Solving Space Conflicts in Map Generalization: Using a Finite Element Method

A finite element method was developed to handle conflicts during the generalization of maps. The method is holistic and solves conflict problems for the entire map surface simultaneously. When a generalized object changes size, the method immediately causes displacements in surrounding objects. Boundary constraints were introduced which make it possible to maintain the shape of objects, and simultaneously change the size of the objects. An iterative solution procedure for the Finite Element problem was shown to give solutions that better fulfill topological requirements than a direct solution of the problem.     

Reducing Linear and Perimeter Measurement Errors in Raster-based Data

An important issue in cartography and GIS is determining the appropriate resolution or cell size when converting vector data to raster. The general consensus is to make the cell size as small as possible to resolve geographic features and provide the most accurate estimates of measurements. Finer resolution results in more accurate estimates of polygon area; however, the raster data structure introduces an artifact that causes errors in the estimation of the length of linear features and of the perimeter of polygon features to increase with increasing resolution. Over-estimation as high as 41 percent is theoretically possible and was found to be around 26 percent for representative polygon maps. A method is described that uses a correction coefficient to reduce overestimation error to less than 3 percent.