Journal ArticleDOI
A new class of fractal interpolation surfaces based on functional values
A. K. B. Chand,N. Vijender +1 more
Reads0
Chats0
TLDR
In this paper, the authors developed two types of rational fractal interpolation surfaces (FISs) on a rectangular grid that contain scaling factors in both directions and two positive real parameters which are referred as shape parameters.Abstract:
Fractal interpolation is a modern technique for fitting of smooth/non-smooth data. Based on only functional values, we develop two types of 𝒞1-rational fractal interpolation surfaces (FISs) on a rectangular grid in the present paper that contain scaling factors in both directions and two types of positive real parameters which are referred as shape parameters. The graphs of these 𝒞1-rational FISs are the attractors of suitable rational iterated function systems (IFSs) in ℝ3 which use a collection of rational IFSs in the x-direction and y-direction and hence these FISs are self-referential in nature. Using upper bounds of the interpolation error of the x-direction and y-direction fractal interpolants along the grid lines, we study the convergence results of 𝒞1-rational FISs toward the original function. A numerical illustration is provided to explain the visual quality of our rational FISs. An extra feature of these fractal surface schemes is that it allows subsequent interactive alteration of the shape of...read more
Citations
More filters
Journal ArticleDOI
Cyclic iterated function systems
TL;DR: In this article, a generalization of the Banach contraction principle, namely cyclic contraction and cyclic �-consistency, was proposed for the application of fractal fractals.
Journal ArticleDOI
Approximation by Hidden Variable Fractal Functions: A Sequential Approach
TL;DR: In this article, the authors establish new kind of hidden variable fractal approximants which possess convergence and non-differentiability simultaneously for any choice of the scaling factors, without imposing any condition on the scaling vector.
Journal ArticleDOI
Partially blended constrained rational cubic trigonometric fractal interpolation surfaces
A. K. B. Chand,K. R. Tyada +1 more
TL;DR: In this article, a new family of partially blended rational cubic trigonometric fractal interpolation surfaces (RCTFISs) with a combination of blending functions and univariate rational trigonal interpolation functions along the grid lines of the interpolation domain is presented.
Journal ArticleDOI
Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces
TL;DR: In this article, the rational cubic fractal interpolation surfaces (FISs) were developed by using the blending functions and rational cubic FIFs with two shape parameters in each sub-interval along the grid lines of the interpolation domain.
Journal ArticleDOI
Shape preserving constrained and monotonic rational quintic fractal interpolation functions
A. K. B. Chand,K. R. Tyada +1 more
TL;DR: In this article, a rational quintic fractal interpolation function (RQFIF) was proposed to preserve the monotonicity aspect of given restricted types of monotonic data.
References
More filters
Book
Fractals Everywhere
TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.
Journal ArticleDOI
Fractal Functions and Interpolation
TL;DR: In this article, the authors introduce iterated function systems whose attractorsG are graphs of continuous functionsf∶I→R, which interpolate the data according tof(x��i)=y fixmei fori e {0,1,⋯,N}.
Journal ArticleDOI
The calculus of fractal interpolation functions
TL;DR: The calculus of deterministic fractal functions is introduced in this article, which can be explicitly indefinitely integrated any number of times, yielding a hierarchy of successively smoother interpolation functions which generalize splines and which are attractors for iterated function systems.
Journal ArticleDOI
Generalized Cubic Spline Fractal Interpolation Functions
G. P. Kapoor,A. K. B. Chand +1 more
TL;DR: In view of wide ranging applications of the classical cubic splines in several mathematical and engineering problems, the explicit construction of cubic spline FIF $f_{\Delta}(x)$ through moments is developed and it is shown that the sequence f_{Delta_k} (x) converges to the defining data function on two classes of sequences of meshes at least as rapidly as the square of the mesh norm approaches to zero.
Journal ArticleDOI
The Study on Bivariate Fractal Interpolation Functions and Creation of Fractal Interpolated Surfaces
Heping Xie,Hongquan Sun +1 more
TL;DR: In this paper, the methods of construction of a fractal surface are introduced, the principle of bivariate fractal interpolation functions is discussed, and the theorem of the uniqueness of an iterated function system of BIFs is proved.
Related Papers (5)
Toward a Unified Methodology for Fractal Extension of Various Shape Preserving Spline Interpolants
S. K. Katiyar,A. K. B. Chand +1 more