Showing papers on "Point (geometry) published in 1984"

On the Complexity of Some Common Geometric Location Problems

Abstract: Given n demand points in the plane, the p-center problem is to find p supply points (anywhere in the plane) so as to minimize the maximum distance from a demand point to its respective nearest supply point. The p-median problem is to minimize the sum of distances from demand points to their respective nearest supply points. We prove that the p-center and the p-median problems relative to both the Euclidean and the rectilinear metrics are NP-hard. In fact, we prove that it is NP-hard even to approximate the p-center problems sufficiently closely. The reductions are from 3-satisfiability.

Method and apparatus for stereotaxic placement of probes in the body utilizing CT scanner localization

Abstract: The method and apparatus are presented which allow for CT guided biopsies of the body. The method is based on the finding of a reference point on the patient's body that exactly correlates to a point on the CT scan. This is accomplished by means of a localization device placed on the patient's skin which can be identified in cross section on the CT scan. Measurements of the localization device on CT scan can then be correlated to the device on the patient.

Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry

Abstract: This paper is concerned with the solution of the following interesting geometrical problem For what set of n points on the sphere is the sum of all Euclidean distances between points maximal, and what is the maximum? Our starting point is the following surprising “invariance principle” due to K B Stolarsky: The sum of the distances between points plus the quadratic average of a discrepancy type quantity is constant Thus the sum of distances is maximized by a well distributed set of points We now introduce some notation to make the statement more precise

The block preconditioned conjugate gradient method on vector computers

Abstract: We present vectorizable versions of the block preconditioners introduced by Concus, Golub & Meurant (2) for use with the conjugate gradient method. In (2) it was shown that the block preconditioners give less computational work than the classical point ones on conventional serial computers. Here we give numerical results for various vector computers, CDC Cyber 205, CRAY l-S, CRAY X- MP and for several problems, which show that for most cases the block method with slight modifications, gives better results also on vector computers.

Local Structure of Feasible Sets in Nonlinear Programming - Part II. Nondegeneracy

Abstract: In this paper we examine the local structure of the feasible set of a nonlinear programming problem under the condition of nondegeneracy. We introduce this condition, examine its relationships to known properties of optimization problems, and show that when it holds at a given point the portion of the feasible set near that point is diffeomorphic to a simple convex set (often polyhedral). Moreover, this diffeomorphic relation is stable under small changes in the problem functions.

A further look at Newmark, Houbolt, etc., time-stepping formulae

Abstract: This paper looks at some well-known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved. New forms are given of the general three-parameter method introduced by Zienkiewicz.1 Some new one-step methods are introduced; these are of great practical importance because of the ease with which the size of time step can be changed.

Approximate Formulas for Average Distances Associated with Zones

Abstract: This paper develops formulas for estimating average distances associated with zones. The average distance between two points, one located at random in a zone and another located at random in another, is first investigated. The average distance from a fixed point to a point located at random in a zone, and the average distance between two points located at random in the same zone, are also examined. The accuracy of the approximations for these average distances are found by examining some simple cases.

The morphological characterization of particles by automated scanning electron microscopy

Abstract: A method is described for the characterization and the classification according to shape of microscopic objects by automated SEM. The classification is performed by a hierarchical cluster analysis on a set of Fourier coefficients that are calculated from a set of radii, measured between a well defined centroid point and the contour lines of the object. This method is incorporated in existing commercial software for automated X-ray and size analysis of airborne particulate matter (PRC, Tracor Northern). Two examples demonstrate the possibilities and limitations of this method.

On computer simulation methods used to study models of two-component lipid bilayers.

Abstract: We show that the use of a computer simulation method introduced to calculate the equilibrium thermodynamic properties of a model of a two-component lipid bilayer membrane [Freire, E., & Snyder, B. (1980) Biochemistry 19, 88-94] is incorrect. This is done by comparing the method to that of Metropolis, which has been proven to generate equilibrium distribution of that model, and by showing that back-processes have been omitted in the implicit master equation of Freire and Snyder. We have illustrated this explicitly by first generating distributions according to the method of Freire and Snyder and then allowing the system to relax via the Kawasaki method, which uses the technique of Metropolis. We show that relaxation to a different distribution occurs. We also remark that the cluster distributions generated by the Freire-Snyder method are substantially different from those occurring in equilibrium distributions. Thus, conclusions about equilibrium thermodynamic properties such as specific heats and transition enthalpies or about transport properties or cluster properties at equilibrium cannot be drawn from the results obtained by using this method. Finally, we point out that the method of Freire and Snyder is appropriate to so-called aggregation models, which have been used to study irreversible growth; and we suggest biological systems that might be simulated by their method.

Automatic finite-element mesh generation from geometric models—A point-based approach

Abstract: A novel algorithm for automatic finite-element mesh generation is described. It uses constructive solid geometry to provide the geometric data for the object to be meshed. The geometric definition of the object and a value for the required mesh density are the only inputs. The method consists of two stages: point generation and mesh construction over the points. It has been implemented in two dimensions and is capable of generating predominantly "good" quadrilateral elements. Triangular elements are only created in circumstances under which quadrilateral elements are not feasible.

