On monotone and convex spline interpolation
Mathematics of Computation
Co-Monotone interpolating splines of arbitrary degree—a local approach
SIAM Journal on Scientific and Statistical Computing
Refinement and subdivision for spaces of integer translates of a compactly supported function
Numerical analysis 1987
An algorithm for monotone piecewise bicubic interpolation
SIAM Journal on Numerical Analysis
On refinement equations determined by Po´lya frequency sequences
SIAM Journal on Mathematical Analysis
Using the refinement equation for evaluating integrals of wavelets
SIAM Journal on Numerical Analysis
Characterization of local strict convexity preserving interpolation methods by C1 functions
Journal of Approximation Theory
Totally positive bases for shape preserving curve design and optimality of B-splines
Computer Aided Geometric Design
C1 comonotone Hermite interpolation via parametric cubics
Journal of Computational and Applied Mathematics
Stationary Subdivision
C1 Interpolatory Subdivision with Shape Constraints for Curves
SIAM Journal on Numerical Analysis
Approximation by GP box-splines on a four-direction mesh
Journal of Computational and Applied Mathematics
Multiresolution analyses originated from nonstationary subdivision schemes
Journal of Computational and Applied Mathematics
Shape Constraints and Optimal Bases for $C^1$ Hermite Interpolatory Subdivision Schemes
SIAM Journal on Numerical Analysis
Rational splines for Hermite interpolation with shape constraints
Computer Aided Geometric Design
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In this paper we present a method for the construction of C^1 Hermite interpolants obtained from a particular family of refinable spline functions introduced by Gori and Pitolli. They constitute a one-parameter subfamily of the Hermite interpolants generated by the general Merrien's subdivision scheme. We compare this family to the other one-parameter subfamily studied by Merrien and Sablonniere and Lyche and Merrien on the solution of two-points Hermite interpolation problems with arbitrary monotonicity or convexity constraints.