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...

Polygons are one of the fundamental building blocks in geometric modeling, and they are used to represent a wide variety of shapes and figures in computer graphics, vision, pattern recognition, robotics, and other computational fields. By a polygon we mean a region of the plane enclosed by a simple cycle of straight line segments; a simple cycle means that nonadjacent segments do not intersect ...

The first purpose of this paper is to propose a formulation of general area-preserving motion of polygonal curves by using a system of ODEs. Solution polygonal curves belong to a prescribed polygonal class, which is similar to admissible class used in the so-called crystalline curvature flow. Actually, if the initial curve is a convex polygon, then our polygonal flow is nothing but the crystall...

A simple polyhedron is weakly-monotonic in direction ~ d provided that the intersection of the polyhedron and any plane with normal ~ d is simply-connected (i.e. empty, a point, a line-segment or a simple polygon). Furthermore, if the intersection is a convex set, then the polyhedron is said to be weakly-monotonic in the convex sense. Toussaint [10] introduced these types of polyhedra as genera...

A numerical method is developed for calculating the buckling loads of tapered columns of regular polygon cross-section with constant volume and both clamped ends. The linear, parabolic and sinusoidal tapers are considered in numerical examples. From the numerical results, the strongest columns by the taper types and side numbers of regular polygon cross-sections are identified.

Interiors of buildings are often represented as two-dimensional spaces with attributes attached to them. Examples can be found everywhere, from architectural design plans to maps showing evacuation routes in emergency cases. Most of the navigation programs use primarily 2D plans for visualization and communication. Some exceptions are historical buildings and museums, which do offer navigation ...

We survey various forms of the problem, primarily in two and three dimensions, for motion of a single point, since most results have focused on these cases. We discuss shortest paths in a simple polygon (Section 31.1), shortest paths among obstacles (Section 31.2), and other metrics for length (Section 31.3). We also survey other related geometric network optimization problems (Section 31.4). H...

In this paper we describe the matter-free toroidal spacetime in ’t Hooft’s polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we find that it is not possible to describe the torus by just one polygon but we need at least two polygons. We also show that the constraint algebra of the polygons closes....