Algebraic research on geometrical characteristics of error band for 2D linear segment uncertainty ε_σ model

The geometrical characteristic of error band for 2D linear segment uncertainty εσ model has been studied in this paper. The monotony and extremum theory of function are applied to prove the geometrical characteristic of error band for 2D linear segment uncertainty εσ model in theory. The result shows that the error band has the geometrical shape of "larger ends and smaller middle" or "one end larger and the other smaller". The minimum width and its exact position of the error band are calculated too. It is proved that the minimum width position of the error hand is near the end with the smaller mean square error. Thus, the paper perfects the 2D linear segment uncertainty ε σ model in theory and makes it more scientific, and also provides a new way to study the space data uncertainty in GIS.