In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...

We consider approximation algorithms for the problem of computing an inscribed rectangle having largest area in a convex polygon on n vertices. If the order of the vertices of the polygon is given, we present a randomized algorithm that computes an inscribed rectangle with area at least (1− ) times the optimum with probability t in time O( 1 log n) for any constant t < 1. We further give a dete...

We introduce a new family of polyominos that are inscribed in a rectangle of given size for which we establish a number of exact formulas and generating functions. In particular, we study polyominos inscribed in a rectangle with minimum area and minimum area plus one. These results are then used for the enumeration of lattice trees inscribed in a rectangle with minimum area plus one. Résumé. No...

We consider approximation algorithms for the problem of computing an inscribed rectangle having largest area in a convex polygon on n vertices. If the order of the vertices of the polygon is given, we present a deterministic approximation algorithm that computes an inscribed rectangle of area at least 1− times the optimum in running time O( 1 log 1 log n). Furthermore, a randomized approximatio...

This paper describes an algorithm to compute, in (log n) time, a rectangle that is contained in a convex n-gon, has sides parallel to the coordinate axes, and has maximum area. With a slight modiication it will compute the smallest perimeter. The algorithm uses a tentative prune-and-search approach, even though this problem does not appear to t into the functional framework of Kirkpatrick and S...

It is shown that ovals admitting circles as orthoptic curves are precisely characterized by the property that every one of their points is the vertex of exactly one maximal-perimeter inscribed parallelogram. This generalizes an old property of ellipses, most recently revived by Connes and Zagier in the paper A Property of Parallelograms Inscribed in Ellipses. Let C be a centrally symmetric smoo...

We prove that there exists a unique ellipse of minimal eccentricity, EI , inscribed in a parallelogram, Ð. We also prove that the smallest nonnegative angle between equal conjugate diameters of EI equals the smallest nonnegative angle between the diagonals of Ð. We also prove that if EM is the unique ellipse inscribed in a rectangle, R, which is tangent at the midpoints of the sides of R, then ...

Determine an optimal set of design parameter of PR whose DW fits a prescribed workspace as closely as possible is an important and foremost design task before manufacturing. In this paper, an optimal design method of a linear Delta robot (LDR) to obtain the prescribed cuboid dexterous workspace (PCDW) is proposed. The optical algorithms are based on the concept of performance chart. The perform...