In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized affine fractal interpolation surfaces (FISs). By using these matrices, we establish relationships between oscillation vectors of different levels, which enables us to obtain the box dimension of generalized affine FISs under certain constraints.

中文翻译：

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具有垂直缩放功能的分形插值曲面的盒维数

在本文中，我们首先提出一个简单的引理，它允许我们通过相关的振荡和和振荡向量来估计给定函数图的框维数。然后我们定义广义仿射分形插值曲面（FIS）的垂直缩放矩阵。通过使用这些矩阵，我们建立了不同级别的振荡向量之间的关系，这使得我们能够在一定约束下获得广义仿射FIS的盒维数。