Paper Info
Title
Integration of generalized B-spline functions on Catmull-Clark surfaces at singularities.
Abstract
Subdivision surfaces are a common tool in geometric modelling, especially in computer graphics and computer animation. Nowadays, this concept has become established in engineering too. The focus here is on quadrilateral control grids and generalized B-spline surfaces of Catmull–Clark subdivision type. In the classical theory, a subdivision surface is defined as the limit of the repetitive application of subdivision rules to the control grid. Based on Stam’s idea, the labour-intensive process can be avoided by using a natural parameterization of the limit surface. However, the simplification is not free of defects. At singularities, the smoothness of the classically defined limit surface has been lost. This paper describes how to rescue the parameterization by using a subdivision basis function that is consistent with the classical definition, but is expensive to compute. Based on this, we introduce a characteristic subdivision finite element and use it to discretize integrals on subdivision surfaces. We show that in the integral representation the complicated parameterization reduces to a decisive factor. We compare the natural and the characteristic subdivision finite element approach solving PDEs on surfaces. As model problem we consider the mean curvature flow, whereby the computation is done on the step-by-step changing geometry.
Year
DOI
Venue
2016
10.1016/j.cad.2016.05.008
Computer-Aided Design
Keywords
Field
DocType
Subdivision surfaces,Catmull–Clark subdivision,Subdivision finite element,PDEs on surfaces,Isogeometric analysis
B-spline,Mathematical optimization,Mean curvature flow,Isogeometric analysis,Finite subdivision rule,Subdivision,Subdivision surface,Quadrilateral,Mathematics,Catmull–Clark subdivision surface
Journal
Volume
Issue
ISSN
78
C
0010-4485
Citations 
PageRank 
References 
1
0.39
10
Authors
2
Name
Order
Citations
PageRank
Anna Wawrzinek1111.12
Konrad Polthier2108985.92