Showing papers on "Visibility graph published in 2001"
TL;DR: This work shows how a set of isovists can be used to generate a graph of mutual visibility between locations, and demonstrates that this graph can also be constructed without reference to isovist and that it is in fact invoking the more general concept of a visibility graph.
Abstract: An isovist, or viewshed, is the area in a spatial environment directly visible from a location within the space. Here we show how a set of isovists can be used to generate a graph of mutual visibility between locations. We demonstrate that this graph can also be constructed without reference to isovists and that we are in fact invoking the more general concept of a visibility graph. Using the visibility graph, we can extend both isovist and current graph-based analyses of architectural space to form a new methodology for the investigation of configurational relationships. The measurement of local and global characteristics of the graph, for each vertex or for the system as a whole, is of interest from an architectural perspective, allowing us to describe a configuration with reference to accessibility and visibility, to compare from location to location within a system, and to compare systems with different geometries. Finally we show that visibility graph properties may be closely related to manifestations of spatial perception, such as way-finding, movement, and space use.
1,029 citations
28 May 2001
TL;DR: This paper describes algorithms based on optimization theory and visibility graph construction, and shows how to integrate them into a comprehensive planner that has a low-order polynomial complexity and produces good results.
Abstract: This paper presents a practical planning system for 2D assembly tasks at the nanoscale. The planner covers a whole range of problems in planning the assembly of nanoparticle patterns, including object assignment, obstacle detection and avoidance, path finding, and path sequencing. We describe algorithms based on optimization theory and visibility graph construction, and show how to integrate them into a comprehensive planner that has a low-order polynomial complexity and produces good results. We provide theoretical analysis and experimental results. This is a first step towards automating assembly tasks in nanorobotics.
38 citations
TL;DR: Given a scene of disjoint polygonal obstacles with totally n vertices in the plane, this work constructs efficient data structures that enable fast reporting of an "optimal" obstacle-avoiding path between two arbitrary query points t that are given in an on-line fashion.
Abstract: In this paper, we study several geometric path query problems. Given a scene of disjoint polygonal obstacles with totally n vertices in the plane, we construct efficient data structures that enable fast reporting of an "optimal" obstacle-avoiding path (or its length, cost, directions, etc) between two arbitrary query points s and t that are given in an on-line fashion. We consider geometric paths under several optimality criteria: Lm length, number of edges (called links), monotonicity with respect to a certain direction, and some combinations of length and links. Our methods are centered around the notion of gateways, a small number of easily identified points in the plane that control the paths we seek. We give efficient solutions for several special cases based upon new geometric observations. We also present solutions for the general cases based upon the computation of the minimum size visibility polygon for query points.
22 citations
TL;DR: This paper presents an efficient approach to represent the environment, which can be used to facilitate dynamic path planning in robot navigation systems and lends well for hardware porting and thus highly suited to high-speed generation of the visibility graph.
Abstract: This paper presents an efficient approach to represent the environment, which can be used to facilitate dynamic path planning in robot navigation systems. The environment is modelled by first defining a ‘virtual rectangle’ to represent an environment that avoids unwanted obstacles. The obstacles within the environment are then represented as convex polygons to generate the required visibility graph. The devised techniques lend well for hardware porting and thus highly suited to high-speed generation of the visibility graph. It has been demonstrated that efficient dynamic path planning can be realised by generating the ‘virtual rectangle’ on the fly such that only the environment needed to facilitate onward traversal can be identified. Finally, the proposed algorithms lend well for high-speed computations as they facilitate a high-degree of parallelism at the architecture level.
19 citations
TL;DR: It is shown that the visibility graph of a set of non-intersecting translates of the same compact convex object in R 2 always contains a Hamiltonian path and that every other edge in the Hamiltonian route can be used to obtain a perfect matching.
7 citations
TL;DR: This paper disproves the conjecture that every hamiltonian maximal planar graph with a 3-clique ordering is a visibility graph.
3 citations
TL;DR: The lower bound for the number of labelled visibility graphs of simple polygons of n vertices is roughly in the order of O (n 2n ) and the upper bound is O ( n 3n) .
2 citations
1 Jan 2001
TL;DR: In this article, the authors present a smooth trajectory planning algorithm which uses the natural behavior model of a mobile robot (MR) and the shortest path in the free configuration space is obtained by using the visibility graph method.
Abstract: This paper represents a novel smooth trajectory planning algorithm which uses the natural behavior model of a mobile robot (MR). The shortest path in the free configuration space is obtained by using the visibility graph method. It is modified according to dynamic constraints which are implicitly included in the natural behavior of the mobile robot. The modified path becomes a smooth, easily tractable time-optimal trajectory. For every points of it, translating/steering velocities and accelerations and reaching times are known. It is applicable to the real-time dynamic configuration spaces, because of simplicity and low computational time.
2 citations
TL;DR: These analyses suggest that measures derived from the visibility graph may be of particular relevance to the growing interest in quantifying the perceptual characteristics of landscapes.
Abstract: Visibility analysis based on viewsheds is one of the most frequently used GIS analysis tools. In this paper we present an approach to visibility analysis based on the visibility graph. A visibility graph records the pattern of mutual visibility relations in a landscape, and provides a convenient way of storing and further analysing the results of multiple viewshed analyses for a particular landscape region. We describe how a visibility graph may be calculated for a landscape. We then give examples, which include the interactive exploration of a landscape, and the calculation of new measures of a landscape's visual properties based on graph metrics-in particular, neighbourhood clustering coefficient and path length analysis. These analyses suggest that measures derived from the visibility graph may be of particular relevance to the growing interest in quantifying the perceptual characteristics of landscapes.
TL;DR: A simple method for recognizing orthogonal polygons using the concept of visibility is addressed, and this concept is extended for recognizing general polygons.