An Algorithm for Monotone Piecewise Bicubic Interpolation

Carlson, R.E.; Fritsch, F.N.

doi:10.1137/0726013

Cited by 58 publications

(28 citation statements)

References 3 publications

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“…Concerning monotonicity preserving surface fitting most research focussed on monotone bivariate interpolation. In [1,2,12] sufficient (and sometimes also necessary) conditions were derived for the monotonicity of piecewise polynomial patches interpolating data given at the grid points of a rectangular mesh. These conditions were transformed into a system of linear inequalities which in turn formed the basis for an algorithm.…”

Section: Related Workmentioning

confidence: 99%

“…The method we present in this paper is inspired by the algorithms given in [1,2,12], where C 1 monotone increasing spline functions interpolating gridded data are constructed by iteratively adjusting initially estimated gradient values at each grid point. It is a kind of Hermite interpolation, where the gradient values are adjusted to ensure monotonicity.…”

Section: Monotonic Polynomial Interpolationmentioning

confidence: 99%

“…be free of critical points inside its domain. Note that the latter property is not guaranteed by the standard axis aligned monotonicity definition as used in [1,2,12].…”

Section: Monotonic Polynomial Interpolationmentioning

confidence: 99%

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Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data

Allemand-Giorgis

Bonneau

Hahmann

et al. 2014

Mathematics and Visualization

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A method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C 1 -continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C 1 surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm.

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Section: Related Workmentioning

confidence: 99%

Section: Monotonic Polynomial Interpolationmentioning

confidence: 99%

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Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data

Allemand-Giorgis

Bonneau

Hahmann

et al. 2014

Mathematics and Visualization

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“…There are several ways to implement interpolation and in this study a shape-preserving piecewise cubic polynomial was chosen [18,19]. This function is directly available in MATLAB and in contrast to for example spline functions, it seeks to preserve local minima and other features of the data such that extreme artifacts are not introduced by the interpolation (see Figure 2).…”

Section: Theorymentioning

confidence: 99%

Handling of Rayleigh and Raman scatter for PARAFAC modeling of fluorescence data using interpolation

Bahram

Bro

Stedmon³

et al. 2006

Journal of Chemometrics

474

168

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Fluorescence excitation-emission matrix (EEM) measurements are useful in fields such as food science, analytical chemistry, biochemistry and environmental science. EEMs contain information which can be modeled using the parallel factor analysis (PARAFAC) model but the data analysis is often complicated due to both Rayleigh and Raman scattering. There are several established ways to deal with scattering effects. However, all of these methods have associated problems. This paper develops a new method for handling scattering using interpolation in the areas affected by first-and second-order Rayleigh and Raman scatter in such a way that the interfering signal is, at best, removed. The suggested method is fast and requires no additional input other than specifying the scattering region. The results of the proposed method were compared with those obtained from common alternative approaches used for preprocessing fluorescence data before analysis with PARAFAC and were shown to be equally good for various types of EEM data. The main advantage of the interpolation method is in its lack of additional metaparameters, its algorithmic speed and subsequent speed-up of PARAFAC modeling. It also allows for using EEM data in software not able to handle missing data.

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“…This allows arbitrary order in the finite difference methods for computing the derivatives and then, by storing the resulting state variables, a simple bilinear interpolation can be used at runtime without concern for derivatives being continuous across grid points. Higher-order interpolation schemes such as BIMOND [42,43] can be introduced at the precompute stage to up-sample the table density, increasing accuracy without significant impact on runtime.…”

Section: Table Interpolationmentioning

confidence: 99%

Modeling asymmetric cavity collapse with plasma equations of state

2016

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We explore the effect that equation of state (EOS) thermodynamics has on shock-driven cavity-collapse processes. We account for full, multidimensional, unsteady hydrodynamics and incorporate a range of relevant EOSs (polytropic, QEOS-type, and SESAME). In doing so, we show that simplified analytic EOSs, like ideal gas, capture certain critical parameters of the collapse such as velocity of the main transverse jet and pressure at jet strike, while also providing a good representation of overall trends. However, more sophisticated EOSs yield different and more relevant estimates of temperature and density, especially for higher incident shock strengths. We model incident shocks ranging from 0.1 to 1000 GPa, the latter being of interest in investigating the warm dense matter regime for which experimental and theoretical EOS data are difficult to obtain. At certain shock strengths, there is a factor of two difference in predicted density between QEOS-type and SESAME EOS, indicating cavity collapse as an experimental method for exploring EOS in this range.

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An Algorithm for Monotone Piecewise Bicubic Interpolation

Cited by 58 publications

References 3 publications

Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data

Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data

Handling of Rayleigh and Raman scatter for PARAFAC modeling of fluorescence data using interpolation

Modeling asymmetric cavity collapse with plasma equations of state

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