The Position Uncertainty Analysis Of Plane Irregular Curves

The spatial data is an important component and operation objects of GIS, so the quality of spatial data directly affects GIS products qualified. In recent years, the GIS data quality question and the resulting data quality control technology become into one of hot topics which the domestic and foreign academic circle study. For a long time, persistent efforts have been devoted to the research in the uncertainty in GIS. Great achievements and abundant experience have been harvested satisfactorily.Spatial points, line, polygons and bodies are the basic contents of GIS positional uncertainty research. Especially the uncertainty research of line, not only is the extension and development on uncertainty research of point, but also is the prerequisite and base for studying uncertainty of polygons and bodies. Therefore, the uncertainty research of line segment has the very important status in the GIS uncertainty research. Has the large numbers of irregular curve in GIS, the data acquisition and curve fitting of irregular curves are more complex than a straight line. And the actual distribution of the errors in GIS position data might be non-normal. Therefore, this article has studied the quality control in the curve data gain and the curve fitting process. Based on this has discussed the uncertainty expression under the irregular curve normal distribution and the non-normal distribution.At present, the GIS data mostly uses the vector to gain. When uses the automatic tracking digitization, curve has flaws such as data redundancy and so on. This article second chapter based on reverse thinking, and adopted a law against the polygon approximation method to extract the feature points of irregular curves. And through tests show that the method than the iterative speed of current method is faster, and the fidelity of the curve is better.When curve fitting must consider the data quality control. In fitting, it is necessary to choose a different model and different function fitting method. The third chapter uses two measurable indicators. First, guaranteed that the error of the fitting data is smallest. The second is to ensure the best shape of the curve.In plane irregular curve uncertainty analysis, distributed two aspects from the data error obedience normal distribution and P-norm distributed to study the erroneous belt's synthesis. When data error obeys normal distribution, error band was by common tangent of the density error ellipse of the end and any point on the curve. And simplified the constitution mechanism of the error band. When the data obeys P-norm distributed, has introduced the concept of the error oblate and introduced synthesis of the fitted curve error band by common tangent of the error oblate. The irregular curve not only includes the error of data, but also has the model error. This article used the Hausdorff distance to study the fitted curve model error.