Topics in matrix analysis
A new subdivision method for bivariate splines on the four-directional mesh
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Stationary Subdivision
Interpolatory rank-1 vector subdivision schemes
Computer Aided Geometric Design
On the convergence of convolved vector subdivision schemes
Applied Numerical Mathematics - Applied scientific computing: Advances in grid generation, approximation and numerical modeling
Stationary and nonstationary affine combination of subdivision masks
Mathematics and Computers in Simulation
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Following the general idea of smoothing through convolution, we discuss schemes for smoothing hat functions on the three-directional and the four-directional mesh. The smoothing masks-which in the four-directional case are matrix masks-have the same support as the refinement mask for the hat functions. Several smoothing schemes are presented, and in some cases the smoothness properties of the smoothed functions are analysed. In particular, the results for the four-directional case follow new and original lines of research.