Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
The input/output complexity of sorting and related problems
Communications of the ACM
Visibility problems for polyhedral terrains
Journal of Symbolic Computation
Visibility preserving terrain simplification: an experimental study
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometrySoCG2002
Approximating the Visible Region of a Point on a Terrain
Geoinformatica
Improved visibility computation on massive grid terrains
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
More efficient terrain viewshed computation on massive datasets using external memory
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
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Given a terrain T and a point v, the viewshed or visibility map of v is the set of points in T that are visible from v. To decide whether a point p is visible one needs to interpolate the elevation of the terrain along the line-of-sight (LOS) vp. Existing viewshed algorithms differ widely in which and how many points they chose to interpolate, how many lines-of-sight they consider, and how they interpolate the terrain. These choices crucially affect the running time and accuracy of the algorithms. In this paper our goal was to obtain an IO-efficient algorithm that computes the viewshed on a grid terrain with as much accuracy as possible given the resolution of the data. We describe two algorithms which are based on computing and merging horizons, and we prove that the complexity of horizons on a grid of n points is O(n), improving on the general O(nα(n)) bound on triangulated terrains. Our finding is that, in practice, horizons on grids are significantly smaller than their theoretical worst case bound, which makes horizon-based approaches very fast. To measure the differences between viewsheds computed with various algorithms we implement an error metric that averages differences over a large number of viewsheds computed from a set of viewpoints with topological significance, like valleys and ridges. Using this metric we compare our current approach, Van Kreveld's model used in our previous work [7], the algorithm of Ferreira et al. [6], and the viewshed module r.los in the open source GIS GRASS.