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 ...

We extend a dynamic-programming algorithm of Keil and Snoeyink for finding a minimum convex decomposition of a simple polygon to the case when both convex polygons and pseudo-triangles are allowed. Our algorithm determines a minimum pseudo-convex decomposition of a simple polygon in O(n) time where n is the number of the vertices of the polygon. In this way we obtain a well-structured decomposi...

This paper considers reconngurations of polygons, where each polygon edge is a rigid link, no two of which can cross during the motion. We prove that one can reconngure any monotone polygon into a convex polygon; a polygon is monotone if any vertical line intersects the interior at a (possibly empty) interval. Our algorithm computes in O(n 2) time a sequence of O(n 2) moves, each of which rotat...