The theory of fractal interpolated surface and its applications

谢和平,; 孙洪泉,; Xie, Heping; Sun, Hongquan

doi:10.1007/bf02457536

Cited by 4 publications

(1 citation statement)

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“…In [9], a different construction of an attractor that contains the interpolation points of a rectangular data set was introduced, but generally is not a graph of a continuous function. This methodology is repeated by the same authors in [10]. The breakthrough realised in [7] permitted the construction of [11] in which a method based on rotations and reflections for constructing fractal interpolation surfaces and volumes through points sampled on rectangular lattices is presented.…”

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

Drakopoulos

Manousopoulos

2020

Mathematics

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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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confidence: 99%