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The applications of modeling visibility on terrains have grown with the increasing use of LiDAR to gather high-resolution terrain data. The most common use of visibility on terrains is the viewshed: given an arbitrary viewpoint v and a grid terrain, the viewshed of v is the set of all points on the terrain that are visible from v. Despite extensive research, finding the total viewshed, which requires computing viewsheds for all points on the terrain, takes too long to run for even moderately-large terrains. Therefore, to be useful in practice, viewshed algorithms must be efficient and accurate. In this thesis, we describe QuadVS: an output-sensitive algorithm which aims to compute viewsheds more efficiently by utilizing a multi-resolution technique. The idea is to divide the grid into layers of blocks around the viewpoint using a quadtree subdivision. Blocks that are determined to be potentially visible are recursively subdivided until they are no longer potentially visible or they reach full resolution. Blocks that are guaranteed to be invisible are not subdivided further. The intuition behind this multi-resolution approach is that a lower resolution will often be sufficient to filter out blocks that are guaranteed to be invisible, and using high resolution only when necessary will lead to improved efficiency. In practice, QuadVS is over 10 times faster on larger terrains compared to the previous fastest algorithm. We find that the number of blocks skipped by QuadVS is consistently large on all terrains, explaining the speedup.
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