Driemel, A.; Haverkort, H.; Löffler, M.; Silveira, R.I.
Journal of Computational Geometry
Vol. 4, num. 1, p. 38-78
Date of publication: 2013
Journal article
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 predened 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, or a set of vertices, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time.
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 prede ned 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 fi xed. For the fi rst 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, or a set of vertices, where n is the number of edges of the graph. On a grid model, we can compute the same in O(n) time.