Closed fractal interpolation surfaces

被引：28
作者：
Bouboulis, P. [1 ]
Dalla, L.
机构：
[1] Univ Athens, Dept Informat & Telecommun, GR-15784 Athens, Greece
[2] Univ Athens, Dept Math, GR-15784 Athens, Greece
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 327卷 / 01期
关键词：
fractal interpolation; iterated function systems; bivariate fractal interpolation surfaces; closed fractal surfaces;
D O I：
10.1016/j.jmaa.2006.04.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Based on the construction of bivariate fractal interpolation surfaces, we introduce closed spherical fractal interpolation surfaces. The interpolation takes place in spherical coordinates and with the transformation to Cartesian coordinates a closed surface arises. We give conditions for this construction to be valid and state some useful relations about the Hausdorff and the Box counting dimension of the closed surface. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：116 / 126
页数：11
相关论文
共 16 条
[1]   RECURRENT ITERATED FUNCTION SYSTEMS [J].
BARNSLEY, MF ;
ELTON, JH ;
HARDIN, DP .
CONSTRUCTIVE APPROXIMATION, 1989, 5 (01) :3-31
[2]  
BOUBOULIS P, 2006, IN PRESS J BIFUR JUL
[3]  
BOUBOULIS P, IN PRESS J APPROX TH
[4]   On the parameter identification problem in the plane and the polar fractal interpolation functions [J].
Dalla, L ;
Drakopoulos, V .
JOURNAL OF APPROXIMATION THEORY, 1999, 101 (02) :289-302
[5]   Bivariate fractal interpolation functions on grids [J].
Dalla, L .
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2002, 10 (01) :53-58
[6]  
Falconer K., 1997, Techniques in Fractal Geometry
[7]  
FALCONER K, 1999, FRACTAL GEOMETRY
[8]   FRACTAL INTERPOLATION SURFACES AND A RELATED 2-D MULTIRESOLUTION ANALYSIS [J].
GERONIMO, JS ;
HARDIN, D .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 176 (02) :561-586
[9]   The Minkowski dimension of the bivariate fractal interpolation surfaces [J].
Malysz, R .
CHAOS SOLITONS & FRACTALS, 2006, 27 (05) :1147-1156
[10]  
Massopust P. R., 1994, FRACTAL FUNCTIONS FR
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