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...

In this paper we define a function R(P ) which is defined for any polygon P and which maps a given polygon P into a number from the interval (0, 1]. The number R(P ) can be used as an estimate of the rectilinearity of P . The mapping R(P ) has the following desirable properties: – any polygon P has the estimated rectilinearity R(P ) which is a number from (0, 1]; – R(P )=1 if and only if P is a...

A variation on the classical polygon illumination problem was introduced in [Aichholzer et. al. EuroCG’09]. In this variant light sources are replaced by wireless devices called k-modems, which can penetrate a fixed number k, of “walls”. A point in the interior of a polygon is “illuminated” by a k-modem if the line segment joining them intersects at most k edges of the polygon. It is easy to co...

Cross-calibration using an autocollimator and a polygon is the traditional method for calibrating rotary encoder. These angles, which can be calibrated this method, are limited by pitch angle of polygon, 15° 24-faced polygon. In work, we propose new shift-angle same setup as method. However, measure smaller than measurement limitation The proposed calibrate every experiment, use to SelfA encode...

Periods of rational polygons. A rational polygon P is a polygon in the plane, all of whose vertices have rational coordinates. If we dilate the polygon P by an integer k, the dilated polygon is written as kP. It is a theorem that the number of integer points in the plane (a, b) ∈ Z2, which are contained in kP, is given by a quasi-polynomial function of k. That is, |Z2 ∩ kP| = area(P)k2 + a1(k)k...