On Non-Tensor Product Bivariate Fractal Interpolation Surfaces on Rectangular Grids
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 pr...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-04-01
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Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/8/4/525 |
Summary: | 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. |
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ISSN: | 2227-7390 |