			Home About us Contact

Convex Hull (convex + hull)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Interactive Cover Design Considering Physical Constraints

COMPUTER GRAPHICS FORUM, Issue 7 2009
Yuki Igarashi
Abstract We developed an interactive system to design a customized cover for a given three-dimensional (3D) object such as a camera, teapot, or car. The system first computes the convex hull of the input geometry. The user segments it into several cloth patches by drawing on the 3D surface. This paper provides two technical contributions. First, it introduces a specialized flattening algorithm for cover patches. It makes each two-dimensional edge in the flattened pattern equal to or longer than the original 3D edge; a smaller patch would fail to cover the object, and a larger patch would result in extra wrinkles. Second, it introduces a mechanism to verify that the user-specified opening would be large enough for the object to be removed. Starting with the initial configuration, the system virtually "pulls" the object out of the cover while avoiding excessive stretching of cloth patches. We used the system to design real covers and confirmed that it functions as intended. [source]

Hierarchical Convex Approximation of 3D Shapes for Fast Region Selection

COMPUTER GRAPHICS FORUM, Issue 5 2008
Marco Attene
Abstract Given a 3D solid model S represented by a tetrahedral mesh, we describe a novel algorithm to compute a hierarchy of convex polyhedra that tightly enclose S. The hierarchy can be browsed at interactive speed on a modern PC and it is useful for implementing an intuitive feature selection paradigm for 3D editing environments. Convex parts often coincide with perceptually relevant shape components and, for their identification, existing methods rely on the boundary surface only. In contrast, we show that the notion of part concavity can be expressed and implemented more intuitively and efficiently by exploiting a tetrahedrization of the shape volume. The method proposed is completely automatic, and generates a tree of convex polyhedra in which the root is the convex hull of the whole shape, and the leaves are the tetrahedra of the input mesh. The algorithm proceeds bottom-up by hierarchically clustering tetrahedra into nearly convex aggregations, and the whole process is significantly fast. We prove that, in the average case, for a mesh of n tetrahedra O(n log2 n) operations are sufficient to compute the whole tree. [source]

Maximality properties for isometric interpolating sequences and sequences of trivial points in the spectrum of H,

MATHEMATISCHE NACHRICHTEN, Issue 5 2005
Raymond Mortini
Abstract Let (xn) be an isometric interpolating sequence or a sequence of trivial points in the spectrum of H,. It is shown that either every cluster point of that sequence has a maximal support set or there exists y , M(H,+C) such that the support of xn is contained in the support of y for infinitely many n. Similar results for Gleason parts are obtained, too. We also investigate the H, -convex hulls of countable unions of support sets and show that whenever supp x , supp y and x /, , then the H, -convex hull of supp x does not meet . (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Generalization of a class of nonlinear averaging integral operators

MATHEMATISCHE NACHRICHTEN, Issue 1-2 2005
Teodor Bulboac
Abstract Let H(U) be the space of all analytic functions in the unit disk U, and let coE denote the convex hull of the set E , ,. If K , H(U) then the operator I : K , H(U) is said to be an averaging operator if For a function h , A , H(U) we will determine simple sufficient conditions on h such that for all f , ,,1/,, where and ,,1/, represents the class of 1/, -convex functions (not necessarily normalized). As an application, we will give sufficient conditions on h to insure that the operators Ih;,,, are averaging operators on certain subsets of H(U), in order to generalize the result of [5]. In addition, some particular cases of this result obtained for appropriate choices of the function h will also be given. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

The one-warehouse multiretailer problem with an order-up-to level inventory policy

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2010
uz Solyal
Abstract We consider a two-level system in which a warehouse manages the inventories of multiple retailers. Each retailer employs an order-up-to level inventory policy over T periods and faces an external demand which is dynamic and known. A retailer's inventory should be raised to its maximum limit when replenished. The problem is to jointly decide on replenishment times and quantities of warehouse and retailers so as to minimize the total costs in the system. Unlike the case in the single level lot-sizing problem, we cannot assume that the initial inventory will be zero without loss of generality. We propose a strong mixed integer program formulation for the problem with zero and nonzero initial inventories at the warehouse. The strong formulation for the zero initial inventory case has only T binary variables and represents the convex hull of the feasible region of the problem when there is only one retailer. Computational results with a state-of-the art solver reveal that our formulations are very effective in solving large-size instances to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010 [source]

The clique partitioning problem: Facets and patching facets

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2001
Maarten Oosten
Abstract The clique partitioning problem (CPP) can be formulated as follows: Given is a complete graph G = (V, E), with edge weights wij , , for all {i, j} , E. A subset A , E is called a clique partition if there is a partition of V into nonempty, disjoint sets V1,,, Vk, such that each Vp (p = 1,,, k) induces a clique (i.e., a complete subgraph), and A = , {{i, j}|i, j , Vp, i , j}. The weight of such a clique partition A is defined as ,{i,j},Awij. The problem is now to find a clique partition of maximum weight. The clique partitioning polytope P is the convex hull of the incidence vectors of all clique partitions of G. In this paper, we introduce several new classes of facet-defining inequalities of P. These suffice to characterize all facet-defining inequalities with right-hand side 1 or 2. Also, we present a procedure, called patching, which is able to construct new facets by making use of already-known facet-defining inequalities. A variant of this procedure is shown to run in polynomial time. Finally, we give limited empirical evidence that the facet-defining inequalities presented here can be of use in a cutting-plane approach for the clique partitioning problem. © 2001 John Wiley & Sons, Inc. [source]

