In the art gallery problem the goal is to place guards (as few as possible) in a polygon so that a maximal area of the polygon is covered. We address here a closely related problem: how to place paintings and guards in an art gallery so that the total value of guarded paintings is a maximum. More formally, a simple polygon is given along with a set of paintings. Each painting, has a length and ...

In different types of information systems, such as multimedia information systems and geographic information systems, object-based information is represented via polygons corresponding to the boundaries of object regions. In many applications, the polygons have large number of vertices and edges, thus a way of representing the polygons with less number of vertices and edges is developed. This a...

A polygon splitting algorithm is a combinatorial recipe. The description and the implementation of polygon splitting should not depend on the embedding geometry. Whether a polygon is being split in Euclidean, in spherical, in oriented projective, or in hyperbolic geometry should not be part of the description of the algorithm. The algorithm should be purely combinatorial, or geometry free. The ...

The nofit polygon an important tool in the area of irregular shape stock cutting problems. It provides efficient handling of the geometric characteristics of the problem. The paper presents a new algorithmic procedure for deriving this tool. Abstract The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing...

Polygon/spline approximation of arbitrary image region shapes is submitted for tool evaluation. First, polygon approximation is performed. Starting with an initial 4–vertices polygon which represents the farest elongations into different directions, the polygon approximation is iteratively refined taking into account the local requirements until a given tolerance criterion is satisfied everywhe...

The author establishes a new mathematical expression for the Frequency Polygon. He uses it to prove strong uniform consistency of Polygon marginal density estimator non-anticipative stationary stochastic processes which are stable in sense Wu (2005). gives examples several time series models this result is relevant.

We give an algorithm that constructs a minimal set of polynomials defining all extension of a (π)-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of the ramification polygon.

A method for creating 3D texture coordinates for a sequence of polygon meshes with changing topology and vertex motion vectors. Keywords— texture, coordinate, uv, uvw, sequence, polygon, mesh, motion, marching, cube, changing, topology, empolygonizer, emtopolizer

Triangulating a given n-vertex simple polygon means to partition the interior of the polygon into n − 2 triangles by adding n − 3 nonintersecting diagonals. Significant theoretical advances have recently been made in finding efficient polygon triangulation algorithms. However, there is substantial effort being made in finding a simple and practical triangulation algorithm. We propose the concep...

We consider the problems of straightening polygonal trees and convexifying polygons by continuous motions such that rigid edges can rotate around vertex joints and no edge crossings are allowed. A tree can be straightened if all its edges can be aligned along a common straight line such that each edge points “away” from a designated leaf node. A polygon can be convexified if it can be reconfigu...