Rational Cubic Spline For Shape Preserving Interpolation
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Date
2017-08
Authors
Abdul Karim, Samsul Ariffin
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
A new rational cubic spline function of the form cubic numerator and quadratic
denominator has been proposed. This rational cubic spline has three parameters. The
parameters can be used to modify the shape of the interpolating curve. Shape
preservation for positivity, monotonicity and convexity interpolations as well as
constrained data interpolation which the data lie on one side of a given constraint line
are investigated in details. The shape preservation conditions are derived on one
parameter while the other two parameters provide freedom in controlling the final
interpolating curves. Degree smoothness attained is C1 . Local control of the rational
interpolant for value-control, inflection point and convexity control also is considered.
The proposed rational cubic splines has able to reduce the complexity of the non-linear
equations. Besides, the error analysis of the rational interpolant when the interpolated
function is C3 also has been discussed. The univariate rational cubic spline is extended
to the bivariate cases using partially blended rational bi-cubic function. The proposed
partially blended rational bi-cubic surface have 12 parameters and 8 of them are free
to be utilized to control the shape of the resulting surface. The conditions for shape
preservation of positive, monotonic, convex interpolations and constrained
interpolation for data that lying on one side of the constraint surface are derived on
four parameters. Numerical examples are illustrated graphically to show the capability
of the proposed schemes.
Description
Keywords
Rational cubic spline , for shape Preserving interpolation