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Topic: Visibility graph

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	Press Release
		In the eight years between 1997 and 2004, reduced visibility occurred at the Chek Lap Kok International Airport 13% of the time on average, far higher than the average of 4% observed between 1980 and 1982 by the Observatory staff at Chek Lap Kok before the new airport was built.
		In winter and spring, reduced visibility usually occurred in association with weak northerly surges of the monsoon or when the northeast monsoon affecting Hong Kong was subsiding.
		Visible imageries received which showed the spatial coverage of smoke and haze were made available to the public through the Observatory's website in November last year (2004).
	www.weather.gov.hk /wxinfo/news/2005/pre0106e.htm (834 words)

	Graph theory - Wikipedia, the free encyclopedia
		In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection.
		Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values.
		Graph theory is also used to study molecules in chemistry and physics.
	en.wikipedia.org /wiki/Graph_theory (1296 words)

	\| Path Planning on a Mobile Robot \| (Site not responding. Last check: 2007-10-17)
		A visibility graph was constructed for the configuration space of the A* algorithm to be utilized in known environments.
		Visibility Graph: A visibility graph was implemented to represent the configuration space for the A* algorithm in known environments.
		The visibility graph was an efficient and optimal representation for the configuration space that allowed for extremely fast searches and convenient paths along which the robot could follow to its goal with little or no difficulty.
	palantir.swarthmore.edu /maxwell/classes/e28/S00/reports/addo-kim-silk-lab2 (2187 words)

	Googlism what is visibility graph
		visibility graph is the graph whose vertices are the endpoints of the free bitangents and whose edges are the free bitangents and the arcs
		visibility graph is the graph whose 2n vertices correspond to the endpoints of the
		visibility graph is a directed graph in which nodes represent classes and arcs indicate that the source of the arc calls at least one method of the class at
	www.googlism.com /what_is/v/visibility_graph (620 words)

	Visibility graph - Wikipedia, the free encyclopedia
		Each node or vertex in the graph represents a point location, and each edge represents a visible connection between them (that is, if two locations can see each other, an edge is drawn between them).
		In addition to theoretical problems, visibility graphs also have practical uses, for example, to calculate the placement of radio antennas, or as a tool used within architecture and urban planning through visibility graph analysis.
		Visibility graphs are also used in mobile robotics as a (generally offline) path-planning tool when the geometry of the environment is known, although robots have been designed that collect isovist information as they explore the environment using ultrasound sensors, which can then be turned into a visibility graph of recognisable known locations.
	en.wikipedia.org /wiki/Visibility_graph (213 words)

	Visibility graphs (Site not responding. Last check: 2007-10-17)
		A graph G is called a visibility graph if there is a polygon P such that the vertices of P are the vertices of G, and two vertices are adjacent in G if they are visible in P.
		A graph H is called an induced visibility graph if there is a polygon P such that H is an induced subgraph of the visibility graph VG(P) of P.
		Observe that an induced visibility graph may not necessarily be the visibility graph of a polygon.
	www.matem.unam.mx /~urrutia/openprob/Visibility (207 words)

	ZAIK preprints & publications
		Two rectangles Ri and Rj are considered visible provided that there exists a closed cylinder C of non-zero radius such that the ends of C are contained in Ri and Rj, the axis of C is parallel to the z-axis, and C does not intersect any other rectangle.
		Finally, we show that the family of graphs with a representation is not closed under graph minors.
		Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets.
	www.zaik.uni-koeln.de /~paper/preprints.html?show=zpr95-205 (514 words)

	Visibility Graphs and Bruhat Order (Site not responding. Last check: 2007-10-17)
		The recognition problem for visibility graphs of simple polygons is not known to be in NP, nor is it known to be NP-hard.
		The proof is based on a direct specialization of a technique used to compute the visibility graph of an arbitrary simple polygon from a combinatorial encoding of the underlying configuration of points.
		The characterization of visibility graphs of general convex fans, and a polynomial time recognition algorithm in the case when a hamiltonian cycle is presented as part of the imput to the problem, follows as a consequence.
	www.cs.ucsb.edu /~omer/personal/abstracts/staircase1.html (348 words)

	Visibility Graph Analysis
		Visibility graph analysis is a spatial analysis technique for urban and building spaces pioneered at the VR Centre, which may also be applied to landscapes.
		It was at this time that we formalised the technique as 'visibility graph analysis' and found its relationship to previous work in landscape analysis and computational geometry.
		Turner, A., Doxa, M., O'Sullivan, D. and Penn, A., 2001, From isovists to visibility graphs: a methodology for the analysis of architectural space.
	www.vr.ucl.ac.uk /research/vga (1995 words)

