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.
CitationDriemel, A. [et al.]. Flow computations on imprecise terrains. "Journal of Computational Geometry", 2013, vol. 4, núm. 1, p. 38-78.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: email@example.com