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Higher isn't Necessarily Better: Visibility Algorithms and Experiments
 Advances in GIS Research: Sixth International Symposium on Spatial Data Handling
, 1994
"... We describe several fast programs to compute viewsheds and weighted visibility indices for observation points in a raster terrain. These programs explore various tradeoffs between speed and accuracy. We have analyzed many cells of data; there is no strong correlation between a point's elevation ..."
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Cited by 31 (5 self)
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We describe several fast programs to compute viewsheds and weighted visibility indices for observation points in a raster terrain. These programs explore various tradeoffs between speed and accuracy. We have analyzed many cells of data; there is no strong correlation between a point's elevation and its weighted visibility index. However, the, very few, high visibility points tend to characterize features of the terrain. This work can form a basis for automatically locating observers jointly to cover a terrain region of interest. Keywords: visibility, viewshed, lineofsight. 1 Introduction Visibility research, calculating linesofsight and viewsheds, on terrain databases, is an established, and important, field in GIS. Nevertheless, progress is still possible, since both more powerful Unix workstation hardware, with tens of megabytes of memory and software environments, and much larger amounts of input data are available. The research reported here would not have been feasible on ...
Guarding Polyhedral Terrains
, 1992
"... We prove that b c vertex guards are always sufficient and sometimes necessary to guard the surface of an nvertex polyhedral terrain. We also show that b guards are sometimes necessary to guard the surface of an nvertex polyhedral terrain. ..."
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Cited by 25 (6 self)
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We prove that b c vertex guards are always sufficient and sometimes necessary to guard the surface of an nvertex polyhedral terrain. We also show that b guards are sometimes necessary to guard the surface of an nvertex polyhedral terrain.
Applications of Analytical Cartography
, 2000
"... Several applications of analytical cartography are presented. They include terrain visibility (including visibility indices, viewsheds, and intervisibility), map overlay (including solving roundoff errors with C++ class libraries and computing polygon areas from incomplete information) , mobility ..."
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Cited by 9 (0 self)
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Several applications of analytical cartography are presented. They include terrain visibility (including visibility indices, viewsheds, and intervisibility), map overlay (including solving roundoff errors with C++ class libraries and computing polygon areas from incomplete information) , mobility, and interpolation and approximation of curves and of terrain (including curves and surfaces in CAD/CAM, smoothing terrains with overdetermined systems of equations, and drainage patterns). General themes become apparent, such as simplicity, robustness, and the tradeoff between different data types. Finally several future applications are discussed, such as the lossy compression of correlated layers, and just good enough computation when high precision is not justified. # to appear, Cartography and Geographic Information Systems, 2000 # http://www.ecse.rpi.edu/Homepages/wrf/research/gisapps/gisapps.pdf 1 Franklin Applications of Analytical Cartography Contents 1 Introduction 3 ...
Geometric Algorithms for Siting of Air Defense Missile Batteries
, 1994
"... Geometric aspects of the visibility problem in the siting of air defense missile batteries were studied in this project. It theoretically analyzed the problem, produced several new and efficient algorithms, implemented them, and tested them on many cells of data. The theoretical analysis studied the ..."
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Cited by 7 (0 self)
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Geometric aspects of the visibility problem in the siting of air defense missile batteries were studied in this project. It theoretically analyzed the problem, produced several new and efficient algorithms, implemented them, and tested them on many cells of data. The theoretical analysis studied the terrain characteristics, formally defined the Hawk siting problem, formalized the optimal placement of observers, and considered the minimum elevation of an airplane flying over varying terrain. Three algorithms for finding the viewshed around a particular observer were studied. R3 is slow but accurate. R2 is much faster, yet almost as accurate. Xdraw computes an approximate viewshed with error bounds. Four visibility index algorithms were studied. VL runs a fixed number of lines of sight out from every possible observer. WeightF weights the points by distance. Weight approximates WeightF, and DEM/LOS skips points along each line of sight for increased speed. The visibility indices of 20 DT...
WorstCaseOptimal Algorithms for Guarding Planar Graphs and Polyhedral Surfaces
, 2003
"... We present an optimal \Theta (n)time algorithm for the selection of a subset of the vertices of an nvertex plane graph G so that each of the faces of G is covered by (i.e. incident with) one or more of the selected vertices. At most bn=2c vertices are selected, matching the worstcase requiremen ..."
