Positivity Preserving Interpolation of Positive Data by Rational Quadratic Trigonometric Spline

Abstract

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.