We present an order n algorithm which computes the convex hull of a two-dimensional non-selfintersecting polygon. The algorithm recovers much of the simplicity of the one presented by Sklansky (Sklansky, 1972), and subsequently disproved. Unlike several algorithms which have been found since then, the modified algorithm executes a truly uniform (modeless) traversal of all the vertices of the po...

In this paper we present a natural and simple procedure to compute all feasible allocation points of a (non-convex) polygon within a (non-convex) polygonal bounded region. This procedure can be seen as a basis of more sophisticated and efficient algorithms for the same task, or for related problems such as finding a single placement point.

Behavior of convex solution polygons to a general crystalline motion is investigated. A polygon is called admissible if the set of its normal angles equals that of the Wulff shape. We prove that if the initial polygon is not an admissible polygon, then all edges disappear simultaneously, or edge disappearing occurs at most finitely many instants and eventually a convex solution polygon becomes ...

A convex polygon that is nearly-similar to a model polygon P has sides parallel and in the same order to the corresponding sides of P. The lengths of the sides are unrestricted and may be zero. Given a set of target convex polygons in the plane with a total of n vertices, and a xed model convex stabbing polygon P, the minimum-perimeter polygon nearly-similar to P that stabs the targets can be f...

The associahedron is a convex polytope whose face poset is based on nonintersecting diagonals of a convex polygon. In this paper, given an arbitrary simple polygon P , we construct a polytopal complex analogous to the associahedron based on convex diagonalizations of P . We describe topological properties of this complex and provide realizations based on secondary polytopes. Moreover, using the...

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 convex rope problem, posed by Peshkin and Sanderson in IEEE J. Robotics Automat, 2 (1986) pp. 53-58, is to find the counterclockwise and clockwise convex ropes starting at the vertex a and ending at the vertex b of a simple polygon, where a is on the boundary of the convex hull of the polygon and b is visible from infinity. In this paper, we present a linear time algorithm for solving this ...

Based on the planar polygon shape classification, we propose a method—Standardized Binary String Descriptor of Convex Polygon—for classification of convex polygons, making it more precise. Thus, the model database space is pruned and the number of shape models compared with, when doing match query and similarity query, is reduced. Furthermore, the number of equivalence class of convex polygon f...