We present two algorithms for packing two largest disks in a polygon. The first algorithm locates two disks in a simple polygon in time O(n log2 n) improving the best previous deterministic result (Bespamyatnikh, 1999) by a factor of logn. The second algorithm finds two disks in a convex polygon such that the disks are separated by a diagonal of the polygon. It runs in time O(n log2 n) improvin...

We present a short elementary proof of the following Twelve Points Theorem: Let M be a convex polygon with vertices at the lattice points, containing a single lattice point in its interior. Denote by m (resp. m) the number of lattice points in the boundary of M (resp. in the boundary of the dual polygon). Then

We consider the problem of nding a corridor (a separating strip) between two polygons, whose intersection with a third (convex) polygon is of maximum area. The application in mind is the interpolation in simple branching cases, where the sought volume branches from one contour in one slice into two polygons in another parallel slice. We present a linear-time plane-sweep algorithm which computes...

In this paper, we present approximation algorithms for the problem of cutting out a convex polygon P with n vertices from another convex polygon Q with m vertices by a sequence of guillotine cuts of smallest total length. Specifically, we give an O(n + m) running time, constant factor approximation algorithm, and an O(n+m) running time, O(log n)-factor approximation algorithm for cutting P out ...

Efficient cutting strategy of a geometric shape, P out of another geometric shape, Q has been extensively studied in recent years. A number of variations of this problem has been addressed including P being convex or concave, cuts being line cut or ray cut, Q being a polygon or a circle etc. In this paper we give a simple linear time O (log n)-approximation algorithm for the problem where Q is ...

We show how to compute the smallest rectangle that can enclose any polygon, from a given set of polygons, in nearly linear time; we also present a PTAS for the problem, as well as a linear-time algorithm for the case when the polygons are rectangles themselves. We prove that finding a smallest convex polygon that encloses any of the given polygons is NP-hard, and give a PTAS for minimizing the ...

Motion planning is studied in a time-varying environment. Each obstacle is a convex polygon that moves in a fixed direction at a constant speed. The robot is a convex polygon that is subject to a speed bound. A method is presented to determine whether or not there is a translational collision-free motion for a polygonal robot from an initial position to a final position, and to plan such a moti...

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...

Patterns of home range overlap between individuals are key parameters used in discussions of sociality in nocturnal prosimians. Despite the importance of space use variables in defining social structure in nocturnal prosimians, researchers have yet to reach a consensus concerning the most reliable techniques for measuring patterns of home range use. In this paper, we review the methods used in ...

We propose new measures to evaluate to which extent the shape of a given convex polygon is close to the shape of some regular polygon. We prove that our parameters satisfy several reasonable requirements and provide algorithms for their efficient computation. The properties we mostly focus on are the facts that regular polygons are equilateral, equiangular and have radial symmetry.