等高线悖论与广义等高线定义的研究

A research on contour paradox and generalized contour definition

根据等高线是地图上可视化的线并与地图比例尺密切相关的条件,推出了等高线悖论,即等高线是地面上一定范围内高程相等或不相等的点的连线在水平面上的投影。提出了点元概念,推导了等高线是地面上的等高点元集在地图平面上的同胚或拓朴映射的广义等高线定义。本定义包容了传统的等高线定义并可解释制图综合规律。因此,广义等高线定义更适用于等高线可视化的地图应用环境。

In this paper the authors infer the contour paradox according to the condition that contour is a visible line on map and it closely related with map scale,namely,the contour is a projection on the level surface of line connecting points on the earth's surface in a limit area.They put forward the concept of point element and infer a generalized definition of contour which is a homomorphism or topological mapping of set of contour point element on the earh's surface to the map plane.This generalized definition includes traditional definition of contour and is explicable the law of cartographic generalization.Therefore,this generalized definition is more suit-able for application environment of visible contour map.