Exploring a new line model for more accurate spatial representation in geographic information systems

This thesis focuses on reducing the error in spatial representation of linear entities of natural resources (called natural linear entities) in vector GIS. For this, a new line model is explored for more accurate spatial representation. The current line model is primarily based on straight line segments on which the error is applied by what is called an epsilon band.; This line model does not effectively represent the natural linear entities because they are usually smooth curves, and are not effectively represented by straight line segments. The difference between the straight lines and the natural linear entities on the map is called the generalization error and which can be quite large; loss of local variability information on the natural linear entities occurs within these line segments (called polylines). To adequately model such error, as well as the error on digitized points, an error band of large width is needed.; In this new line model, the thesis focuses on recovering the loss of local variability information generated by the current line model by employing higher order spline interpolation techniques to replace the straight line segments with spline curves. Potential spline interpolation methods, First and Second Order Continuity Conditions, Parabolic Blending, and Bezier methods, were tested. In addition, a method from a leading commercial CAD package, AutoCAD, was included. For the selected methods, a series of tests was performed to examine whether the spline curves produced could be better alternatives to polylines. Two different data sets were generated for the tests; a set of simulated mathematical curves for feasibility examination and a set of hydrologic features on USGS 7.5-minute topographic maps which were selected by two stage cluster sampling for formal statistical inferences. The test results showed that the Parabolic Blending and Bezier methods produced spline curves that resemble the linear entities better than the polylines.; To enhance performance of the methods, a new spline interpolation method was proposed which is actually a modification of the Bezier method, adopting three equations for more flexible local control of the spline curves. This is called the "New method." The test results using the same test data sets showed that the New method was better not only than the polylines but also than the Parabolic Blending method. When the Bezier method was compared, the New method was better at {dollar}alpha{dollar} = 0.69, but this is not statistically significant.; Using the new line model based on spline curves, the spatial representation could be more accurate, resulting in an error band of narrower width.; Finally, several practical application issues were examined. These include the impact of digitization rules on the performance of the spline interpolation methods, methods to incorporate the spline curves into the current topological data model, and an alternative application of the new line model.; In conclusion, it was revealed throughout this thesis that straight line segments could be replaced by spline segments in the new line model for more accurate spatial representation of natural linear entities and such replacement reduces width of the error band.