Drainage reality in terrains with higher-order Delaunay triangulations

Terrains are often modeled by triangulations, which ideally should have 'nice shape' triangles and reality of drainage in terrains (few local minima and drainage lines in the bottoms of valleys). Delaunay triangulation is a good way to formalize nice shape, and if higher-order Delaunay triangulations are used, drainage reality can be achieved. Two heuristics are presented, one for reducing the number of local minima and one for reducing the number of valley edges and components. The empirical results show how well they perform on real-world data; on average we see a 16% improvement over known algorithms.