Intergraphic Fractal Interpolation On Triangle Domain

In this paper we study intergraphic method based on arbitrary times equidistant subdivision surfaces fractal interpolation problem(m?-SFIP)on triangle domain of holographic method.First of all holographic method is given structured intergraphic iterated function systems proved it is compression,and has non-empty compact attractor.Secondly,the concept of intergraphic interpolation prediction operator on triangle domain is given and proved it is compression;defined the intergraphic continuous blending condition for function and obtained the necessary and sufficient condition on continuous blending sufficient condition on continuous blending for.intergraphic interpolation;the function space of fractal interpolation on triangle domain is given and proved it is complete metric space;received the intergraphic interpolation operator on the function space of fractal interpolation and proved it is compression.So it exist fixed function the image of this function is fractal.Thirdly we obtain intergraphic dimension and holographic dimension is equality by means of proving intergraphic iterated function systems and holographic iterated function systems is topologically conjugate intergraphic interpolation operator and holographic interpolation operator is topologically conjugate.Finally defined intergraphic quasidimension given continuous blending condition and obtained four kinds of simple forms,drew the instance of fractal surface.In this paper we study holographic method on triangle extended to the situation of intergraphic method,let the conclusions more flexibility and generally.Provided systematic tools for the theoretical study in the fractal interpolation problem on a triangle domain.