We present an algorithm for the two-dimensional translational containment problem: find translations for k polygons (with up to m vertices each) which place them inside a polygonal container (with n vertices) without overlapping. The polygons and container may be nonconvex. The containment algorithm consists of new algorithms for restriction, evaluation, and subdivision of two-dimensional configuration spaces. The restriction and evaluation algorithms both depend heavily on linear programming; hence we call our algorithm an LP containment algorithm. Our LP containment algorithm is distinguished from previous containment algorithms by the way in which it applies principles of mathematical programming and also by its tight coupling of the evaluation and subdivision algorithms. Our new evaluation algorithm finds a local overlap minimum. Our distance-based subdivision algorithm eliminates a "false" (local but not global) overlap minimum and all layouts near that overlap minimum, a...

enclosures by rectangles for few regions of given areas

We study five problems of finding minimal enclosures comprised of elements of a connected, planar graph with a plane embedding. The first three problems consider the identification of a shortest enclosing walk, cycle or trail surrounding a polygonal, simply connected obstacle on the plane. We

enclosures of the range of a function over a box, considerations of possible hardware support facilitating the implementation of such methods, and the results of a simple interval challenge that I had posed to the reliable computing mailing list on November 26, 2008. Also given is an example of a bound

that any perturbation of the polygons increases the chosen measure of overlap. Experiments show that the algorithm works well in practice. It is shown how to apply overlap minimization to create algorithms for other layout tasks: compaction, containment, and minimal enclosure. Compaction: starting with a

An enclosure is a two-sided approximation of a uni- or multivariate function by a pair of typically simpler functions 3688 such that 1 over the domain of interest. Enclosures are optimized by minimizing the width and refined by enlarging the space . This paper develops a

: choosing high-value resins and minimizing enclosure disassembly time. Uncertainty analysis is performed to quantify the uncertainty surrounding economic conditions in the future when the enclosure is ultimately recycled.

thermal conductivity: minimization and maximization of thermal conductivity. The annulus material is made of Graphite/epoxy laminated composite materials. The annulus enclosure is filled with porous media between two inclined concentric cylinders with 12 fins attached to the inner cylinder. The system

Inverse thermal problem is applied to natural convective flow with radiative heat transfer. The bottom wall temperature in the 2-D cavity domain is estimated by using gas tempera-ture measurements in the flow field. The inverse problem is solved through a minimization of an objective function using

inclination angle which minimizes the average Nusselt number. Key words: free convection, enclosure, interferometry, Mach-Zehnder