Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P . We build a data structure in O(n) time and O(n) space that can compute the visibility polygon for any query line segment s in O(k log n) time, where k is the size of the visibility polygon of s and n is the number of vertices of P . Al...

The scattering support is an estimate of the support of a source or scatterer, based on a limited set of far field measurements. In this paper, we suppose that the far field is measured at all wavenumbers, but only at a few, say N, angles θi ∈ . From these measurements, we produce a -convex polygon (a convex polygon with normals in the θi directions). We show that this polygon must be contained...

An example is presented of a cubic Bézier curve that is the unknot (a knot with no crossings), but whose control polygon is knotted. It is also shown that there is no upper bound on the number of crossings in the control polygon for an unknotted Bézier curve. These examples complement known upper bounds on the number of subdivisions sufficient for a control polygon to be ambient isotopic to its...

In this paper we solve the following optimization problem: Given a simple polygon P , what is the maximum-area polygon that is axially symmetric and is contained by P? We propose an algorithm for solving this problem, analyze its complexity, and describe our implementation of it (for the case of a convex polygon). The algorithm is based on building and investigating a planar map, each cell of w...

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 Newton polygon of the implicit equation of a rational plane curve is explicitly determined by the multiplicities of any of its parametrizations. We give an intersection-theoretical proof of this fact based on a refinement of the KušnirenkoBernštein theorem. We apply this result to the determination of the Newton polygon of a curve parameterized by generic Laurent polynomials or by generic r...

We examined whether visual working memory (WM) capacity allocation is determined solely by complexity, with the number of objects being redundant, as suggested by flexible resource models. Participants performed the change detection task with random polygons as stimuli, while we monitored the contralateral delay activity (CDA), an electrophysiological marker whose amplitude rises as WM capacity...

Let P be a polygon with r > 0 reflex vertices and possibly with holes. A subsuming polygon of P is a polygon P ′ such that P ⊆ P ′, each connected component R′ of P ′ subsumes a distinct component R of P , i.e., R ⊆ R′, and the reflex corners ofR coincide with the reflex corners ofR′. A subsuming chain of P ′ is a minimal path on the boundary of P ′ whose two end edges coincide with two edges o...

Let P be a polygon inscribed in a circle. The shadow of P is a polygon P ′ whose vertices are at the midpoints of the arcs of consecutive points of P . The shadow sequence P , P , P , . . . is a sequence of inscribed polygons such that each P t is the shadow of P t−1 for all t ≥ 0. We show in this abstract that the shadow sequence converges to the regular polygon, and in such way that variance ...