Abstract
A newC1piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated asO(h3). Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.
Highlights
Shape preserving interpolation spline is an effective tool to visualize the data in the form of curves and surfaces
Hussain and Saleem [4] introduced a C1 piecewise rational quadratic trigonometric polynomial spline which defines two shape parameters in each subinterval, and they extended the spline to piecewise rational biquadratic function with four shape parameters in each rectangular patch
A C1 piecewise rational quadratic trigonometric spline is discussed in this paper to address the problem of the scientific data visualization
Summary
Shape preserving interpolation spline is an effective tool to visualize the data in the form of curves and surfaces. The constrains on the shape parameters are derived so as to obtain a shape preserving C1 piecewise rational quadratic trigonometric interpolation spline for positive, monotone, and constrained data. Two of these parameters are constrained by simple data-dependent conditions to preserve the inherited shape feature of the data while the other two are kept free to modify the shape of the generated curve.
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