:   Rieck, Bastian  (2010) Smoothness analysis of subdivision algorithms.  [Master's thesis]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/13011/1/diploma_thesis_brieck.pdf