	Visibility graph analysis - Wikipedia, the free encyclopedia
		Visibility graph analysis (VGA) is a method of analysing the inter-visibility connections within buildings or urban networks.
		Visibility graph analysis was developed from the architectural theory of space syntax by Turner et al (2001), and is applied through construction of a visibility graph within the open space of a plan.
		Visibility graph analysis uses various measures from the theory of small-world networks and centrality in network theory in order to assess perceptual qualities of space and the possible usage of it.
	en.wikipedia.org /wiki/Visibility_graph_analysis (144 words)

	University of Bonn, Computer Science Dept. I: The Visibility Graph
		A visibility graph of a polygon scene shows the visibility relations between the separate vertexes of a scene.
		The idea of constructing a visibility graph is based on a radial sweep.
		The obstacle edges also belong to the visibility graph, but are displayed blue because of clarity reasons.
	web.informatik.uni-bonn.de /I/GeomLab/VisGraph/VisGraph.html.en (1237 words)

	Graph theory Summary
		Graphs with weights can be used to represent many different concepts; for example if the graph represents a road network, the weights could represent the length of each road.
		Definitions of graphs vary in style and substance, according to the level of abstraction that is approriate to a particular approach or application.
		Graph theory is also used to study molecules in chemistry and physics.
	www.bookrags.com /Graph_theory (3094 words)

	[No title]
		Regional haze - visibility impairment that is produced by a multitude of sources and activities which emit fine particles and their precursors (sulfates, nitrates, organic carbon, elemental carbon, soil dust and particulates) and which are located across a broad geographic area.
		In addition to determining adverse impacts on visibility, data from the network is used to determine improvements in visibility as progress towards the national visibility goal is achieved.
		Since visibility impairment attributable to specific sources has not been identified in New Mexico, the current permitting programs of the Air Quality Bureau are considered by the state to meet the long-term strategy requirements for preventing future impairment from major stationary sources or major modifications.
	www.nmenv.state.nm.us /aqb/Visibility_Report_2003-New_Mexico.doc (7285 words)

	The Visibility Graph Method (Site not responding. Last check: 2007-10-17)
		The first algorithms to solve the shortest paths' problem employed visibility graphs to do so.
		Formally, a visibility graph for this problem, G = (V, E) is an undirected graph whose set of nodes (V) are the vertices of the polygons along with the source and end points, and whose set of edges (E) consists of pairs of vertices that are mutually visible.
		A visibility graph can have O(n^2) edges in the worst case however, so basing any shortest paths' algorithm on a visibility graph will have this time complexity in the worst case.
	www.cs.caltech.edu /~cesar/report/vis_graph.html (127 words)

	Combinatorics Seminar - Fall 2005
		We construct a connected cubic graph on 60 vertices with domination number 21 and a sequence of connected cubic graphs where the limit of the ratio of the domination number to the number of vertices is at least 8/23, which equals 1/3+1/69.
		A bar visibility representation of a graph G is a collection of horizontal bars in the plane corresponding to the vertices of G such that two vertices are adjacent if and only if the corresponding bars can see each other along an unobstructed vertical sightline.
		The edge-bandwidth of a graph G is the minimum bandwidth among all edge-labelings.
	www.math.uiuc.edu /~jozef/seminar/fall2005.html (1686 words)

	CHEMTRAILS - CONTRAILS (Site not responding. Last check: 2007-10-17)
		Remaining in need of further accounting is the significant degradation in visibility as evidenced by the data which follows this change in standard.
		The graphs shown are taken from climatic archive data available for Santa Fe, NM from Jan 1994 to Mar 2001.
		This graph showns a period from Jan 1996 to Dec 1998; the change in reporting standard was made in Oct 1997.
	www.carnicom.com /visib1.htm (446 words)

	Introduction
		Whereas the discussion above about visibility problems in the plane was not concerned with a particular output device, one can partition the work done on visibility in space clearly to one of two categories depending on the stage at which we are concerned with the output device.
		Also, the advantage of using the visibility map rather than the SVBSP for shadow computation under a point light source is that it makes it possible to preserve the solids in the input because all adjacency information in the solids can be maintained after determining the shadows.
		After the visibility step from each patch, which takes quadratic time in n, the number of patches in the scene, a system of n equations in n needed to be solved requiring cubic time which makes it possible to handle only small scenes.
	www.cs.ualberta.ca /~ghali/thesis/node3.html (7094 words)

	Visibility Algorithms in the Plane - Cambridge University Press (Site not responding. Last check: 2007-10-17)
		However, computations of visible portions of objects from a viewpoint involving thousands of objects is a time consuming task even for high speed computers.
		Specifically, basic algorithms for point visibility, weak visibility, shortest paths, visibility graphs, link paths and visibility queries are all discussed.
		It will also be useful as a reference for researchers working in algorithms, robotics, computer graphics and geometric graph theory, and some algorithms from the book can be used in a first course in computational geometry.
	www.cambridge.org /catalogue/print.asp?isbn=0521875749&print=y (225 words)

