Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces

Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces

Blog Article

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 zipper fractal interpolation curves and surfaces.First, we Custom Shaped Acrylic Plaque construct zipper fractal interpolation curves for the given univariate Hermite interpolation data.

Then, we generate zipper fractal interpolation surfaces over a rectangular grid 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 Lip Care numerical illustrations are given to verify the theoretical convexity results.