Flow computations on imprecise terrains
Document typeConference report
Rights accessRestricted access - confidentiality agreement
European Commission's projectMFHQTERRAINS - Mathematical Foundations of High-Quality Terrain Models (EC-FP7-251235)
We study water flow computation on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and one where water only flows along the edges of a predefined graph, for example a grid or a triangulation. In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x, y)-coordinates are fixed. For the first model, we show that the problem of deciding whether one vertex may be contained in the watershed of another is NP-hard. In contrast, for the second model we give a simple O(n log n) time algorithm to compute the minimal and the maximal watershed of a vertex, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time.
CitationDriemel, A. [et al.]. Flow computations on imprecise terrains. A: Algorithms and Data Structures Symposium. "2011 Workshop on Algorithms and Data Structures Symposium (WADS)". Brooklyn: Springer Verlag, 2011, p. 350-361.