	Math Forum: MacPOW 895: Polar Visibility (Site not responding. Last check: 2007-10-17)
		A "polar visibility graph" is a network (graph) whose vertices are closed arcs of circles centered at the origin, with two arcs considered to be adjacent if they can see each other along a radial line, possibly passing through the origin.
		But this visibility must be at more than just a single point.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /wagon/fall99/p895.html (250 words)

	Navigation Using Behavior-Based and Path Planning Strategies
		Since the visibility graph planner knew the location of all obstacles beforehand, integration consisted of planning and then letting the robot follow it all the way to the goal.
		For the first portion of the lab, the implementation of A, we added a trace of the complete visibility* graph and of the optimal path to make it clear that the algorithm is finding the optimal path.
		visibility graph plotting, ASCII art graphs of the robot's world representation, TIFF output of evidence grid data) to gain a clear understanding of what the planning software was doing.
	www.sccs.swarthmore.edu /users/02/jill/cs81/lab02/lab02.html (1172 words)

	Visibility Graphs (Site not responding. Last check: 2007-10-17)
		The visibility graph of a polygon is a graph whose nodes corresponds to the vertices of the polygon, and whose edges correspond to the edges in the polygon formed by joining the vertices that can “see” each other.
		The visibility graph of a set of obstacles is a bit more complicated.
		It is the graph of nodes from the same and from different obstacles that can see each other.
	cs.smith.edu /~streinu/Teaching/Courses/274/Spring98/Projects/Philip/fp/visibility.htm (771 words)

	Visibility and Graph Drawing Research Home Page
		Visibility and Graph Drawing Research at the University of Lethbridge
		Version 2.0 includes the computation of the full visibility graph of a set of line segments and also the ability to interactively draw arrangements of lines and is now available.
		OrthoPak is a 3-d orthogonal drawing package that implements several algorithms for constructing 3-d VRML layouts of graphs which can then be viewed with a VRML browser (not supplied).
	www.cs.uleth.ca /~wismath/vis.html (276 words)

	University of Bonn, Computer Science Dept. I: The Visibility Graph
		A visibility graph of a polygon scene shows the visibility relations between the separate vertexes of a scene.
		In this process the visible edges are calculated radial from south to north for every vertex.
		The obstacle edges also belong to the visibility graph, but are displayed blue because of clarity reasons.
	www.geometrylab.de /VisGraph/VisGraph.html.en (1237 words)

	Problem Set 4
		Free space is defined as the complement of P. The visibility graph of P is defined as the graph whose nodes are the vertices of P, and whose edges join pairs of nodes for which the corresponding segment lies in free space.
		However, in typical cases, the number of edges in the visibility graph is often closer to O(n).
		which, given a graph and a vertex in the graph, returns a list of vertices that can be reached from the vertex by traversing a single edge in the graph.
	www.cs.dartmouth.edu /brd/Teaching/AI/Homeworks/DFA/ps4.html (3463 words)

	rectvis (Site not responding. Last check: 2007-10-17)
		A rectangle-visibility graph is one whose vertices can each be represented by a closed rectangle in the plane with sides parallel to the axes, having pairwise disjoint interiors, with two vertices adjacent in the graph if and only if the corresponding rectangles are vertically or horizontally visible.
		These graphs have thickness at most two since their edges can be divided into vertical and horizontal visibilities, each forming a planar graph.
		It is known that a thickness-two graph that is the union of two bar-visibility graphs need not be a rectangle-visibility graph, though the converse is true.
	www.emba.uvm.edu /~archdeac/newlist/rectvis.htm (311 words)

	Parasol Seminar Spring 2003 \| Parasol Laboratory Intranet
		In general, if the free configuration space is a k-manifold and given a suitable definition for straight lines, an infinite analog of a visibility graph over the set of points in free space.
		A further abstraction of this notion leads to a formulation of visibility in terms of a measure theoretic framework.
		Probabilistic roadmap method planning is then cast as an algorithm for computing parts of the transitive closure of such a "visibility" graph.
	parasol.tamu.edu /seminar/abstract.php?talk_id=367 (319 words)

	Path-Planning Strategies (Site not responding. Last check: 2007-10-17)
		We found that the visibility graph with A* planning almost instantly gives optimal paths, but only the D* algorithm with evidence grids would be suitable for real-world environments with dynamic obstacles.
		The visibility graph object then creates a visibility graph by comparing every pair of nodes against every obstacle to determine whether or the two nodes can be connected.
		As mentioned above, our visibility graph code has a bug that causes it to ocassionally drop an edge, but this occurance is rare enough that it did not merit the intensive effort that would be required to fix the problem.
	palantir.swarthmore.edu /maxwell/classes/e28/S00/reports/groom-johnson-nelson-olshfski-lab2 (3950 words)

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