A simple proof for visibility paths in simple polygons

The purpose of this note is to give a simple proof for a necessary and sufficient condition for visibility paths in simple polygons. A visibility path is a curve such that every point inside a simple polygon is visible from at least one point on the path. This result is essential for finding the shortest watchman route inside a simple polygon specially when the route is restricted to curved paths

Vertex-Edge Pseudo-Visibility Graphs: Characterization and Recognition

We extend the notion of polygon visibility graphs to pseudo-polygons defined on generalized configurations of points. We consider both vertex-to-vertex, as well as vertex-to-edge visibility in pseudo-polygons. We study the characterization and recognition problems for vertex-edge pseudo-visibility graphs. Given a bipartite graph G satisfying three simple properties, which can all be checked in polynomial time, we show that we can define a generalized configuration of points and a pseudo-polygon on it, so that its vertex-edge pseudo-visibility graph is G. This provides a full characterization of vertex-edge pseudo-visibility graphs and a polynomial-time algorithm for the decision problem. It also implies that the decision problem for vertex visibility graphs of pseudo-polygons is in NP (as opposed to the same problem with straight-edge visibility, which is only known to be in PSPACE)

The Vertex-Edge Visibility Graph of a Polygon

We introduce a new polygon visibility graph, the vertex-edge visibility graph GV E, and demonstrate that it encodes more geometric information about the polygon than does the vertex visibility graph GV. © 1998 Elsevier Science B.V

A Novel Approach to Assess the Influence of Rockfall Source Areas: The Case Study of Bardonecchia (Italy)

In this research article, we propose a practical methodology for evaluating the affecting potential of detachment areas in rockfalls. Our innovative approach combines an assessment of the visibility of rockfall source areas, with reference to specific rockfall scenarios and elements at risk, considering the rockfall Susceptibility Index to Failure (SIF) of these areas. The result is the characterization of source areas through a rockfall Source Affecting Index (SAI), which considers both the morphology of the slope and the geostructural conditions of the rock walls. This information can be very useful since it aids in optimizing more in-depth analyses, as well as the placement of monitoring instruments or stabilization systems. The proposed methodology has been implemented in the open-source software QGIS through the development of an easy-to-use plugin named Ranking of the Affecting Potential of Detachment Areas in Rockfalls, or “RADAR”. RADAR is designed to be used in conjunction with QPROTO, a well-known QGIS plugin for preliminary rockfall susceptibility/hazard analyses based on a visibility analysis and a simplified mechanical method. To demonstrate the effectiveness of the proposed approach, an application to a case study located in the Western Alps (Bardonecchia, Italy) is presented and discussed in the paper

Multitriangulations, pseudotriangulations and primitive sorting networks

We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration algorithm for arrangements with a given support, based on the properties of certain greedy pseudoline arrangements and on their connection with sorting networks. Both the running time per arrangement and the working space of our algorithm are polynomial. As the motivation for this work, we provide in this paper a new interpretation of both pseudotriangulations and multitriangulations in terms of pseudoline arrangements on specific supports. This interpretation explains their common properties and leads to a natural definition of multipseudotriangulations, which generalizes both. We study elementary properties of multipseudotriangulations and compare them to iterations of pseudotriangulations.Comment: 60 pages, 40 figures; minor corrections and improvements of presentatio

Enabling collaboration in virtual reality navigators

In this paper we characterize a feature superset for Collaborative Virtual Reality Environments (CVRE), and derive a component framework to transform stand-alone VR navigators into full-fledged multithreaded collaborative environments. The contributions of our approach rely on a cost-effective and extensible technique for loading software components into separate POSIX threads for rendering, user interaction and network communications, and adding a top layer for managing session collaboration. The framework recasts a VR navigator under a distributed peer-to-peer topology for scene and object sharing, using callback hooks for broadcasting remote events and multicamera perspective sharing with avatar interaction. We validate the framework by applying it to our own ALICE VR Navigator. Experimental results show that our approach has good performance in the collaborative inspection of complex models.Postprint (published version