Guarding a polygon with few guards is an old and well-studied problem in computational geometry. Here we consider the following variant: We assume that the polygon is orthogonal and thin in some sense, and we consider a point p to guard a point q if and only if the minimum axis-aligned rectangle spanned by p and q is inside the polygon. A simple proof shows that this problem is NP-hard on ortho...

Given a planar polygon (or chain) with a list of edges {e1, e2, e3, . . . , en−1, en}, we examine the effect of several operations that permute this edge list, resulting in the formation of a new polygon. The main operations that we consider are: reversals which involve inverting the order of a sublist, transpositions which involve interchanging subchains (sublists), and edge-swaps which are a ...

“Trixel Buffers is a new spatial data-structure for fast point in multiple polygon inclusion queries. The algorithm utilizes a pre-processing step in which the inside/outside status of a quadtree ́s leaf triangles without polygon geometry is pre-computed automatically; at run-time point queries lying within these triangles simply inherit their inclusion status. If a point query lies in a leaf tr...

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.