Analysis of algebraic systems arising from fourth-order compact discretizations of convection-diffusion equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2002
Ashvin Gopaul
Abstract We study the properties of coefficient matrices arising from high-order compact discretizations of convection-diffusion problems. Asymptotic convergence factors of the convex hull of the spectrum and the field of values of the coefficient matrix for a one-dimensional problem are derived, and the convergence factor of the convex hull of the spectrum is shown to be inadequate for predicting the convergence rate of GMRES. For a two-dimensional constant-coefficient problem, we derive the eigenvalues of the nine-point matrix, and we show that the matrix is positive definite for all values of the cell-Reynolds number. Using a recent technique for deriving analytic expressions for discrete solutions produced by the fourth-order scheme, we show by analyzing the terms in the discrete solutions that they are oscillation-free for all values of the cell Reynolds number. Our theoretical results support observations made through numerical experiments by other researchers on the non-oscillatory nature of the discrete solution produced by fourth-order compact approximations to the convection-diffusion equation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 155,178, 2002; DOI 10.1002/num.1041 [source]

Reduction of a set of elementary modes using yield analysis

BIOTECHNOLOGY & BIOENGINEERING, Issue 2 2009
Hyun-Seob Song
Abstract This article proposes a new concept termed "yield analysis" (YA) as a method of extracting a subset of elementary modes (EMs) essential for describing metabolic behaviors. YA can be defined as the analysis of metabolic pathways in yield space where the solution space is a bounded convex hull. Two important issues arising in the analysis and modeling of a metabolic network are handled. First, from a practical sense, the minimal generating set spanning the yield space is recalculated. This refined generating set excludes all the trivial modes with negligible contribution to convex hull in yield space. Second, we revisit the problem of decomposing the measured fluxes among the EMs. A consistent way of choosing the unique, minimal active modes among a number of possible candidates is discussed and compared with two other existing methods, that is, those of Schwartz and Kanehisa (Schwartz and Kanehisa, 2005. Bioinformatics 21: 204,205) and of Provost et al. (Provost et al., 2007. Proceedings of the 10th IFAC Symposium on Computer Application in Biotechnology, 321,326). The proposed idea is tested in a case study of a metabolic network of recombinant yeasts fermenting both glucose and xylose. Due to the nature of the network with multiple substrates, the flux space is split into three independent yield spaces to each of which the two-staged reduction procedure is applied. Through a priori reduction without any experimental input, the 369 EMs in total was reduced to 35 modes, which correspond to about 91% reduction. Then, three and four modes were finally chosen among the reduced set as the smallest active sets for the cases with a single substrate of glucose and xylose, respectively. It should be noted that the refined minimal generating set obtained from a priori reduction still provides a practically complete description of all possible states in the subspace of yields, while the active set covers only a specific set of experimental data. Biotechnol. Bioeng. 2009;102: 554,568. © 2008 Wiley Periodicals, Inc. [source]

Rapid Human-Assisted Creation of Bounding Models for Obstacle Avoidance in Construction

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2004
J. McLaughlin
A practical, interactive method for doing so is described here. The method: (1) exploits a human operator's ability to quickly recognize significant objects or clusters of objects in a scene, (2) exploits the operator's ability to acquire sparse range point clouds of the objects quickly, and then (3) renders models, such as planes, boxes, and generalized convex hulls, to be displayed graphically as visual feedback during equipment operation and/or for making proximity calculations in an obstacle detection system. Experiments were performed in which test subjects were asked to model objects of varying complexity and clutter. These models were then compared to control models using a ray-tracing algorithm to determine the operator's ability to create conservative models that are critical to construction operations. To demonstrate the applicability of the modeling method to obstacle avoidance, a scripted motion robot simulation was conducted using an artificial potential formulation that monitors position (closest point on manipulator link to nearest obstacle) as well as velocity (link inertia). Experimental results indicate that bounding models can be created rapidly and with sufficient accuracy for obstacle avoidance with the aid of human intelligence and that human-assisted modeling can be very beneficial for real-time construction equipment control. [source]

Translation of variables and implementation of efficient logic-based techniques in the MINLP process synthesizer MIPSYN

AICHE JOURNAL, Issue 11 2009
Marcel Ropotar
Abstract This article describes alternative GDP formulation and convex hull representations for process synthesis problems and their implementation in a unique MINLP process synthesizer MIPSYN. A special translation of variables in mixed-integer, relaxed, and logic-based variations has been proposed, which enables modeling and solving process alternatives in a narrowed lifted space of variables, defined by nonzero lower and upper bounds. Based on these translation variations, alternative formulations have been developed for convex hulls, multiple-term generalized disjunctive programming problems, and logic-based outer-approximation algorithm, all of them being specialized for the synthesis of process flowsheets. Several studies were performed and three different large-scale synthesis problems were solved to test the performance and efficiency of different formulations. This initial research indicates that the proposed alternative convex hull representation usually outperforms the conventional one when solving both MILP and NLP steps in highly combinatorial MINLP process networks problems. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]