A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Ten lectures on wavelets
Interpolatory subdivision schemes and wavelets
Journal of Approximation Theory
Multidimensional Interpolatory Subdivision Schemes
SIAM Journal on Numerical Analysis
Approximation properties of multivariate wavelets
Mathematics of Computation
Multivariate refinement equations and convergence of subdivision schemes
SIAM Journal on Mathematical Analysis
Optimal Interpolatory Subdivision Schemes in Multidimensional Spaces
SIAM Journal on Numerical Analysis
Analysis and construction of optimal multivariate biorthogonal wavelets with compact support
SIAM Journal on Mathematical Analysis
Stationary Subdivision
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
Computer Aided Geometric Design
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
Computer Aided Geometric Design
Bi-frames with 4-fold axial symmetry for quadrilateral surface multiresolution processing
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
Bessel multiwavelet sequences and dual multiframelets in Sobolev spaces
Advances in Computational Mathematics
Journal of Approximation Theory
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We analyze the approximation and smoothness properties of quincunx fundamental refinable functions. In particular, we provide a general way for the construction of quincunx interpolatory refinement masks associated with the quincunx lattice in R2. Their corresponding quincunx fundamental refinable functions attain the optimal approximation order and smoothness order. In addition, these examples are minimally supported with symmetry. For two special families of such quincunx interpolatory masks, we prove that their symbols are nonnegative. Finally, a general way of constructing quincunx biorthogonal wavelets is presented. Several examples of quincunx interpolatory masks and quincunx biorthogonal wavelets are explicitly computed.