The center of area of a convex planar set is the point for which the minimum area of intersected by any halfplane containing is maximized. We describe a simple randomized linear-time algorithm for computing the center of area of a convex -gon.

We consider the problems of finding two optimal triangulations of convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programmi...

Developments in data storage technologies and image acquisition methods have led to the assemblage of large data banks. Management of these large chunks of data in an efficient manner is a challenge. Content-based Image Retrieval (CBIR) has emerged as a solution to tackle this problem. CBIR extracts images that match the query image from large image databases, based on the content. In this pape...

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic program...

We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP in an n-sided polygon in O(n2) time. Achieving this running time requires proving several new structural properties of the MAP, and combining them with a rotating technique of Toussaint [10]. We also discuss applications of our result to th...

The support measures of a convex body are a common generalization of the curvature measures and the area measures. With respect to the Hausdorff metric on the space of convex bodies, they are weakly continuous. We provide a quantitative improvement of this result, by establishing a Hölder estimate for the support measures in terms of the bounded Lipschitz metric, which metrizes the weak converg...

It is shown that every equi-affine invariant and upper semicontinuous valuation on the space of convex discs is a linear combination of the Euler characteristic, area, and affine length. Asymptotic formulae for approximation of convex discs by polygons are derived, extending results of L. Fejes Tóth from smooth convex discs to general convex discs. 1991 AMS subject classification: 52A10, 53A15,...

We develop a theory of planar, origin-symmetric, convex domains that are inextensible with respect to lattice covering, that is, domains such that augmenting them in any way allows fewer domains to cover the same area. We show that originsymmetric inextensible domains are exactly the origin-symmetric convex domains with a circle of outer billiard triangles. We address a conjecture by Genin and ...

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...