Shape preserving rational spline interpolation

1984 ◽  
pp. 431-441 ◽  
Author(s):  
John A. Gregory
Keyword(s):  
Spline Interpolation ◽  
Shape Preserving ◽  
Rational Spline

scholarly journals Shape preserving spline interpolation

1986 ◽  
Vol 18 (1) ◽  
pp. 53-57 ◽  
Author(s):  
John A Gregory
Keyword(s):  
Spline Interpolation ◽  
Shape Preserving

Application of shape-preserving spline interpolation to interactive editing of photogrammetric data

1978 ◽  
Author(s):  
L. E. Deimel ◽  
C. L. Doss ◽  
R. J. Fornaro ◽  
D. F. McAllister ◽  
J. A. Roulier
Keyword(s):  
Spline Interpolation ◽  
Shape Preserving ◽  
Interactive Editing

scholarly journals Shape Preserving Interpolation UsingC2Rational Cubic Spline

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Samsul Ariffin Abdul Karim ◽  
Kong Voon Pang
Keyword(s):  
Spline Interpolation ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Cubic Spline ◽  
Shape Preserving ◽  
Cubic Spline Interpolation ◽  
Positive Data ◽  
Shape Preserving Interpolation ◽  
Systems Of Linear Equations ◽  
Two Parameters

This paper discusses the construction of newC2rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parametersαi,βi, andγi. The sufficient conditions for the positivity are derived on one parameterγiwhile the other two parametersαiandβiare free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation withC2continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion andC2continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivativesdi,i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the newC2rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated isft∈C3t0,tnis also investigated in detail.

Monotone linear rational spline interpolation

1992 ◽  
Vol 9 (4) ◽  
pp. 313-319 ◽  
Author(s):  
Richard D. Fuhr ◽  
Michael Kallay
Keyword(s):  
Spline Interpolation ◽  
Rational Spline

scholarly journals Wind Velocity Data Interpolation Using Rational Cubic Spline

2018 ◽  
Vol 225 ◽  
pp. 04006
Author(s):  
Samsul Ariffin Bin Abdul Karim ◽  
S. Suresh Kumar Raju
Keyword(s):  
Wind Velocity ◽  
Hermite Polynomial ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Numerical Results ◽  
Data Interpolation ◽  
Velocity Data ◽  
Cubic Spline Interpolation ◽  
Rational Spline ◽  
The Given

Wind velocity data is always having positive value and the minimum value approximately close to zero. The standard cubic spline interpolation (not-a-knot and natural) as well as cubic Hermite polynomial may be produces interpolating curve with negative values on some subintervals. To cater this problem, a new rational cubic spline with three parameters is constructed. This rational spline will be used to preserve the positivity of the wind velocity data. Numerical results shows that the proposed scheme work very well and give visually pleasing interpolating curve on the given domain.

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