Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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TL;DR: Simulation results demonstrate that the proposed approach outperforms the classical Francos-Friedlander technique in terms of lower SNR threshold.
24 citations
Book•
18 Oct 2013
TL;DR: The exponential spline as discussed by the authors is a generalization of the semiclassical cubic spline known in the literature as the exponential splines, which can preserve convexity and monotonicity present in the data.
Abstract: Herein, we discuss a generalization of the semiclassical cubic spline known in the literature as the exponential spline In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline A particular member of this family is uniquely specified by the choice of certain "tension" parameters
We first outline the theoretical underpinnings of the exponential spline This development roughly parallels the existing theory for cubic splines The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data
We next discuss the numerical computation of the exponential spline A variety of numerical devices are employed to produce a stable and robust algorithm An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines
We conclude with a consideration of the broad spectrum of possible uses of exponential splines in the applications Our primary emphasis is on computational fluid dynamics although the imaginative reader will recognize the wider generality of the techniques developed
24 citations
TL;DR: The results confirm the validity of constant velocity motion as a first-order model for frequency domain analysis of motion.
Abstract: Translations with piecewise cubic trajectories are studied in the frequency domain. This class of motion has as an important subcase: cubic spline trajectories. Translations with trajectories depending on time with general polynomial law are preliminarily considered, and a general theorem concerning this type of motion is introduced. The application of this theorem to the case of cubic time dependence and the consideration of finite-duration effects lead to the solution of the piecewise cubic trajectory case. The results, which are remarkably different from those concerning constant velocity translations, clearly indicate the importance of the role of velocity and time duration. In this respect, they confirm the validity of constant velocity motion as a first-order model for frequency domain analysis of motion. >
24 citations
TL;DR: In this article, the classical interpolation problems for cubic and rational splines are merged to get an adaptive rational interpolating spline which automatically uses cubic pieces to model unavoidable inflection points and retain convexity/concavity elsewhere.
Abstract: The classical interpolation problems for cubic and rational splines are merged to get an “adaptive” rational interpolating spline which automatically uses cubic pieces to model unavoidable inflection points and retain convexity/concavity elsewhere. An existence proof, a numerical method, and a series of examples are presented. Furthermore, the two-dimensional case is discussed.
24 citations
TL;DR: A rational bi-cubic function involving six shape parameters is presented for shape preserving interpolation problem for visualization of 3D positive data which is an extension of piecewise rational function in the form of cubic/quadratic involving three shape parameters.
24 citations