On Non-Tensor Product Bivariate Fractal Interpolation Surfaces on Rectangular Grids

Mathematics

Vasileios Drakopoulos¹  Polychronis Manousopoulos² 

[1] Department of Computer Science and Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 157 84 Athens, Greece;

关键词: attractor;    bivariate surfaces;    dynamic system;    fractal interpolation;    iterated function system;   

DOI  :  10.3390/math8040525

来源: DOAJ

【 摘 要 】

Some years ago, several authors tried to construct fractal surfaces which pass through a given set of data points. They used bivariable functions on rectangular grids, but the resulting surfaces failed to be continuous. A method based on their work for generating fractal interpolation surfaces is presented. Necessary conditions for the attractor of an iterated function system to be the graph of a continuous bivariable function which interpolates a given set of data are also presented here. Moreover, a comparative study for four of the most important constructions and attempts on rectangular grids is considered which points out some of their limitations and restrictions.

【 授权许可】

Unknown