Fractal Interpolation On Arbitrary Triangle Domain

This article discusses the surface fractal interpolation problem, proposed within the triangle domain of arbitrary multilayer equidistant subdivision mesh line self rotation blending surfaces fractal interpolation problem(m?-SFIP). Firstly, it introduced the concepts of continuous interpolation space, and holographic interpolation per- operator and holographic iterated function systems. At the same time it proved holographic iterated function systems is compression, and has nonempty compact attractor of unique set. Secondly, it introduced necessary and sufficient conditions of holographic continuous blending interpolation in the triangle domain of arbitrary multilayer equidistant subdivision. Thirdly, it introduced the concepts of fractal interpolation function space and holographic interpolation operator.When the holographic interpolation operator was limited in fractal interpolation function space, it became a real operator, and a compression operator. Then there exited unique fixed continuous interpolation function. At the same time proved the image is holographic iterated function systems of unique non-empty compact set attractor of holographic fractal interpolation function. Finally it introduced the simplified form of continuous blending conditions, and gave two examples, and drawn some interpolation surface of different conditions. The results of this article made more complete of surface fractal interpolation on arbitrary triangle domain. At the same time the conclusions were more generally, and can be generalization to intergraphic interpolation form. The methods of this article raised provided system theoretical tools and practical method for constructing self-similarity surface on multilayer triangle domain.