Given a grid terrain T and a viewpoint v, the viewshed of v is the set of grid points of 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 vp. Existing viewshed algorithms differ widely in what points they chose to interpolate and how they interpolate the terrain. These choices crucially affect the running time and accuracy of the algorithms. This paper describes I O-efficient algorithms for computing visibility maps in a couple of different models. First, we describe two algorithms that sweep the terrain by rotating a ray around the viewpoint while maintaining the terrain profile along the ray. Second, we describe an algorithm which sweeps the terrain centrifugally, growing a star-shaped region around the viewpoint while maintaining the approximate visible horizon of the terrain within the swept region. Our last two algorithms are based on computing and merging horizons. All algorithms are I O-efficient in the I O-model of Aggarwal and Vitter. We present an experimental analysis on large terrains obtained from NASA SRTM data. All our algorithms are scalable to volumes of data that are over 50 times larger than main memory. Our main finding is that, in practice, horizons are significantly smaller than their theoretical worst case bound, which makes horizon-based approaches very fast. Our last two algorithms, which compute the most accurate viewshed, turn out to be very fast in practice, although their worst-case bound is inferior.
Haverkort, Toma and Zhuang @cite_12 presented the first IO-efficient viewshed algorithm using Van Kreveld's model. Using a technique called they turned Van Kreveld's algorithm into an algorithm running in @math time and @math , cache-obliviously. The authors also presented practical results showing that their algorithm scales well to large data and outperforms Van Kreveld's algorithm running in (virtual) memory.
@cite_12
2145588009
Given an arbitrary viewpoint v and a terrain, the visibility map or viewshed of v is the set of points in the terrain that are visible from v. In this article we consider the problem of computing the viewshed of a point on a very large grid terrain in external memory. We describe algorithms for this problem in the cache-aware and cache-oblivious models, together with an implementation and an experimental evaluation. Our algorithms are a novel application of the distribution sweeping technique and use O(sort(n)) I Os, where sort(n) is the complexity of sorting n items of data in the I O-model. The experimental results demonstrate that our algorithm scales up and performs significantly better than the traditional internal-memory plane sweep algorithm and can compute visibility for terrains of 1.1 billion points in less than 4 hours on a low-cost machine compared to more than 32 hours with the internal-memory algorithm.