基本地貌形态数学定义的研究

A Reseach on the Mathematical Definition of the Basic Landform Shape

根据拓扑学中覆盖和同胚的定义 ,论证等高线图形保持着覆盖它的三维曲面的拓扑性质 ,据此我们可以在平面上定义和描述三维曲面的空间特性。继而给出了如斜坡、山、山脊、凹地、谷地、鞍部等基本地貌形态的数学定义。这些数学定义使局限于定性描述的基本地貌概念获得了精密的数学形式和定量的刻划 。

According to the definition of covering and homeomorphism is the topology,the authors proof that the contour map keeps the topologic property of covering its three dimensions surface,according to it,we may define and describe the space specific property of 3 dimensions surface on the plane.Further,give the mathematical definition of basic lardform shape as the slope,mountain,ridge,depression,groge,saddle,etc.respectively.These mathematical definitions make basic landform shape concept of limit determine nature discribe are got accurate mathematical form and fixed quantity depict,and announce the thing transformation law from quantity to quality and internal relations.