On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1594" altimg="si2.svg"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> cubic quasi-interpolating splines and their computation by subdivision via blossoming

Fast Computation by Subdivision of Multidimensional Splines and Their Applications

We present theory and algorithms for fast explicit computations of uniand multi-dimensional periodic splines of arbitrary order at triadic rational points and of splines of even order at diadic rational points. The algorithms use the forward and the inverse Fast Fourier transform (FFT). The implementation is as fast as FFT computation. The algorithms are based on binary and ternary subdivision ...

Computation of interpolatory splines via triadic subdivision

We present an algorithm for computation of interpolatory splines of arbitrary order at triadic rational points. The algorithm is based on triadic subdivision of splines. Explicit expressions for the subdivision symbols are established. These are rational functions. The computations are implemented by recursive filtering.

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...

Variational Subdivision for Natural Cubic Splines

This paper explores the intrinsic link between natural cubic splines and subdivision. Natural cubic splines are deened via the varia-tional problem of minimizing a simple approximation of bending energy. A subdivision scheme is derived which converges to the minimizer of this particular variational problem. x1. Introduction Geometric design is the study of the representation of shapes with math...

A Blossoming Development of Splines