Hidden Variable Parametric Fractal Interpolation

This paper discusses parametric fractal interpolating problem with hidden variable ( H 2 P _FIP ), gives seven geometric forms of H 2 P _FIP . At first, it clearly put out the parametric fractal interpolation problem in space with Cartesian value, cylindrical value, spherical value, and defines the corresponding hidden variable parametric fractal interpolating curves . This paper analyses three geometric forms of space parametric fractal interpolating problem and seven geometric forms of hidden variable parametric fractal interpolating problem in coordinate surface. Hence, this paper gives the definition of parametric fractal interpolating function space, and points out the basic properties they have. This paper gives affine parametric fractal interpolation IFS with hidden variables, holographic parametric fractal interpolation IFS with hidden variables, intergraphic parametric fractal interpolation IFS with hidden variables on the base of affine fractal interpolation IFS of Barnslay, holographic fractal interpolation IFS and intergraphic fractal interpolation IFS of ShengZhongping, also treats several fractal interpolating problem uniformly. It proves that the affine IFS, holographic IFS and intergraphic IFS for seven kinds of interpolating curves is hyperbolic IFS. This paper also gives the hyperbolic conditions of the three forms of space IFS, and it proves that the attractor of the parametric fractal interpolation IFS with hidden variables is the projection in coordinate surface that is the attactor of parametric fractal interpolation space IFS.