The associahedron is a convex polytope whose face poset is based on nonintersecting diagonals of a convex polygon. In this paper, given an arbitrary simple polygon P , we construct a polytopal complex analogous to the associahedron based on convex diagonalizations of P . We describe topological properties of this complex and provide realizations based on secondary polytopes. Moreover, using the...

Ron Wein et al. [4] introduced the Visibility-Voronoi diagram for clearance c, denoted by V V , which is a hybrid between the visibility graph and the Voronoi diagram of polygons in the plane. It evolves from the visibility graph to the Voronoi diagram as the parameter c grows from 0 to ∞. This diagram can be used for planning natural-looking paths for a robot translating amidst polygonal obsta...

Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. A three-dimensional visibility representation that has been studied is one in which each vertex of the graph maps to a closed rectangle in R 3 and edges are expressed by vertical visibility between rectangles. The rectangles representing vertices are disjoin...

This paper presents a new technique for determining a small set of views that allow the observation and acquisition of the surfaces of the objects present in a target scene through a range sensor that moves over a sphere containing that scene. No a priori knowledge about the shape of those objects is assumed. Instead of applying costly visibility analysis techniques from the beginning as in mos...

We study the sensor and movement capabilities that simple robots need in order to create a map of an unknown polygon of size n, and to meet. We consider robots that can move from vertex to vertex, can backtrack movements, and see distant vertices in counter-clockwise order but have no means of visibly identifying them. We show that such robots can always solve the weak rendezvous problem and re...

Tracking humans that are interacting with the other subjects or environment remains unsolved in visual tracking, because the visibility of the human of interests in videos is unknown and might vary over time. In particular, it is still difficult for state-of-the-art human trackers to recover complete human trajectories in crowded scenes with frequent human interactions. In this work, we conside...

Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a...

In this paper we describe a model for navigation of an autonomous agent in which localization, path planning, and locomotion is performed in a qualitative manner instead of relying on exact coordinates. Our approach is grounded in a decomposition of navigable space based on a novel model of visibility and occlusion relations between extended objects for agents with very limited sensor abilities...

A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertexsegments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices; beyond that segments do not intersect. We generalize visibility to 1-visibility, where each edge(vertex-) segment crosses at most one vertex(edge-) segment. ...

Tracking humans that are interacting with the other subjects or environment remains unsolved in visual tracking, because the visibility of the human of interests in videos is unknown and might vary over time. In particular, it is still difficult for state-of-the-art human trackers to recover complete human trajectories in crowded scenes with frequent human interactions. In this work, we conside...