Constructions And Properties Of Fractal Interpolation Functions On Restricted Domain

Fractal interpolation is an efficient interpolating method to model irregular data.The fractal interpolation function?FIF?used in this method is generated by iterated function systems?IFS?,and the vertical scaling factor parameters in the IFS have an important influence on the shapes and properties of the FIF.A fractal surface is a fractal set inR³ which is a graph of some continuous function onR².The construction of fractal surfaces is closely related to the fractal interpolation functions?FIF?.The problem of parameter identification of the FIFs with function vertical scaling factors is investigated in the present paper.Furthermore,we study the methods of constructions and properties of several kinds of fractal surfaces on the basis of the FIF.Some sufficient conditions on the function vertical scaling factors are proposed so that the corresponding FIFs are restricted within a given range.In addition,the relationships between the fractal surface and the FIFs are illustrated by using several numerical examples in this paper.The details are organized as follows:In Chapter I,a brief introduction of the background about the fractal and the fractal interpolation is given.In addition,we summarize the domestic and foreign literature and describe the research significance of the thesis.In Chapter II,we briefly recall some basic definitions and related results on the content of the present article.In Chapter III,some sufficient conditions on the function vertical scaling factors are proposed so that the corresponding FIFs are restricted within a given range.Furthermore,several numerical examples are given,which illustrate the relationships between the graphs of the FIFs and the variable parameters in the restricted range.In Chapter IV,several kinds of fractal surfaces are constructed on R³ according to the responding FIF.Furthermore,we discuss the relationships between the fractal surfaces and vertical scaling factors.In Chapter V,we make a summary of the full text and give a prospect.