Positivity Preserving Interpolation of Positive Data by Rational Quadratic Trigonometric Spline
نویسندگان
چکیده
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 description of the rational quadratic trigonometric spline interpolant, positivity is preserved everywhere. Constraints are derived for shape parameters to preserve the positivity thorough positive data. The curves scheme under discussion is attained C 1 continuity.
منابع مشابه
C Rational Cubic/Linear Trigonometric Interpolation Spline with Positivity-preserving Property
A class of C rational cubic/linear trigonometric interpolation spline with two local parameters is proposed. Simple sufficient conditions for constructing positivity-preserving interpolation curves are developed. By using the boolean sum of quadratic trigonometric interpolating operators to blend together the proposed rational cubic/linear trigonometric interpolation splines as four boundary fu...
متن کاملMonotone Rational Trigonometric Interpolation
This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...
متن کاملTENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE
In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...
متن کاملShape Preserving Interpolation Using C2 Rational Cubic Spline
Abstract: This study proposes new C rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets. Sufficient conditions for the positivity and data constrained modeling of the rational interpolant are derived on one parameter while the remaining two parameters can further be utilized to change and modify t...
متن کاملShape Preserving Surfaces for the Visualization of Positive and Convex Data using Rational Bi-quadratic Splines
A smooth surface interpolation scheme for positive and convex data has been developed. This scheme has been extended from the rational quadratic spline function of Sarfraz [11] to a rational bi-quadratic spline function. Simple data dependent constraints are derived on the free parameters in the description of rational bi-quadratic spline function to preserve the shape of 3D positive and convex...
متن کامل