TY - JOUR
T1 - Coalescence Cubic Spline Fractal Interpolation Surfaces.
AU - ARYA KUMAR BEDABRATA CHAND
JO - International Journal of Numerical Analysis Modeling Series B
VL - 3
SP - 207
EP - 223
PY - 2012
DA - 2012/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/279.html
KW - Fractals
KW - Iterated Function System
KW - Fractal Interpolation Surface
KW - Cardinal Cubic Spline
KW - Hidden Variables
KW - CHFIS
KW - Non-self-affine and Surface Approximation
AB - Fractal geometry provides a new insight to the approximation and modelling of scientific data.This paper presents the construction of coalescence cubic spline fractal interpolation
surfaces over a rectangular grid D through the corresponding univariate basis of coalescence cubic
fractal splines of Type-I or Type-II. Coalescence cubic spline fractal surfaces are self-affine or nonself-
affine in nature depending on the iterated function systems parameters of these univariate
fractal splines. Upper bounds of L_&#8734-norm of the errors between between a coalescence cubic
spline fractal surface and an original function f &#8712 C^4[D], and their derivatives are deduced.
Finally, the effects of free variables, constrained free variables and hidden variables are discussed
for coalescence cubic spline fractal interpolation surfaces through suitably chosen examples.