C¹ -Rational Quadratic Trigonometric Spline Fractal Interpolation Functions

Trigonometric interpolation has an essential role in geometric modeling of conic data. In this paper, a novel C1 -rational quadratic trigonometric spline fractal interpolation function with variable scaling and two families of shape parameters is introduced. We have investigated the convergence analysis of this fractal interpolant to a data-generating function in C3 from the uniform error bound. When the conic data is positive and monotone, we have derived sufficient conditions based on the scaling functions and shape parameters so that the resultant trigonometric spline FIF preserves these fundamental shapes of conic data. The proposed results are verified by generating positive and monotonic trigonometric spline fractal interpolation functions.