A flipturn on a polygon consists of reversing the order of edges inside a pocket of the polygon, without changing lengths or slopes. Any polygon with n edges must be convexified after at most (n− 1)! flipturns. A recent paper showed that in fact it will be convex after at most n(n−3)/2 flipturns. We give here lower bounds. We construct a polygon such that if pockets are chosen in a bad way, at ...

A polygon is called k-guardable if it is possible to find a collection G of points in the interior of the edges of P such that every point in P is visible from at least k elements of G, and such that no edge of P contains more than one element of G. In this paper we prove that every simple polygon can be 1-guarded using at most n/2 guards, and that every polygon with 0 or 1 polygonal hole can...

The generation of random simple polygon and the pseudo-triangulation of a polygon are regarded as the proposed problems in computational geometry. The production of a random polygon is used in the context of the consideration of the accuracy of algorithms. In this paper, a new algorithm is presented to generate a simple spiral polygon on a set of random points S in the plane using convex hull l...

A classic problem in computer graphics is to decompose a simple polygon into a collection of triangles whose vertices are only those of the simple polygon. By definition, a simple polygon is an ordered sequence of n points, ~ V0 through ~ Vn−1. Consecutive vertices are connected by an edge 〈~ Vi, ~ Vi+1〉, 0 ≤ i ≤ n − 2, and an edge 〈~ Vn−1, ~ V0〉 connects the first and last points. Each vertex ...

In this paper we present a polynomial time algorithm for computing a Hausdorff core of a polygon with a single reflex vertex. A Hausdorff core of a polygon P is a convex polygon Q contained inside P which minimizes the Hausdorff distance between P andQ. Our algorithm essentially consists of rotating a line about the reflex vertex; this line defines a convex polygon by cutting P . To determine t...

Polygon approximation plays a vital role in abquitious applications like multimedia, geographic and object recognition. An extensive number of polygonal approximation techniques for digital planar curves have been proposed over the last decade, but there are no survey papers on recently proposed techniques. Polygon is a collection of edges and vertices. Objects are represented using edges and v...

We present a new method for line drawing, triangle filling, polygon filling, and antialiasing. Current statistics show that our method improves line drawing and antialiasing about 6 times and polygon filling functions significantly over all existing methods. Specifically, it can improve finding the span extrema of polygons about 2 times and drawing the antialiased polygon edges more than 2 time...

Given an orthogonal polygon P with n vertices, the goal of the watchman route problem is finding a path S of the minimum length in P such that every point of the polygon P is visible from at least one of the point of S. In the other words, in the watchman route problem we must compute a shortest watchman route inside a simple polygon of n vertices such that all the points interior to the polygo...

An algorithm for computing the convex hull of a simple polygon is presented. Its correctness and complexity are also shown. Computational geometry Convex hull Simple polygon Algorithm

The no-fit polygon (NFP) is the set of feasible locations that one polygon may take with respect to another polygon, such that the polygons do not overlap. Feasible locations are required for most of the solutions to two-dimensional packing problems, and also for other problems such as robot motion planning. Efficient methods to calculate the NFP of two convex polygons, or one convex and one no...