一类分形插值曲面及其截线

A family of fractal interpolation surfaces and their sections

文中讨论了正方形区域分形插值曲面问题.基于分形插值曲线的构造,给出了正方形区域上的一类分形插值曲面构造方法,并证明了它们的连续性;讨论了这类分形插值曲面上截线的性质,给出了分形插值曲面上的截线为仿射分形插值曲线的条件,并进行了证明.

The fractal interpolation surface on the square domain was discussed in this paper.Based on construction of fractal interpolation curves,the method of constructing a family of fractal interpolation surfaces on a square domain was proposed.The continuity of the surfaces was proved.Moreover,the properties of the sections of the fractal interpolation surfaces were studied.The conditions that the sections of the fractal interpolation surface were affine fractal interpolation curves were given,and the result was proved.