A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Approximation properties of multivariate wavelets
Mathematics of Computation
Multivariate refinement equations and convergence of subdivision schemes
SIAM Journal on Mathematical Analysis
Edge and vertex insertion for a class of C1 subdivision surfaces
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Computing the Smoothness Exponent of a Symmetric Multivariate Refinable Function
SIAM Journal on Matrix Analysis and Applications
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity
SIAM Journal on Numerical Analysis
Subdivision Surfaces
Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
An heuristic analysis of the classification of bivariate subdivision schemes
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
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We establish results on convergence and smoothness of subdivision rules operating on manifold-valued data which are based on a general dilation matrix. In particular we cover irregular combinatorics. For the regular grid case results are not restricted to isotropic dilation matrices. The nature of the results is that intrinsic subdivision rules which operate on geometric data inherit smoothness properties of their linear counterparts.