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Quantitative $ L ^{ 2 } $ Error Analysis for Interpolation Methods and Wavelet Expansions

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Construction of animation models out of captured data

Daniel Thalmann

This article describes a method of constructing parametric models out of captured motion and skeleton data. Casting the problem as scattered data interpolation, our work is based on a multi-step approximation for the interpolation function with motion data ...

IEEE2002

Approximation for the exponential integral (Theis well function)

David Andrew Barry

In this note, we provide an analytical approximation to the exponential integral valid for all values of its argument. The approximation is constructed by interpolation between the exponential integral's small and large asymptotes.The interpolation contain ...

2000

Interpolation Revisited

Michaël Unser, Philippe Thévenaz, Thierry Blu

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are ...

IEEE2000

Image Interpolation and Resampling

Michaël Unser, Philippe Thévenaz, Thierry Blu

This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as ...

Academic Press2000

Stable spectral methods on tetrahedral elements

Jan Sickmann Hesthaven

A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equa ...

SIAM PUBLICATIONS2000

Quantitative Fourier Analysis of Approximation Techniques: Part I—Interpolators and Projectors

Michaël Unser, Thierry Blu

We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes ...

IEEE1999

Minimum Support Interpolators with Optimum Approximation Properties

Michaël Unser, Philippe Thévenaz, Thierry Blu

We investigate the functions of given approximation order L that have the smallest support. Those are shown to be linear combinations of the B-spline of degree L-1 and its L-1 first derivatives. We then show how to find the functions that minimize the asym ...

IEEE1998

Digital position and velocity determination in controlled drive systems

Motion control of robotic or manipulator joints, tool machines axes or more genrally of drive systems require accurate position, velocity and possibly acceleration control. Today, these controls are almost always realized using digital controllers. Therefo ...

1992

Interpolation method for solving the transport equation in soil columns with irreversible kinetics

David Andrew Barry

This paper presents an approximate analytical method for describing irreversible kinetics in soil columns. The method, which produces exact results for the limiting cases of zero- and first-order kinetics, uses an interpOlation technique between those two ...

1986