Flow Computations on Imprecise Terrains
Abstract
We study the computation of the flow of water 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.
Cite
@article{arxiv.1111.1651,
title = {Flow Computations on Imprecise Terrains},
author = {Anne Driemel and Herman J. Haverkort and Maarten Löffler and Rodrigo Silveira},
journal= {arXiv preprint arXiv:1111.1651},
year = {2012}
}