NATURAL CUBIC SPLINE COALESCENCE HIDDEN VARIABLE FRACTAL INTERPOLATION SURFACES

作者：Chand A K B^*

来源：Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 2012, 20(2): 117-131.

DOI：10.1142/S0218348X12500119

• Fractals
• Iterated Function System
• Hidden Variables
• Cardinal CHFIF
• Non-Self-Affine
• Fractal Interpolation Surface
• Surface Approximation

Fractal interpolation functions provide a new light to the natural deterministic approximation and modeling of complex phenomena. The present paper proposes construction of natural cubic spline coalescence hidden variable fractal interpolation surfaces (CHFISs) over a rectangular grid R through the tensor product of univariate bases of cardinal natural cubic spline coalescence hidden variable fractal interpolation functions (CHFIFs). Natural cubic CHFISs are self-affine or non-self-affine in nature depending on the IFS parameters of univariate natural cubic spline CHFIFs. An upper bound of the error between the natural cubic spline blended coalescence fractal interpolant and the original function is deduced. Convergence of the natural cubic CHFIS to the original function f is an element of C-4[R], and their derivatives are deduced. The effects free variables, constrained free variables and hidden variables are discussed on the natural cubic spline CHFIS with suitably chosen examples.

• 出版日期2012-6