Showing papers on "Visibility graph published in 2003"
24 Sep 2003
TL;DR: The hypothesis is that an additional factor is cognitively relevant for the selection of appropriate salient features: advance visibility for a person approaching a destination point, and a computational measure for advance visibility is proposed.
Abstract: Human communication on wayfinding makes extensive use of landmarks. With a formal model of salience, route planning services can include landmarks as well. Such a model was presented considering visual, semantic, and structural properties of spatial features. This model measures saliency independent from a given route. Our hypothesis is that an additional factor is cognitively relevant for the selection of appropriate salient features: advance visibility for a person approaching a destination point. We will propose a computational measure for advance visibility. The new measure is used to identify suited salient features at route decision points: a feature is suited for a wayfinding instruction if it is (a) salient, and (b) in advance visible. The relevance of advance visibility is tested by a comparison of wayfinding success with instructions made with and without this additional measure. Computational effort is observed to check feasibility.
112 citations
30 Jul 2003
TL;DR: In this paper, the authors studied the properties of Schnyder realizers and canonical ordering trees of plane graphs and obtained compact drawings of two styles for any plane graph G with n vertices.
Abstract: We study the properties of Schnyder’s realizers and canonical ordering trees of plane graphs Based on these newly discovered properties, we obtain compact drawings of two styles for any plane graph G with n vertices First we show that G has a visibility representation with height at most \(\lceil \frac{15n}{16} \rceil\) This improves the previous best bound of n-1 The drawing can be obtained in linear time Second, we show that every plane graph G has a straight-line grid embedding on an (n − Δ0 − 1) × (n − Δ0 − 1) grid, where Δ0 is the number of cyclic faces of G with respect to its minimum realizer This improves the previous best bound of (n-1) × (n-1) This embedding can also be found in O(n) time
41 citations
ILOG1
TL;DR: A layout algorithm for directed hypergraphs, where for the majority of hyperedges the source nodes are placed in a higher layer than the target nodes, similar to traditional hierarchical layout.
Abstract: We present a layout algorithm for directed hypergraphs. A hypergraph contains hyperedges that have multiple source and target nodes. Hyperedges are drawn with orthogonal segments. Nodes are organized in layers, so that for the majority of hyperedges the source nodes are placed in a higher layer than the target nodes, similar to traditional hierarchical layout [8,11]. The algorithm was implemented using ILOG JViews [10] for a project that targeted electrical signal visualization.
37 citations
10 Nov 2003
TL;DR: A path expression methodology consisting of line segments, circular arcs and clothoid arcs, and a method of global path generation with a visibility graph is proposed.
Abstract: To achieve smooth motion of car-like robots, it is necessary to generate paths that satisfy the following conditions: maximum curvature, maximum curvature derivative, and curvature continuity. Another requirement is that human operators can manipulate the robots with ease. In this paper, a path expression methodology consisting of line segments, circular arcs and clothoid arcs is presented. In addition, a method of global path generation with a visibility graph is proposed. To establish this method, the following steps are proposed: (a) the arrangement of subgoals (middle points) and (b) the construction of the graph for path generation. By using the proposed method, the paths were shortened 14% on average.
36 citations
TL;DR: It is shown that every segment endpoint visibility graph on n disjoint line segments in the plane admits an alternating path of length Ω(log n), and this bound is optimal apart from a constant factor.
21 citations
1 Jan 2003
TL;DR: Differences of four approaches in finding the visibility graph of a polygonal region with obstacles defined by simple polygons are examined.
Abstract: This paper examines differences of four approaches in finding the visibility graph of a polygonal region with obstacles defined by simple polygons. Each has been implemented and tuned. Experimental comparisons via time measurements have been carried out against a variety of testcases ranging in graph density from maximal, O(
18 citations
1 Jan 2003
12 citations
Journal Article•
TL;DR: Tight bounds are established on the size of a maximal visibility matching for a set of f-equal width objects by showing that [2n/3] ≤ h(n) ≤ 2n/ 3.
