Solving visibility problems on MCCs of smaller size (original) (raw)
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A parallel algorithm for the visibility problem from a point
Journal of Parallel and Distributed Computing, 1990
The problem of the visibilityfrom apoint is defined as follows: given a set 8 of n nonintersecting line segments and a point x, determine the region of the plane that is visible from x. A simpler instance of this problem is the visibility from a point inside a simple polygon. In this paper we present an optimal parallel algorithm for determining the visibility from a point. The algorithm is based on a divide-and-conquer strategy and has time complexity O(log n) on a PRAM with 0 (n) processors. o 1990 Academic Press, Inc.
An Optimal Parallel Algorithm for Computing the Visibility Complex
Abstract Geometric structures of various kinds play a central role in robotics, visibility computations, and motions planning. Of particular interest are structures such as visibility graphs, tangent graphs, Voronoi diagrams, and visibility complex. Pacchiola and Vegter [13] introduced the visibility complex of a collection O of n pairwise disjoint convex objects in the plane. This 2–dimensional cell complex may be considered as a generalization of the tangent visibility graph of O.
Geometric Algorithms for Digitized Pictures on a Mesh-Connected Computer
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1985
Although mesh-connected computers are used almost exclusively for low-level local image processing, they are also suitable for higher level image processing tasks. We illustrate this by presenting new optimal (in the 0-notational sense) algorithms for computing several geometric properties of figures. For example, given a black/white picture stored one pixel per processing element in an n X n mesh-connected computer, we give 0(n) time algorithms for determining the extreme points of the convex hull of each component, for deciding if the convex hull of each component contains pixels that are not members of the component, for deciding if two sets of processors are linearly separable, for deciding if each component is convex, for determining the distance to the nearest neighboring component of each component, for determining internal distances in each component, for counting and marking minimal internal paths in each component, for computing the external diameter of each component, for solving the largest empty circle problem, for determining internal diameters of components without holes, and for solving the all-points farthest point problem. Previous meshconnected computer algorithms for these problems were either nonexistent or had worst case times of 0 (n 2). Since any serial computer has a best case time of 0(n 2) when processing an n X n image, our algorithms show that the mesh-connected computer provides significantly better solutions to these problems.
An O(log N log log N) time RMESH algorithm for the simple polygon visibility problem
2002
In this paper we consider the simple polygon visibility problem: Given a simple polygon P with N vertices and a point t in the interior of the polygon, find all the boundary points of P that are visible from 2. We present an O(log N log log N) time algorithm that solves the simple polygon visibility problem on a f i x f i RMESH. Previously, the best known algorithm for the problem on a f i x f l RMESH takes O(logz N) time.
Efficient visibility queries in simple polygons
Computational Geometry, 2002
We present a method of decomposing a simple polygon that allows the preprocessing of the polygon to efficiently answer visibility queries of various forms in an output sensitive manner. Using O(n 3 log n) preprocessing time and O(n 3) space, we can, given a query point q inside or outside an n vertex polygon, recover the visibility polygon of q in O(log n + k) time, where k is the size of the visibility polygon, and recover the number of vertices visible from q in O(log n) time. The key notion behind the decomposition is the succinct representation of visibility regions, and tight bounds on the number of such regions. These techniques are extended to handle other types of queries, such as visibility of fixed points other than the polygon vertices, and for visibility from a line segment rather than a point. Some of these results have been obtained independently by Guibas, Motwani and Raghavan [18].
Parallelizing an Algorithm for Visibility on Polyhedral Terrain
International Journal of Computational Geometry & Applications, 1997
The best known output-sensitive sequential algorithm for computing the viewshed on a polyhedral terrain from a given viewpoint was proposed by Katz, Overmars, and Sharir 10 , and achieves time complexity O((k + n (n)) log n) where n and k are the input and output sizes respectively, and () is the inverse Ackermann's function. In this paper, we present a parallel algorithm that is based on the work mentioned above, and achieves O(log 2 n) time complexity, with work complexity O((k + n (n)) log n) in a CREW PRAM model. This improves on previous parallel complexity while maintaining work e ciency with respect to the best sequential complexity known.
Parallelizing visibility computations on triangulated terrains
1994
Abstract 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 triangle-sorting visibility approach proposed by De Floriani et al.(1989). Static and dynamic parallelization strategies, both in terms of partitioning criteria and scheduling policies, are discussed.
Canadian Conference on …, 1997
In this paper we describe a unified data-structure, the 3D Visibility Complex which encodes the visibility information of a 3D scene of polygons and smooth convex objects. This datastructure is a partition of the maximal free segments and is based on the characterization of the topological changes of visibility along critical line sets. We show that the size k of the complex is Ω (n) and O (n4) and we give an output sensitive algorithm to build it in time O ((n3+ k) logn). This theoretical work has already been used to define a ...