Paper Info
Title
An heuristic analysis of the classification of bivariate subdivision schemes
Abstract
Alexa [1] and Ivrissimtzis et al. [2] have proposed a classification mechanism for bivariate subdivision schemes. Alexa considers triangular primal schemes, Ivrissimtzis et al. generalise this both to quadrilateral and hexagonal meshes and to dual and mixed schemes. I summarise this classification and then proceed to analyse it in order to determine which classes of subdivision scheme are likely to contain useful members. My aim is to ascertain whether there are any potentially useful classes which have not yet been investigated or whether we can say, with reasonable confidence, that all of the useful classes have already been considered. I apply heuristics related to the mappings of element types (vertices, face centres, and mid-edges) to one another, to the preservation of symmetries, to the alignment of meshes at different subdivision levels, and to the size of the overall subdivision mask. My conclusion is that there are only a small number of useful classes and that most of these have already been investigated in terms of linear, stationary subdivision schemes. There is some space for further work, particularly in the investigation of whether there are useful ternary linear, stationary subdivision schemes, but it appears that future advances are more likely to lie elsewhere.
Year
DOI
Venue
2005
10.1007/11537908_10
IMA Conference on the Mathematics of Surfaces
Keywords
Field
DocType
face centre,heuristic analysis,classification mechanism,useful class,useful member,overall subdivision mask,stationary subdivision scheme,different subdivision level,bivariate subdivision scheme,element type,subdivision scheme
Discrete mathematics,Heuristic,Polygon mesh,Vertex (geometry),Computer science,Computational geometry,Heuristics,Subdivision,Quadrilateral,Bivariate analysis
Conference
ISBN
Citations 
PageRank 
3-540-28225-4
5
0.49
References 
Authors
20
1
Name
Order
Citations
PageRank
Neil A. Dodgson172354.20