Cartographic Line Generalization with Waterlines and Medial-Axes

Abstract

A line generalization solution is presented based on the operations known as water-lining and medial-axis transformation. Although the solution is of general application, this report focuses on shorelines. The method is shown to preserve the general shape of a line through very broad scale changes; it also makes it possible to perform feature aggregation and elimination, where needed. Each scale change is proven to depend on the maximum distance spanned by the waterlining operation, which distance can be equated to the quantity known as ε in the generalization literature. The challenges encountered in the development of the generalization procedure are discussed; these challenges are less on the side of line simplification and more in the aggregation of features. Solutions are presented for broadening isthmus, linkages to streams and rivers, and the collapsing of straits into double and coincident lines. Particular shoreline configurations are shown to lead to ambiguities in feature aggregation and elimination that require user's input in order to be resolved. Intermediate results are found to replicate those submitted 39 years ago by Julian Perkal in his proposal for an objective generalization.