A half-plane probe through a polygon measures the area of intersection between a half-plane and the polygon. We dev elop techniques based on xray probing to determine convex n-gons in 7n + 7 half-plane probes. We also show n + 1 half-plane probes are sufficient to verify a specified convex polygon and prove linear lower bounds for determination and verification.

Strong visibility is a generalization of standard visibility, defined with respect to a fixed set of line orientations. We investigate computational properties of this generalized visibility, as well as the related notion of strong convexity. In particular, we describe algorithms for the following tasks: 1. Testing the strong visibility of two points in a polygon and the strong convexity of a p...

Let M be an m-sided simple polygon and N be an n-sided polygon with holes. In this paper we consider the problem of computing the feasible region i.e., the set of all placements by translation of M so that M lies inside N without intersecting any hole. First we propose an O(mn 2) time algorithm for computing the feasible region for the case when M is a monotone polygon. Then we consider the gen...

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, ...