The proofs and applications are based on a Riemannian version of Gromov’s non-squeezing theorem and classical integral geometry. Given a convex surface Σ ⊂ R and a point q in the unit sphere S we denote by UΣ(q) the perimeter of the orthogonal projection of Σ onto a plane perpendicular to q. We obtain a function UΣ on the sphere which is clearly continuous, even, and positive. Let us denote the...

We give analytic inclusion-exclusion formulas for the area and perimeter derivatives of a union of finitely many disks in the plane.

Convexity estimators are commonly used in the analysis of shape. In this paper we define and evaluate a new easily computable measure of convexity for polygons. Let be an arbitrary polygon. If denotes the perimeter in the sense of metrics of the polygon obtained by the rotation of by angle with the origin as the center of the applied rotation, and if is the Euclidean perimeter of the minimal re...

Given a set of points in 2 or 3 dimensions, the problem of computing a geometric structure enclosing the point set while optimizing some criteria of the enclosing structure such as area, perimeter, surface area or volume has been widely studied in the literature [1, 2, 9, 7, 11, 16, 3, 5, 4, 6, 17, 14, 18]. In this paper, we are particularly interested in the 2 dimensional setting where the enc...

in the present research necessities of instream flow needs (ifn) assessment in the rivers with focusing on delichai river as case study is investigated using the hydro-ecological methods. at first, ifn is assessed using two common approaches of the tennant and wetted perimeter. then considering that rainbow trout is the most important and dominant species in this river, ecological condition of ...

The site perimeter enumeration of polyominoes that are both columnand row-convex is a well-understood problem that always yields algebraic generating functions. Counting more general families of polyominoes is a far more difficult problem. Here Mireille BousquetMélou and Andrew Rechnitzer enumerate (by their site perimeter) the simplest family of polyominoes that are not fully convex—bargraphs....

We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For Ω ⊂ D = (0, 1), with d ≥ 2, we are given n random i.i.d. points on D whose membership in Ω is known. We consider the sample as a random geometric graph with connection distance ε > 0. We estimate the perimeter of Ω (relative to D) by the, appropriately rescaled, graph cut between the vertices...

Global placement of hypergraphs is critical in the top-down placement of large timing-driven designs 10, 16]. Placement quality is evaluated in terms of the half-perimeter wirelength (HPWL) of hyperedges in the original circuit hypergraph provided timing constraints are met. Analytical placers are instrumental in handling non-linear timing models 9, 3], but have two important drawbacks: (a) cor...