Shape Preserving Interpolation by Curves in Three Dimensions

1996 ◽  
pp. 39-46 ◽  
Author(s):  
Tim Goodman ◽  
Boon-Hua Ong
Keyword(s):  
Three Dimensions ◽  
Shape Preserving ◽  
Shape Preserving Interpolation

Shape-preserving interpolation by cubic splines

2010 ◽  
Vol 88 (5-6) ◽  
pp. 798-805 ◽  
Author(s):  
Yu. S. Volkov ◽  
V. V. Bogdanov ◽  
V. L. Miroshnichenko ◽  
V. T. Shevaldin
Keyword(s):  
Cubic Splines ◽  
Shape Preserving ◽  
Shape Preserving Interpolation

Shape-Preserving Interpolation by Parametrically Defined Curves

1988 ◽  
Vol 25 (6) ◽  
pp. 1453-1465 ◽  
Author(s):  
T. N. T. Goodman ◽  
K. Unsworth
Keyword(s):  
Shape Preserving ◽  
Shape Preserving Interpolation

Approximation by shape preserving interpolation splines

2001 ◽  
Vol 37 (3) ◽  
pp. 271-288 ◽  
Author(s):  
A. Kouibia ◽  
M. Pasadas
Keyword(s):  
Shape Preserving ◽  
Shape Preserving Interpolation

scholarly journals A Moment Problem for Discrete Nonpositive Measures on a Finite Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
M. U. Kalmykov ◽  
S. P. Sidorov
Keyword(s):  
Lower Bounds ◽  
Moment Problem ◽  
Finite Interval ◽  
Optimal Shape ◽  
Chebyshev System ◽  
Shape Preserving ◽  
Generalized Convex Functions ◽  
Moment Conditions ◽  
Shape Preserving Interpolation ◽  
Discrete Measures

We will estimate the upper and the lower bounds of the integral∫01Ω(t)dμ(t), whereμruns over all discrete measures, positive on some cones of generalized convex functions, and satisfying certain moment conditions with respect to a given Chebyshev system. Then we apply these estimations to find the error of optimal shape-preserving interpolation.

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.

Shape preserving interpolation by cubic G 1 splines in $${\mathbb{R}^3}$$

2008 ◽  
Vol 54 (2) ◽  
pp. 259-267 ◽  
Author(s):  
Gašper Jaklič ◽  
Emil Žagar
Keyword(s):  
Shape Preserving ◽  
Shape Preserving Interpolation

Shape preserving interpolation by space curves

1997 ◽  
Vol 15 (1) ◽  
pp. 1-17 ◽  
Author(s):  
T.N.T. Goodman ◽  
B.H. Ong
Keyword(s):  
Shape Preserving ◽  
Space Curves ◽  
Shape Preserving Interpolation
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