From Local to Global and Back Again

This paper considers the cost of preprocessing a digital terrain model (DTM) represented as a trian-gulated irregular network (TIN) so that drainage queries|e.g., what is the watershed of a query point, or how much water passes through a point given that rain is falling at a known rate|can be answered by simply evaluating a summary function. Although the worst-case storage and preprocessing costs are high, the experimentally-observed costs are reasonable. In order to compute a compact and consistent summary function, the drainage network needs a rigorous deenition. This paper, therefore, also surveys some of the previous deenitions, extends them, and establishes a number of properties of drainage networks with a focus on TINs.