The focus of our research is on a new automated smoothing method and its applications. Traditionally, the application of a smoothing method to a collection of polylines produces a new smoothed dataset. Although the new dataset was derived from the original dataset, it is stored independently. Since many smoothing methods are slow to execute, this is a valid trade-off. However, this greatly increases the data storage requirements for each new smoothing. A consequence of this approach is that interactive map systems can only offer maps at a discrete set of scales. It is desirable to have a fast enough method that would support the reuse of a single base dataset for on-the-fly smoothing for the production of maps at any scale.

We were able to create a framework for the automated smoothing of river networks based on the following major contributions:

– A wavelet--based method for polyline smoothing and endpoint preservation

– Inverse Mirror Periodic (IMP) representation of functions and signals, and dimensional wavelets

– Smoothing of features that does not change abruptly between scales

– Features are pruned in a continuous manner with respect to scale

– River network connectedness is maintained for all scales

– Reuse of a base geographic dataset for all scales

– Design and implementation of an interactive map viewer for linear hydrographic features that renders in subsecond time

We have created an interactive map that can smoothly zoom to any region. Numerical experiments show that our wavelet-based method produces cartographically appropriate smoothing for tributaries. The system is implemented to view hydrographic data, such as the USGS National Hydrography Dataset (NHD). The map demonstrates that a wavelet--based approach is well suited for basic generalization operations. It provides smoothing and pruning that is continuously dependent on map scale.