In this paper we introduce the notion of general position. We also show some auxiliary theorems for proving Jordan curve theorem. The following main theorems are proved: 1. End points of a polygon are in the same component of a complement of another polygon if number of common points of these polygons is even; 2. Two points of polygon L are in the same component of a complement of polygon M if ...

We present several algorithms for computing the visibility polygon of a simple polygon P from a viewpoint inside the polygon, when the polygon resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O(nr̄) time, where r̄ denotes the number of reflex vertices of P that are...

We present several algorithms for computing the visibility polygon of a simple polygon P from a viewpoint inside the polygon, when the polygon resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O(nr̄) time, where r̄ denotes the number of reflex vertices of P that are...

We study the problem of reconstructing a simple polygon from angles measured at the vertices of the polygon. We assume that at each vertex, a sensing device returns the sequence of angles between each pair of vertices that are visible. We prove that the sequence of angle measurements at all vertices of a simple polygon in cyclic order uniquely determines the polygon up to similarity. Furthermor...

We are interested in the problem of guarding simple orthogonal polygons with the minimum number of r-guards. The interior point p belongs an orthogonal polygon P is visible from r-guard g, if the minimum area rectangle contained p and q lies within P . A set of point guards in polygon P is named guard set (as denoted G) if the union of visibility areas of these point guards be equal to polygon ...

In this paper, different topologies of dual-frequency modified 3-way Bagley polygon power dividers are designed and analyzed. Equal split power division is achieved at arbitrary design frequencies. In the first structure, two-section transmission line transformer is used to realize the dual-frequency operation. In the second and third structures, dual-frequency T-shaped and π-shaped matching ne...

We present a.n algorithm to decompose the edges of planar curved object so that the carrier polygon of decomposed boundary is a simple polygon. We also present an algoritbm to compute a simple characteristic carrier polygon. By refining this decomposition further and using the chords and wedges of decomposed edges, we obtain an inner polygon (resp. an outer polygon) which is a simple polygon to...

The aim of the present numerical study is to analyze the conjugate natural convection heat transfer in a differentially heated square enclosure containing a conductive polygon object. The left wall is heated and the right wall is cooled, while the horizontal walls are kept adiabatic. The COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parame...

The geodesic center of a simple polygon is a point inside the polygon which minimizes the maximum internal distance to any point in the polygon. We present an algorithm which calculates the geodesic center of a simple polygon with n vertices in time O(n log n).