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...

the purpose of this paper is the generalization of structure factor for rods by polygon section in two dimensional phononic crystals. if we use the plane wave expansion method (pwe) for the propagation of acoustic waves in 2d phononic crystals, structure factor will be an important quantity. in order to confirm the obtained relations, we have calculated the band structure for xy and z vibration...

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...

In this paper we resolve the following problem: Given a simple polygon , what is the maximum-area polygon that is axially symmetric and is contained by ? We propose an algorithm for answering this question, analyze the algorithm’s complexity, and describe our implementation of it (for convex polygons). The algorithm is based on building and investigating a planar map, each cell of which corresp...

A floodlight of size α is a light source that projects light in a cone of size α . In this paper we study the problem of illuminating a convex polygon using floodlights. We give an O(n 2 ) time algorithm to find an optimal pair of floodlights to illuminate a convex polygon P with n vertices; that is a pair of floodlights to illuminate a convex polygon in such a way that the sum of their sizes i...

We present two algorithms for packing two largest disks in a polygon. The first algorithm locates two disks in a simple polygon in time O(n log2 n) improving the best previous deterministic result (Bespamyatnikh, 1999) by a factor of logn. The second algorithm finds two disks in a convex polygon such that the disks are separated by a diagonal of the polygon. It runs in time O(n log2 n) improvin...

Many psychological tasks vary in difficulty with the complexity of the stimulus objects involved. Complex visual objects are not only harder to reproduce from memory than simple ones (4, 6), but also harder to learn by name (4, 7) and to match (11). Complexity is an ill-defined variable, however. No two of the experiments referenced above employ exactly the same operations of physical measureme...