The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be...

In this paper we address several variants of the polygon an-nulus placement problem: given an input polygon P and a set S of points, nd an optimal placement of P that maximizes the number of points in S that fall in a certain annulus region deened by P and some ooset distance > 0. We address the following variants of the problem: placement of a convex polygon as well as a simple polygon; placem...

In this paper we present a very simple proof of the following result due to Abello et al [5], concerning the visibility graphs of simple polygons. The result says that the visibility graph of any simple nondegenerate polygon is isomorphic to the visibility graph of some simple staircase polygon. As a result of the above proof we also give an O(n log n) time algorithm for the following problem: ...

To support tempoml operators efficiently, indexing based on tempoml attributes must be supported. In this paper, we pmpose a dynamic and eficient index scheme called the time polygon (TP-index) for tempoml databases. In the scheme, tempoml data are mapped into a two-dimensional tempoml space, where the data can be clustered based on time. The data space is then partitioned into time polygons wh...

By connecting the points which are the kind of linear combinations of Bézier control points, a broken line polygon called quasi-control polygon is produced. Using it to approximate Bézier segment, this paper obtains two sharp, quantitative bounds, besides depending on the degree of the polynomial, the bounds depend only on the maximal absolute second differences or the sum of absolute second di...

Let P be a simple polygon with n vertices. We present a new O(n)-time algorithm to compute the visible part of one edge from another edge of P . The algorithm does not alter the input and only uses O(1) variables and is therefore a constant-workspace algorithm. The algorithm can be used to make a constant-workspace algorithm for computing the weak visibility polygon from an edge in O(mn) time, ...

We present an algorithm for a pair of pursuers, each with one flashlight, searching for an unpredictable, moving target in a 2D environment (simple polygon). Given a polygon with n edges and m concave regions, the algorithm decides in time O(n + nm + m) whether the polygon can be cleared by the two 1-searchers, and if so, constructs a search schedule. The pursuers are allowed to move on the bou...

There are many di-erent kinds of guards in a simple polygon that have been proposed and discussed. In this paper, we consider a new type of guard, boundary guard, which is a guard capable of moving along a boundary of a polygon and every interior point of the polygon can be seen by the mobile guard. We propose an algorithm to 1nd the shortest boundary guard of a simple polygon P in O(n log n) t...

The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can often be described by a scaling function. We develop the method of qlinear approximants in order to extract the approximate scaling behaviour of polygon models ...

We establish the relation between the ISO(2, 1) homotopy invariants, and the polygon representation of (2+1)-dimensional gravity. The polygon closure conditions, together with the SO(2, 1) cycle conditions, are equivalent to the ISO(2, 1) cycle conditions for the representations ρ : π 1 (Σ g,N) → ISO(2, 1). Also, the symplectic structure on the space of invariants is closely related to that of ...