Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces

Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces

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A class of zipper fractal functions is more versatile than corresponding classes of traditional and fractal interpolants due to a binary vector called a signature.A zipper fractal function constructed through a zipper iterated function system (IFS) allows one to use negative and positive horizontal scalings.In contrast, a fractal function constructed with an IFS uses positive horizontal scalings only.

This article introduces some novel classes of continuously differentiable convexity-preserving synovex one grass zipper fractal interpolation curves and surfaces.First, we construct zipper fractal interpolation curves for the given univariate Hermite interpolation data.Then, we generate zipper fractal interpolation surfaces over a rectangular grid click here without using any additional knots.

These surface interpolants converge uniformly to a continuously differentiable bivariate data-generating function.For a given Hermite bivariate dataset and a fixed choice of scaling and shape parameters, one can obtain a wide variety of zipper fractal surfaces by varying signature vectors in both the x direction and y direction.Some numerical illustrations are given to verify the theoretical convexity results.