Abstract: Let s denote a compact convex object in R 2 . The f-width of s is the perpendicular distance between two distinct parallel lines of support of s with direction f. A set of disjoint convex compact objects in R 2 is of equal f-width if there exists a direction f such that every pair of objects have equal f-width. A visibility matching, for a set of equal f-width objects is a matching using non-crossing lines of site in the visibility graph of the set. In this note we establish tight bounds on the size of a maximal visibility matching for a set of f-equal width objects by showing that [2n/3] ≤ h(n) ≤ 2n/3.
6 citations
TL;DR: A natural class of graphs is defined by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary, and some applications of the concept are given.
Abstract: . We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results giving necessary properties of visibility graphs, and giving some examples of classes of graphs that can be so represented. Finally, we give some applications of the concept, and we provide potential avenues for future research in the area.
6 citations
TL;DR: This work investigates computational properties of strong visibility, a generalization of standard visibility, defined with respect to a fixed set of line orientations, as well as theoretical properties of this generalized visibility.
Abstract: Strong visibility is a generalization of standard visibility, defined with respect to a fixed set of line orientations. We investigate computational properties of this generalized visibility, as we...
5 citations
15 Oct 2003
TL;DR: An algorithm that automatically generates an aesthetically 'pleasing' and 'readable' visibility diagram is presented and a new set of layout specifications suitable for easy visualization of the distribution system have been proposed.
Abstract: An novel method of generating one-line diagrams of radial distribution systems in the form of a visibility graph is proposed. An algorithm that automatically generates an aesthetically 'pleasing' and 'readable' visibility diagram is presented. In addition to the basic property of a visibility graph that nodes and edges be represented by axis-parallel horizontal and vertical lines, respectively, a new set of layout specifications (aesthetic criteria) suitable for easy visualization of the distribution system have been proposed. This work is based on the premise that, in general, the network data of distribution systems does not contain any geographical information of node locations. Therefore the algorithm assumes that only the identity of the terminal nodes of all the edges are known. The proposed algorithm automatically determines node positions such that the specified aesthetic criteria are satisfied.
Journal Article•
TL;DR: In this article, the authors studied 3D visibility representations of complete graphs where vertices are represented by equal convex polygons lying in planes parallel to the xy-plane.
Abstract: This paper continues the study of 3D visibility representations of complete graphs where vertices are represented by equal convex polygons lying in planes parallel to the xy-plane. Edges correspond to the z-parallel visibility among these polygons. We give several bounds on the size of the largest complete graph that has a 3D visibility representation with particular properties. Namely we improve the best known lower bound for representations by regular n-gons from [(n+1)/2] + 2 to n + 1 and the upper bound from 2 2n to ( 6n-3 3n-1 ) - 3.
21 Sep 2003
TL;DR: This paper continues the study of 3D visibility representations of complete graphs where vertices are represented by equal convex polygons lying in planes parallel to the xy-plane and edges correspond to the z-parallel visibility among these polygons.
Abstract: This paper continues the study of 3D visibility representations of complete graphs where vertices are represented by equal convex polygons lying in planes parallel to the xy-plane. Edges correspond to the z-parallel visibility among these polygons.
TL;DR: It is shown that the visibility graph of a set of disjoint congruent discs in R2 is Hamiltonian, as long as the discs are not all supported by the same line.
Abstract: We show that the visibility graph of a set of disjoint congruent discs in R2 is Hamiltonian, as long as the discs are not all supported by the same line. The proof is constructive, and leads to efficient algorithms for obtaining a Hamilton circuit.
Journal Article•
TL;DR: A polynomial time algorithm is given for recognizing a topological rectangle visibility graph and for constructing, when possible, a realizing set of rectangles on the unit grid.
Abstract: Non-overlapping axis-aligned rectangles in the plane define visibility graphs in which vertices are associated with rectangles and edges with visibility in either the horizontal or vertical direction. The recognition problem for such graphs is known to be NP-complete. This paper introduces the topological rectangle visibility graph. We give a polynomial time algorithm for recognizing such a graph and for constructing, when possible, a realizing set of rectangles on the unit grid. The bounding box of these rectangles has optimum length in each dimension. The algorithm provides a compaction tool: given a set of rectangles, one computes its associated graph, and runs the algorithm to get a compact set of rectangles with the same visibility properties.
Proceedings Article•
1 Jan 2003
TL;DR: This paper automated the process of inspecting the outside of a simple two-dimensional polygon, given a few user parameters, using an algorithm that preprocesses the polygon using Visibility Graph like concepts, and creates a visibility data structure for each polygon edge.
