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Cardinal Hermite Spline Interpolation with Shifted Nodes

Gerlind Plonka, Manfred Tasche
1994 Mathematics of Computation  
Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes.  ...  This algorithm is shown to be also applicable to computing the periodic Hermite spline interpolant.  ...  For solving the generalized Hermite spline interpolation problem for r > 2, the Euler-Frobenius functions hrm " (u = 0, ... , r -1) can be similarly introduced by using B-splines with r-fold knots. 3.  ... 
doi:10.2307/2153287 fatcat:3p7yanj6xbfz5ba7mssqzq7kya

Geodesic Hermite Spline Curve on Triangular Meshes

Yujin Ha, Jung-Ho Park, Seung-Hyun Yoon
2021 Symmetry  
The conventional Hermite interpolation method is extended such that the generated curve lies on M.  ...  By combining cubic Hermite interpolation and newly devised geodesic operations, a geodesic Hermite spline curve is constructed on a triangular mesh.  ...  Finally, the geodesic Hermite spline curve consists of a set of cubic Bézier curves generated by this method. Hermite Spline Curve The method is based on Hermite interpolation.  ... 
doi:10.3390/sym13101936 fatcat:s67gft3g6jg6djbbi6leecgjcm

Cardinal Hermite spline interpolation with shifted nodes

Gerlind Plonka, Manfred Tasche
1994 Mathematics of Computation  
Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes.  ...  This algorithm is shown to be also applicable to computing the periodic Hermite spline interpolant.  ...  For solving the generalized Hermite spline interpolation problem for r > 2, the Euler-Frobenius functions hrm " (u = 0, ... , r -1) can be similarly introduced by using B-splines with r-fold knots.  ... 
doi:10.1090/s0025-5718-1994-1250775-2 fatcat:5cddj5ywarbgzjxifmrf3fpoh4

Real-time interpolation of streaming data

Roman Dębski
2020 Computer Science  
The results presented show that the cubic Hermite splines generated by heuristic MinAJ2 significantly outperformed these based on finite difference schemas in terms of all tested performance measures (  ...  One of the key elements of real-time $C^1$-continuous cubic spline interpolation of streaming data is an estimator of the first derivative of the interpolated function that is more accurate than the ones  ...  The proposed approach is quite general. It can be directly applied to streams of univariate functional data like time-series.  ... 
doi:10.7494/csci.2020.21.4.3932 fatcat:vcixlw2obbaknn6tmmluhrqhdq

Efficient Algorithms for Periodic Hermite Spline Interpolation

G. Plonka, M. Tasche
1992 Mathematics of Computation  
Periodic Hermite spline interpolants on an equidistant lattice are represented by the Bézier technique as well as by the fi-spline method.  ...  Applying the known de Casteljau algorithm and the de Boor algorithm, respectively, we obtain new efficient real algorithms for periodic Hermite spline interpolation. (cf. [2]).  ...  Further, one can see that the generalized Euler-Frobenius polynomials are very important for periodic Hermite spline interpolation.  ... 
doi:10.2307/2153209 fatcat:o5ogpkybsrbudlctgzqvpdoyta

Efficient algorithms for periodic Hermite spline interpolation

G. Plonka, M. Tasche
1992 Mathematics of Computation  
Periodic Hermite spline interpolants on an equidistant lattice are represented by the Bézier technique as well as by the fi-spline method.  ...  Applying the known de Casteljau algorithm and the de Boor algorithm, respectively, we obtain new efficient real algorithms for periodic Hermite spline interpolation. (cf. [2]).  ...  Further, one can see that the generalized Euler-Frobenius polynomials are very important for periodic Hermite spline interpolation.  ... 
doi:10.1090/s0025-5718-1992-1122075-0 fatcat:omlw2upwvrgttcl7buh3nvlaou

Adjustable Piecewise Quartic Hermite Spline Curve with Parameters

Jin Xie, Xiaoyan Liu, Shaojian Qu
2021 Mathematical Problems in Engineering  
the classical cubic Hermite interpolating spline curves.  ...  In this paper, the quartic Hermite parametric interpolating spline curves are formed with the quartic Hermite basis functions with parameters, the parameter selections of the spline curves are investigated  ...  Basic Concepts of Cubic Hermite Interpolation Spline Definition 1.  ... 
doi:10.1155/2021/2264871 fatcat:77aoxtfyavdzzkiypamhgeurli

