GIS中平面面位误差环的解析模型

本文基于随机场理论，导出了随机面元的分布函数和概率密度函数。为了衡量随机面元的位置不确定性，将点位误差椭圆和线位误差带进一步扩展到面位误差环指标。根据推求包括线的原理，导出了多边形面位误差环边界线的解析表达式，并分析了面位误差环的构成机理，证明了误差环边界线为连续闭合曲线的结论。最后通过实例绘制了面位误差环的可视化图形。

THE MODEL OF PLANAR POLYGON'S POSITIONAL ERROR DONUT IN GIS

Based on the theory of random field, this paper derives the random area unit's distribution and probability density functions. In order to measure the area unit's positional uncertainties in GIS, the paper extends the point's error ellipse and line's band to the area unit's error donut, derives its boundary curves formula by means of envelop theory, analyses the configuration and gives the visual figures of the error donut according to different examples, testifies the continuation of the functions at the break point, and draws a conclusion that the error donut boundary is a continuous closed curve.