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Cited by 5 (0 self)
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We present an optimal \Theta (n)time algorithm for the selection of a subset of the vertices of an nvertex plane graph G so that each of the faces of G is covered by (i.e. incident with) one or more of the selected vertices. At most bn=2c vertices are selected, matching the worstcase requirement. Analogous results for edgecovers are developed for two different notions of &quot;coverage&quot;. In particular,our lineartime algorithm selects at most n \Gamma 2 edges to strongly cover G, at most bn=3c diagonals to cover G, and in the case where G has no quadrilateral faces, at most bn=3c edges to cover G. All these bounds are optimal in the worstcase. Most of our results flow from the study of a relaxation of thefamiliar notion of a 2coloring of a plane graph which we call a facerespecting 2coloring that permits
Efficient Algorithms for Guarding or Illuminating the Surface of a Polyhedral Terrain
 Proceedings of the 8th Canadian Conference on Computational Geometry, volume 5 of International Informatics Series
, 1996
"... We present efficient polynomial time algorithms that place bn=2c vertex guards which cover the surface of an nvertex polyhedral terrain, and similarly, bn=3c edge guards which cover the surface of an nvertex polyhedral terrain. The time complexity of both algorithms, dominated by the cost of fi ..."
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Cited by 5 (0 self)
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We present efficient polynomial time algorithms that place bn=2c vertex guards which cover the surface of an nvertex polyhedral terrain, and similarly, bn=3c edge guards which cover the surface of an nvertex polyhedral terrain. The time complexity of both algorithms, dominated by the cost of finding a maximum matching in a graph, is O(n ).
Parallelizing Visibility Computations on Triangulated Terrains
 International Journal of Geographical Information Systems
, 1994
"... In this paper we address the problem of computing visibility information on digital terrain models in parallel. We propose a parallel algorithm for computing the visible region of an observation point located on the terrain. The algorithm is based on a sequential trianglesorting visibility approach ..."
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Cited by 2 (0 self)
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In this paper we address the problem of computing visibility information on digital terrain models in parallel. We propose a parallel algorithm for computing the visible region of an observation point located on the terrain. The algorithm is based on a sequential trianglesorting visibility approach proposed in [De Floriani et al. 1989]. Static and dynamic parallelization strategies, both in terms of partitioning criteria and scheduling policies, are discussed. The different parallelization strategies are implemented on an MIMD multicomputer and evaluated through experimental results.
Silicon Graphics Inc.
"... Summary: Mission planners can benefit from determining regions of space occluded by terrain from sensor positions, e.g. in order to determine ingress and egress paths. Conventional approaches to computing occlusion using 2D or 2.5D representations of terrain are inefficient and do not scale well. Bi ..."
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Summary: Mission planners can benefit from determining regions of space occluded by terrain from sensor positions, e.g. in order to determine ingress and egress paths. Conventional approaches to computing occlusion using 2D or 2.5D representations of terrain are inefficient and do not scale well. Binary Adaptive Ray Casting uses intersection calculations accelerated by 3D hierarchical bounding volumes to perform adaptive interval probing. Candidate regions of dead ground are tested against a required tolerance for “shallowness ” caused by grazing rays. The approach can be scaled arbitrarily on a cachecoherent nonuniform memory architecture to compute occluded terrain in near realtime.
Geometric Algorithms for Siting of Air Defense Missile Batteries
"... Geometric aspects of the visibility problem in the siting of air defense missile batteries were studied in this project. It theoretically analyzed the problem, produced several new and efficient algorithms, implemented them, and tested them on many cells of data. The theoretical analysis studied the ..."
Abstract
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Geometric aspects of the visibility problem in the siting of air defense missile batteries were studied in this project. It theoretically analyzed the problem, produced several new and efficient algorithms, implemented them, and tested them on many cells of data. The theoretical analysis studied the terrain characteristics, formally defined the Hawk siting problem, formalized the optimal placement of observers, and considered the minimum elevation of an airplane flying over varying terrain. Three algorithms for finding the viewshed around a particular observer were studied. R3 is slow but accurate. R2 is much faster, yet almost as accurate. Xdraw computes an approximate viewshed with error bounds. Four visibility index algorithms were studied. VL runs a fixed number of lines of sight out from every possible observer. WeightF weights the points by distance. Weight approximates WeightF, and DEM/LOS skips points along each line of sight for increased speed. The visibility indices of 20 ...
Region Intervisibility in Terrains Esther Moet Marc van Kreveld Ren'e van Oostrum
, 2005
"... Abstract A polyhedral terrain is the graph of a continuous piecewise linear function definedover the triangles of a triangulation in the xyplane. Two points on or above a terrainare visible to each other if the lineofsight does not intersect the space below the terrain. In this paper, we look at ..."
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Abstract A polyhedral terrain is the graph of a continuous piecewise linear function definedover the triangles of a triangulation in the xyplane. Two points on or above a terrainare visible to each other if the lineofsight does not intersect the space below the terrain. In this paper, we look at three related visibility problems in terrains. Suppose we aregiven a terrain T with n triangles and two regions R1 and R2 on T, i.e., two simplyconnected subsets of at most m triangles. First, we present an algorithm that determines,for any constant ffl> 0, within O(n1+fflm) time and storage whether or not R1 and R2 arecompletely intervisible. We also give an O(m3n4) time algorithm to determine whetherevery point in R1 sees at least one point in R2. Finally, we present an O(m2n2 log n) timealgorithm to determine whether there exists a pair of points p 2 R1 and q 2 R2, such that p and q see each other.