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559
ROAMing Terrain: Realtime Optimally Adapting Meshes
, 1997
"... Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and groundbased aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, viewdepend ..."
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Cited by 287 (10 self)
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and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.
Fast Polygonal Approximation of Terrains and Height Fields
, 1995
"... Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically a rectangular grid of elevation data H(x; y), and approximate it with a mesh of triangles, also known as a tri ..."
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Cited by 160 (5 self)
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Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically a rectangular grid of elevation data H(x; y), and approximate it with a mesh of triangles, also known as a
Approximation Algorithms For Terrain Guarding
, 2002
"... We present approximation algorithms and heuristics for several variations of terrain guarding problems, where we need to guard a terrain in its entirety by a minimum number of guards. Terrain guarding has applications in telecommunications, namely in the setting up of antenna networks for wireless c ..."
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Cited by 23 (1 self)
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is the number of vertices in the input terrain. We also briefly discuss some heuristic approaches for solving other variations of terrain guarding problems, for which no approximation algorithms are known. These heuristic approaches do not guarantee nontrivial approximation ratios but may still yield good
Terrain Guarding is NPHard
, 2009
"... A set G of points on a 1.5dimensional terrain, also known as an xmonotone polygonal chain, is said to guard the terrain if every point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. ..."
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Cited by 8 (0 self)
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. The minimum terrain guarding problem asks for a minimum guarding set for the given input terrain. Using a reduction from PLANAR 3SAT we prove that the decision version of this problem is NPhard. This solves a significant open problem and complements recent positive approximability results
On Realistic Terrains
, 2006
"... Keywords: Realistic input models, polyhedral terrains, visibility maps, shortest paths, Voronoidiagrams. 1 Introduction One of the main objectives of computational geometry is to uncover the computational complexityof geometric problems. It provides a theory that explains how efficiently geometric p ..."
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Keywords: Realistic input models, polyhedral terrains, visibility maps, shortest paths, Voronoidiagrams. 1 Introduction One of the main objectives of computational geometry is to uncover the computational complexityof geometric problems. It provides a theory that explains how efficiently geometric
Input/Output Characteristics of Scalable Parallel Applications
 In Proceedings of the Supercomputing ’95
, 1995
"... Rapid increases in computing and comm unication performance are exacerbating the longstanding problem of performancelimited input/output. Indeed, for many otherwise scalable parallel applications, input/output is emerging as a major performance bottleneck. The design of scalable input/output syste ..."
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Cited by 124 (3 self)
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parallel applications (electron scattering, terrain rendering, and quantum chemistry) on the Intel Paragon XP/S. As part of an ongoing parallel input/output characterization e ort, we used instrumented versions of the application codes to capture
The Complexity of Guarding Terrains
, 2009
"... A set G of points on a 1.5dimensional terrain, also known as an xmonotone polygonal chain, is said to guard the terrain if any point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. Th ..."
Abstract

Cited by 1 (1 self)
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. The minimum terrain guarding problem asks for a minimum guarding set for the given input terrain. We prove that the decision version of this problem is NPhard. This solves a significant open problem and complements recent positive approximability results for the optimization problem. Our proof uses a
First Person Sketchbased Terrain Editing
"... We present a new method for first person sketchbased editing of terrain models. As in usual artistic pictures, the input sketch depicts complex silhouettes with cusps and Tjunctions, which typically correspond to nonplanar curves in 3D. After analysing depth constraints in the sketch based on p ..."
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Cited by 1 (0 self)
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We present a new method for first person sketchbased editing of terrain models. As in usual artistic pictures, the input sketch depicts complex silhouettes with cusps and Tjunctions, which typically correspond to nonplanar curves in 3D. After analysing depth constraints in the sketch based
MultiLevel Surface Maps for Outdoor Terrain Mapping and Loop Closing
 In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS ’06
, 2006
"... Abstract — To operate outdoors or on nonflat surfaces, mobile robots need appropriate data structures that provide a compact representation of the environment and at the same time support important tasks such as path planning and localization. One such representation that has been frequently used i ..."
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Cited by 85 (20 self)
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. Throughout this paper we present algorithms for updating these maps based on sensory input, to match maps calculated from two different scans, and to solve the loopclosing problem given such maps. Experiments carried out with a real robot in an outdoor environment demonstrate that our approach is well
Inapproximability Results for Guarding Polygons and Terrains
, 2001
"... Past research on art gallery problems has concentrated almost exclusively on bounds on the numbers of guards needed in the worst case in various settings. On the complexity side, fewer results are available. For instance, it has long been known that placing a smallest number of guards for a given in ..."
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Cited by 36 (0 self)
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input polygon is NPhard. In this paper we initiate the study of the approximability of several types of art gallery problems.
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