## Christopher O'Donnell '10

### Computing flow on triangulated terrains

We are working on modeling flow and efficiently computing river networks on terrain elevation data. While terrain elevation data is becoming more and more available from remote sensing, flow data is not available and modeling flow based on elevation is an important problem in GIS. We are implementing methods for terrains represented as a triangulation, or TIN (triangulated irregular network), which stores the terrain as a mesh of triangles. The other representation of a terrain is the grid, which, by comparison, stores the terrain as a regular grid of points with their associated elevations. While grids are generally simpler to work with, TINs are more versatile and allow for the possibility to simplify the terrain and eliminate any data redundancy. In particular, flow models on TINs are more accurate and allow water to flow in a continuous manner, following the path of steepest descent at any point; the flow models on grids, on the other hand, are "discrete", assuming that water goes to one of the eight neighbors of a point.

Our goal for this project is to complete a module for computing the river network on a triangulated terrain and compare the results with those obtained on grids. We are using modules for simplifying a grid into a TIN (developed by Jon Todd, Bowdoin 2005). We'll look at the running time , precision of the river newtork, and size. While the methods on TINs are more involved (especially due the the numerical precision issues that arise) and most likely slower, we expect that the results will be significantly better.

Flow path on a triangulated terrain