Statistical optimality of Hermite splines

Virginie Uhlmann, Julien Fageot, Harshit Gupta, Michael Unser
2015 2015 International Conference on Sampling Theory and Applications (SampTA)  
Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation.  ...  We focus on second-order Lévy processes-the integrated version of Lévy processes-and rely on cubic Hermite splines to approximate the original continuous-time signal from its samples and its derivatives  ...  (e) Reconstruction s Her of the original continuous-time process s using Hermite spline interpolation.  ... 
doi:10.1109/sampta.2015.7148885 fatcat:ag64j4mafzeinjzmrz4fgmw4rm

Developments in bivariate spline interpolation

G. Nürnberger, F. Zeilfelder
2000 Journal of Computational and Applied Mathematics  
The aim of this survey is to describe developments in the ÿeld of interpolation by bivariate splines.  ...  We summarize results on the dimension and the approximation order of bivariate spline spaces, and describe interpolation methods for these spaces. Moreover, numerical examples are given.  ...  Generally, given a basis {B i ; i = 1; : : : ; d}, of a spline space and a set of linear functionals { i : i = 1; : : : ; d}, a quasi-interpolant s f of a su ciently smooth function f from this spline  ... 
doi:10.1016/s0377-0427(00)00346-0 fatcat:42yhs4ss7zapzng54jhwewst6m

About one method of constructing Hermite trigonometric splines [article]

V.P. Denysiuk
2021 arXiv   pre-print
The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered.  ...  Examples of construction of trigonometric Hermite splines of the first and second orders are given. The proposed method can be recommended for practical use.  ...  Note that the problem of constructing a Hermite polynomial polynomial on a segment in general is considered in detail, for example, in [2] ; the construction of Hermite polynomial splines is considered  ... 
arXiv:2110.04779v1 fatcat:tepxzrb75rbbxnzc6ftrqlfvk4

On Convexity Preserving C1 Hermite Spline Interpolation

I. Verlan
1995 Computer Science Journal of Moldova  
The problem of convexity preserving interpolation using C1 Hermite splines with one free generating function is considered.  ...  The aim of this paper is to present a general approach to the problem of shape preserving interpolation.  ...  For the parabolic Hermite splines generated by the function (4) we get that these splines preserve convexity(concavity) of data if the additional knot τ on the mesh is choosen so, that τ > 1 − 2λ i for  ... 
doaj:876618499e2445d2a68cc755c18c8d7d fatcat:yqndh36zh5bzxmfhbpkftjncs4

Page 8485 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
The authors discuss generalized B-splines (GB-splines).  ...  Interconnections between generalized B-splines and B- splines are established. Special attention is paid to the case of the uniformly spaced knots.” 99m:41013 41A15 41A29 Ksasov, Boris I.  ... 

Page 8027 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
This is a survey of recent progress on generalized Hermite-Fejér interpolation, in particular for Chebyshev nodes.  ...  Generalized Hermite-Fejér interpolation is an interpolation method which uses polynomials whose derivatives up to a certain order m vanish at the prescribed interpolation nodes.  ... 

Hermite Snakes With Control of Tangents

Virginie Uhlmann, Julien Fageot, Michael Unser
2016 IEEE Transactions on Image Processing  
Our curve model relies on Hermite spline interpolation and can easily generate curves with sharp discontinuities; it also grants direct access to the tangent at each location.  ...  With these two features, the Hermite snake distinguishes itself from classical spline-snake models and allows one to address certain bioimaging problems in a more efficient way.  ...  Fig. 6 . 6 Generation of sharp corners using (a) traditional cubic-spline snake, (b) exponential-spline snake, and (c) Hermite-spline snake.  ... 
doi:10.1109/tip.2016.2551363 pmid:27071167 fatcat:wqw76nheajhp7flz55u4fpkbn4

Support and Approximation Properties of Hermite Splines [article]

Julien Fageot, Shayan Aziznejad, Michael Unser, Virginie Uhlmann
2019 arXiv   pre-print
Then, we precisely quantify the approximation power of Hermite splines for reconstructing functions and their derivatives, and show that they are asymptotically identical to cubic B-splines for these tasks  ...  Hermite splines therefore combine optimal localization and excellent approximation power, while retaining interpolation properties and closed-form expression, in contrast to existing similar approaches  ...  ), and interpolating, which is not the case for cubic B-splines.  ... 
arXiv:1902.02565v2 fatcat:pgujjgiytbhwdaoc5hycimxhhi
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