Abstract: Many applications, ranging from visualization applications such as architectural walkthroughs to robotic applications such as surveillance, could benefit from an automatic camera trajectory planner. This paper deals with that problem. We have automated the process of inspecting the outside of a simple two-dimensional polygon, given a few user parameters. Our algorithm preprocesses the polygon using Visibility Graph like concepts, and creates a visibility data structure for each polygon edge. From these structures, "good" camera zones are computed. Natural cubic splines are then used to create a closed camera trajectory that passes solely inside the zones. An iterative process refines the trajectory by minimizing a cost function until it converges to the optimal result. CR
15 Oct 2003
TL;DR: This paper presents a new hardware-directed method for construction of the complete visibility graph of a planar domain valuable for mobile robot path planning and points to the possibilities of developing a low-cost and high speed system for environment representation.
Abstract: Various geometric structures play an important role in the solution of the robotic path planning problem These include convex hulls, visibility graphs, tangent graphs and Voronoi diagrams While substantial work has been done on sequential algorithms for constructing various geometric structures, reports on algorithms that can be easily ported to hardware are relatively scarce With an increasing need to handle cluttered and dynamic environments, real-time solutions for constructing geometric structures via custom hardware is desirable This paper presents a new hardware-directed method for construction of the complete visibility graph of a planar domain valuable for mobile robot path planning Initial results of implementation of the hardware design are promising and point to the possibilities of developing a low-cost and high speed system for environment representation
27 Feb 2003
TL;DR: In this article, a polynomial time algorithm for recognizing a topological rectangle visibility graph and constructing a realizing set of rectangles on the unit grid is presented. But the problem of computing the visibility graph is NP-complete.
Abstract: Non-overlapping axis-aligned rectangles in the plane define visibility graphs in which vertices are associated with rectangles and edges with visibility in either the horizontal or vertical direction. The recognition problem for such graphs is known to be NP-complete. This paper introduces the topological rectangle visibility graph.We give a polynomial time algorithm for recognizing such a graph and for constructing, when possible, a realizing set of rectangles on the unit grid. The bounding box of these rectangles has optimum length in each dimension. The algorithm provides a compaction tool: given a set of rectangles, one computes its associated graph, and runs the algorithm to get a compact set of rectangles with the same visibility properties.
TL;DR: A coloring argument is used to prove that the minimum number of connected guards which are necessary to watch any polygon with n sides is ⌊(n - 2)/2⌋, which was originally established by induction by Hernandez-Penalver [3].
Abstract: In this paper we consider a variation of the Art Gallery Problem. A set of points G in a polygon Pn is a connected guard set for Pn provided that is a guard set and the visibility graph of the set of guards G in Pn is connected. We use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any polygon with n sides is ⌊(n - 2)/2⌋. This result was originally established by induction by Hernandez-Penalver [3]. From this result it easily follows that if the art gallery is orthogonal (each interior angle is 90° or 270°), then the minimum number of connected guards is n/2 - 2.
1 Aug 2003
TL;DR: It is shown that the segment endpoint visibility graph of any finite set of disjoint line segments in the plane admits a simple Hamiltonian polygon, if not all segments are collinear.
Abstract: We show that the segment endpoint visibility graph of any finite set of disjoint line segments in the plane admits a simple Hamiltonian polygon, if not all segments are collinear. This proves a conjecture of Mirzaian.
1 Jan 2003
TL;DR: In this article, the authors present a new method to implement in constant amortized time the flip operation of the Greedy Flip Algorithm, an optimal algorithm to compute the visibility complex of a collection of pairwise disjoint bounded convex sets of constant complexity (disks).
Abstract: We present a new method to implement in constant amortized time the flip operation of the so-called Greedy Flip Algorithm, an optimal algorithm to compute the visibility complex of a collection of pairwise disjoint bounded convex sets of constant complexity (disks). The method uses simple data structures and only the left-turn predicate for disks; it relies, among other things, on a sum of squares like theorem for visibility complexes stated and proved in this paper. (The sum of squares theorem for a simple arrangement of lines states that the average value of the square of the number of vertices of a face of the arrangement is bounded by a constant.)