A novel approach to surface interpolation: Marriage of Coons technique and univariate fractal functions

The current article is intended to demonstrate that the theory of fractal functions when applied in conjunction with methods in the classical numerical analysis can supply new solution techniques that supplement and subsume the existing ones. To this end, in the first part of the paper, we review a C1-continuous rational cubic fractal interpolation function (FIF) introduced recently [Viswanathan and Chand, Elec. Trans. Numer. Anal. 41 (2014), pp. 420-442]. We carry out the con- vergence analysis of this univariate rational FIF and determine suitable values of the derivative parameters so that its global smoothness enhances to C2. In the subsequent part of the article, we apply Coons technique of transfinite interpolation in order to construct a new kind of C1-continuous bivariate fractal interpolation surface.