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Journal of Algorithms
Quadratic bounds for hidden line elimination
SCG '86 Proceedings of the second annual symposium on Computational geometry
Making data structures persistent
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Planar realizations of nonlinear Davenport-Schinzel sequences by segments
Discrete & Computational Geometry
Visibility and intersectin problems in plane geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
Dynamic computational geometry
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
An algorithm for constructing the aspect graph
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Efficient hidden surface removal for objects with small union size
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
New bounds for lower envelopes in three dimensions, with applications to visibility in terrains
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Height distributional distance transform methods for height field ray tracing
ACM Transactions on Graphics (TOG)
Approximation algorithms for curvature-constrained shortest paths
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for Petersen's matching theorem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Visibility with a moving point of view
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On incremental rendering of silhouette maps of polyhedral scene
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Fast Horizon Computation at All Points of a Terrain With Visibility and Shading Applications
IEEE Transactions on Visualization and Computer Graphics
On the Planar Two-Watchtower Problem
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Worst-case-optimal algorithms for guarding planar graphs and polyhedral surfaces
Computational Geometry: Theory and Applications
Guarding a terrain by two watchtowers
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On incremental rendering of silhouette maps of a polyhedral scene
Computational Geometry: Theory and Applications
Line transversals of convex polyhedra in R3
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Improved visibility computation on massive grid terrains
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Linear data structures for fast ray-shooting amidst convex polyhedra
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Parallel algorithm to find minimum vertex guard set in a triangulated irregular network
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
On the complexity of sets of free lines and line segments among balls in three dimensions
Proceedings of the twenty-sixth annual symposium on Computational geometry
Line Transversals of Convex Polyhedra in $\mathbb{R}^3$
SIAM Journal on Computing
An optimal hidden-surface algorithm and its parallelization
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Approximation algorithms for art gallery problems in polygons and terrains
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Geometric heuristics for rural radio maps approximation
Journal of Heuristics
Viewsheds on terrains in external memory
SIGSPATIAL Special
Low-Complexity Intervisibility in Height Fields
Computer Graphics Forum
Efficient algorithms for pursuing moving evaders in terrains
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
On IO-efficient viewshed algorithms and their accuracy
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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In this paper we study several problems concerning the visibility of a polyhedral terrain @s from a point (or several points) lying above it. Our results are: (1) For a fixed point a, one can preproeess a in time O(n@a(n) log n), to produce a data structure of size O(n@a(n) log n), which supports fast ray shooting queries, where each such query asks for the point on @s that is visible from a in a specified direction. Here n is the number of faces of @s and @a(n) is the extremely slowly growing functional inverse of Ackermann's function. (2) If the viewing point a can vary along a fixed vertical line L, then the entire visibility structure of @s from L is of combinatorial complexity O(n@l"4(n)), where @l"4(n) is the maximal length of an (n, 4) Davenport-Sehinzel sequence, and is nearly linear in n, and where the visibility structure in question is the decomposition of L x S^2 into maximal connected regions, such that for each such region R, all points (a, u)@? R are such that the ray from a @? L in direction u @? S^2 first intersects @s at a point on the same face of @s. Furthermore, we present an O(n@l"4(n)log n)-time algorithm that preprocesses L and @s into a data-structure of size O(n@l"4(n)) which supports O(log^2n) time ray shooting queries. (3) Concerning the results in (2) we show that (i) if L is not vertical, then the resulting visibility structure can be of size @W(n^3); (ii) there exist a vertical line L and a polyhedral terrain a with n faces, for which the resulting visibility structure is of size @W(n^2@a(n)). (4) Finally, we consider the problem of placing on the surface @s one or several viewing points which collectively cover the entire surface (i.e. each point on @s is visible from at least one of these viewing ''stations''). We show (i) in the case of a single viewing station, one can determine in time O(n log n) whether such a station exists, and if so, produce such a point; (ii) the problem of finding the smallest number of points on @s that can collectively see the entire surface @s is NP-hard.