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In the present paper a new method is developed for smooth rational cubic trigonometric interpolation based on values of function which is being interpolated. This rational cubic trigonometric spline is used to constrain the shape of the interpolant such as to force it to be in the given region by selecting suitable parameters. The more important achievement(More)
A weighted rational cubic spline interpolation has been constructed using rational spline with quadratic denominator. GC 1-piecewise rational cubic spline function involving parameters has been constructed which produces a monotonic interpolant to given mono-tonic data. The degree of smoothness of this spline is GC 2 in the interpolating interval when the(More)
I. Introduction Rational spline is a commonly used spline function. In many cases the rational spline curves better approximating functions than the usual spline functions. It has been observed that many simple shapes including conic section and quadric surfaces can not be represented exactly by piecewise polynomials, whereas rational polynomials can(More)
The aim of this paper presents an analysis of weighted quadratic trigonometric spline with two shape parameters which interpolate on function value. This interpolating is C 1 continuous with quadratic denominator. Constrain control of this rational quadratic trigonometric spline is derived which force it be bound in the given region. Approximation property(More)
A C 2 cubic rational spline with cubic numerator and linear denominator has been constructed .This rational spline belongs to C 2 in the interpolating interval.By selecting the suitable value of shape parameters,it is easy to find the constrains for the shape of interpolating curve to lie above,below or between the given straight lines.Also the error bound(More)
— This paper describes the use of GC 1 quadratic trigonometric spline interpolant for preserving the shape of monotonic data. Simple data dependent constraints are derived for shape parameters to preserve the monotonicity through monotonic data. The necessary and sufficient conditions for the monotonicity of the trigonometric quadratic interpolant have been(More)
In Computer Aided Geometric Design it is often needed to produce a positivity preserving curve according to the given positive data. The main focus of this work is to visualize the positive data in such a way that its display looks smooth and pleasant. A rational quadratic trigonometric spline function with three shape parameters has been developed. In the(More)