Calculating the number of Euclidean triangulations of a convex polygon P with vertices in a finite subset C ⊂ R2 containing all vertices of P seems to be difficult and has attracted some interest, both from an algorithmic and a theoretical point of view, see for instance [1], [2], [3], [4], [5], [7], [9], [10], [11]. The aim of this paper is to describe a class of configurations, convex near-go...

A finite set of points in the plane is described as in convex position if it forms the set of vertices of a convex polygon. This work studies the ratio between the maximum area of convex heptagons with vertices in P and the area of the convex hull of P, where the planar point set P is in convex position.

Given a convex polygon in the plane, we are interested in triangulations of its interior, i.e. maximal sets of nonintersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest area triangle in the triangulation. There exists a dynamic programming algorithm that computes ...

We describe an algorithm for computing the outer common tangents of two disjoint simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies on the same side of the line. An outer common tangent of two polygons is a tangent of both polygons such that the polygons lie on the same side of the tangent. Each ...

We describe the first algorithm to compute the outer common tangents of two disjoint simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies on the same side of the line. An outer common tangent of two polygons is a tangent of both polygons such that the polygons lie on the same side of the tangent. E...

Given a convex polygon with n vertices in the plane, we are interested in triangulations of its interior, i.e., maximal sets of nonintersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest triangle in the triangulation. Similarly, the MinMax area triangulation is the...

os-Nagy Theorem and its Rami cations Godfried Toussaint School of Computer Science McGill University Montr eal, Qu ebec, Canada June 29, 1999 Abstract Given a simple polygon in the plane, a ip is dened as follows: consider the convex hull of the polygon. If there are no pockets do not perform a ip. If there are pockets then re ect one pocket across its line of support of the polygon to obtain a...