A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Refinement operators for triangle meshes
Computer Aided Geometric Design
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Recursive Subdivision and Hypergeometric Functions
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
A Corner-Cutting Scheme for Hexagonal Subdivision Surfaces
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
A generative classification of mesh refinement rules with lattice transformations
Computer Aided Geometric Design
Fast hierarchical importance sampling with blue noise properties
ACM SIGGRAPH 2004 Papers
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
On the support of recursive subdivision
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Computer Aided Geometric Design
Deriving Box-Spline Subdivision Schemes
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Journal of Approximation Theory
A topological lattice refinement descriptor for subdivision schemes
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
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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.