We consider the problem of recognizing star-polygons under staircase visibility (s-visibility). We show that the s-visibility polygon from a point inside a simple orthogonal polygon of n sides can be computed in O(n) time. When the polygon contains holes the algorithm runs in O(n log n) time, which we prove to be optimal by linear time reduction from sorting. We present an algorithm for computi...

In Gold et al. (1996) a simple polygon digitizing technique was described where ‘fringe’ points were digitized around the interior of each map polygon, the Voronoi diagram constructedand the relevant polygon boundary segments extracted from the Voronoi cells. Gold (1997a) extended this to work with scanned map input, where the fringe points were generated automatically, and complete polygon bou...

An important problem in robotics is searching for a target point in an unknown polygonal region [5]. In this problem, a robot with vision is placed at a starting point s in a polygon and must traverse a path to some target point t in the polygon. The robot has no prior information about the geometry of the polygon or the location of the target, however, the robot will recognize the target when ...

A polygon P is x-monotone if any line orthogonal to the x-axis has a simply connected intersection with P . A set G of points inside P or on the boundary of P is said to guard the polygon if every point inside P or on the boundary of P is seen by a point in G. An interior guard can lie anywhere inside or on the boundary of the polygon. Using a reduction fromMonotone 3SAT, we prove that interior...

We show that any simple n-vertex polygon can be made convex, without losing internal visibilities between vertices, using n moves. Each move translates a vertex of the current polygon along an edge to a neighbouring vertex. In general, a vertex of the current polygon represents a set of vertices of the original polygon that have become co-incident. We also show how to modify the method so that ...

A hidden guard set G is a set of point guards in polygon P that all points of the polygon are visible from some guards in G under the constraint that no two guards may see each other. In this paper, we consider the problem for finding minimum hidden guard sets in histogram polygons under orthogonal visibility. Two points p and q are orthogonally visible if the orthogonal bounding rectangle for ...

We present the first polynomial-time algorithm for computing the Fréchet distance for a non-trivial class of surfaces: simple polygons. For this, we show that it suffices to consider homeomorphisms that map an arbitrary triangulation of one polygon to the other polygon such that diagonals of the triangulation are mapped to shortest paths in the other polygon.

We explore the connection between polygon posets, which is a class of ranked posets with an edgelabeling which satisfies certain 'polygon properties', and the weak order of Coxeter groups. We show that every polygon poset is isomorphic to a join ideal in the weak order, and for Coxeter groups where no pair of generators have infinite order the converse is also true. The class of polygon posets ...

Many classes of scenes contain objects that are (approximately) two-dimensional polygons—for example, buildings in an aerial photograph, or flat mechanical parts on a tabletop. This paper deals with the problem of recovering (an approximation to) an unknown polygon from noisy digital data, obtained by digitizing either an image of the (solid) polygon or a sequence of points on its boundary. Not...

We consider the problem of sweeping (or grazing) the inte-rior/exterior of a polygon by a exible rope whose one end point (anchor) is attached on the boundary of the polygon. We present a linear time algorithm to compute the grazing area inside a simple polygon. We show how to extend the algorithm for computing the internal grazing area, without increasing its time complexity, to compute the gr...