Visualization of Polygon-based Data as a Continuous Surface

The choropleth map is the most frequently used for the car- tographic visualization of normalized variables associated with polygonal units. The range of the values is divided into a small number of classes each of which is represented by a unique color or pattern which is used to depict units in that class. The colors are explained in the map legend. Strictly two-dimensional choropleth maps have the disad- vantage that only class membership can be derived from the Abstract Most information for spatial analysis and research in economic and social geography is aggregated into totals as- sociated with units which are polygons. To facilitate comparisons between the units the totals are normalized by a reference variable, such as the area of the polygon. Such kind of data is usually visualized as 2D or 3D choropleth maps, but an alternative is a continuous surface. The main property of the 3D choropleth map, the volume above the polygons, must be preserved, requiring a volume-preserving interpolation method. The average of the heights in a polygon are kept constant by changing heights of the points within the polygon. Obtaining a smooth surface requires additional points to be inserted into the polygon arranged on a regular square or triangular grid. But a regular grid may not be the best solution, especially if the polygons have irregular shapes and wide range of sizes, or if the input geometry of the polygon boundaries must be maintained in the map. In this case an irregular mesh of triangles can be used which must meet certain criteria. The triangles should not have very small or very large interior angles, to avoid arithmetic and visual problems, and the maximum area of any triangle may be limited. Good meshes with customized properties can be constructed using the Triangle program. Only minor modifi ca- tions in the interpolation algorithm are required for an irregular mesh.