样条分形插值函数定义及其若干性质

Definition and Some Properties of Spline Fractal Interpolation Function

文章介绍一类可微的分形插值函数,探讨了它的产生机理以及生成它的迭代函数系所满足的充要条件,在此基础上给出样条分形插值函数(SFIF)的定义,并讨论它所具有的部分收敛性质。研究样条分形插值函数的插值问题为计算机图形学和景物仿真从理论上提供了新的方法,是对传统样条理论的补充和扩展,具有重要的实际应用价值。

The paper introduces a kind of differentiable fractal interpolation function,discusses its generating mechanismas well as the sufficient condition that generates its IFS.On the basis of the previous process,the definition of SFIF is given and some convergence properties are discussed.The interpolation of the spline fractal interpolation function provides a newmethod for the subject of computer graph and vision simulation.The significance of SFIF exists not only in the traditional spline theory but also in the engineering application.