Shape preserving affine fractal interpolation surfaces

  • N. Vijender
  • A. K. B. Chand


We propose a class of affine fractal interpolation surfaces (FISs) that stitch a given set of surface data arranged on a rectangular grid. The proposed FISs are blending of the affine fractal interpolation functions (FIFs) constructedalong the grid lines of given interpolation domain. We investigate the stability results of the developed affine FIS with respect to its independent and dependent variables at the grids. These affine FISs preserve the inherited shape of given surface data (like monotonicity, positivity, and convexity), whenever the associated affine FIFs mimic the shape of the univariate data sets along the grid lines of interpolation domain. By using suitable conditions on the scaling factors, we study the monotonicity preserving interpolation via $\mathcal{C}^0$-continuous affine FIFs. Under these conditions, apart from one scaling factor, the rest depend only on the functional values but not on both the horizontal contractive factors and slopes at the grids.
This weak restriction provides a large flexibility in the
selection of the scaling factors for monotonicity preserving $\mathcal{C}^0$-continuous affine FIFs/FISs. The positivity criterion for $\mathcal{C}^0$-continuous affine FIF is also deduced.