Extension of projection method to nonuniformly linear antenna arrays

Abstract: The study of linear arrays has been developed in different regions. The computerized techniques that appeared in this century motivated the researchers to find a new techniques that save time. In this work the method of succesive projection is used in solving the nonuniform space and phase arrays. This technique was used before to solve the nonuniform current arrays. The main concept of this method is to find a common point of many different sets. This point will have the best solution to satisfy all conditions. In this technique the solution of the set of inequalities is the main scope. The addition of one or more constraints to the array is only as adding one more set to the group of sets we have. This means that the solution of constrained arrays also is available. Several illustrations are discussed and compared with different other techniques. A simple program is available and easy to establish. In this work, the broadside direction pattern is divided into 180\deg that represent 180 sets. At each set the synthesized pattern must satisfy the desired pattern.

An efficient point in polyhedron algorithm

Abstract: An algorithm is presented which efficiently determines whether a point is interior to or on a polyhedron boundary. Such algorithms are useful in 3-D CAD/CAM and solid modeling software as well as geoscience and mining software applications. The algorithm has advantages over others that have been published in terms of preprocessing time and ease of implementation. The algorithm presented decides whether or not a point is contained within a given polyhedron by examining how the polyhedron radially projects to the unit sphere centered at the point in question. If the point is inside the polyhedron, the net area covered by the projection is the total area of the sphere; if outside the net area covered is nil. Within the algorithm these determinations are made by using the Gauss-Bonnet formula to compute the areas of the regions on the sphere covered by radially projected faces.

Amount of rotation about a point and the Morse index

Abstract: For the case of exact, area preserving, monotone twist diffeomorphisms, we give formulas relating the amount of rotation about an orbit and certain Morse indices.

The Multiobjective Optimization Problem of Set Function

Abstract: The multiobjective optimization problem of a set function defined on a σ-algebra If in a finite atomless measure space (X, II, m) is investigated. A constrained local minimum is formulated and its necessary conditions are derived. Also, the sufficient conditions of a constrained local lower efficient point are given. Further, a necessary condition of a constrained minimum is shown in a form of a saddle point of a Lagrangian set function and a theorem for Lagrangian duality is given.

Duality and an Algorithm for a Class of Continuous Transportation Problems

Abstract: In this paper we treat the problem of transferring mass at least cost from one line segment to another, when there is a continuous cost function cx, y giving the cost of transferring material from the point x on the first line segment to the point y on the second. The mass has to be arranged with uniform density on the second line segment after the transfer. This is a one-dimensional form of the well-known mass-transfer problem. It is an infinite-dimensional linear program. We discuss duality theory for this problem and give an algorithm which converges to an optimal solution.

Domain independent object description and decomposition

Abstract: A significant problem in image understanding (IU) is to represent objects as models stored in a machine environment for IU systems to use in model driven pattern matching for object recognition. This paper presents a technique for autonomous machine description of objects presented as spatial data, i.e., data presented as point sets in Euclidean n-space. This general definition of objects as spatial data encompasses the cases of explicit listings of points, lines or other spatial features, objects defined by light pen in a CAD system, generalized cone representations, polygonal boundary representations, quad-trees, etc. The description technique decomposes an object into component sub-parts which are meaningful to a human being. It is based upon a measure of symmetry of point sets. Most spatial data has no global symmetry. In order to arrive at a reasonable description of a point set, we attempt to decompose the data into the fewest subsets each of which is as symmetric as possible. The technique is based upon statistics which capture the opposing goals of fewest pieces and most symmetry. An algorithm is proposed which operates sequentially in polynomial time to reach an optimal (but not necessarily unique) decomposition. The semantic content of the descriptions which the technique produces agrees with results of experiments on qualitative human perception of spatial data. In particular, the technique provides a step toward a quantitative measure of the old perceptual Gestalt school of psychology's concept of "goodness of figure".

Device for vertically adjusting an upper holding point of a safety belt system

Abstract: A device for vertically adjusting an upper holding point of a safety belt system, which device can be produced cheaply and takes up little space, comprises a pivot arm which can be operated manually, is designed so as to be resilient at least in sections and is rotatably mounted on one side, while on the other side it engages under pretensioning in one of a plurality of lock-in positions, which are arranged one above the other, of a holding device provided on the backrest.

Apparatus for disposing packings in predetermined relative positions

Abstract: In a conveying system for transporting a sequence of articles to a suspending point in captured relation and then transporting them by vacuum suspension to a plurality of separate discharge stations, comprising the combination of: at least a pair of conveyor belts disposed in vertically spaced, overlapping relation to define an elongate nip therebetween extending from a capturing point to a suspending point, the upper of said belts extending beyond the suspending point and being provided with a series of openings extending longitudinally thereof; feed apparatus for feeding articles to the capturing point in sequentially spaced relation so as to be captured between the belts and transported therebetween to the suspending point; suction apparatus overlying the upper belt beyond the suspending point and defining a first chamber for subjecting the articles to vacuum through the openings to suspend them after they pass beyond the suspending point, the suction apparatus defining a plurality of further and separate chambers in spaced sequence beyond said suspending point; and control apparatus for independently controlling vacuum to the further suction chambers to release the articles sequentially at their respective stations beginning at that station located most remotely from the suspending point.

A geometrical classification of cubic point configurations

Abstract: The point configurations of cubic lattice complexes with less than three degrees of freedom, i.e. of all special cubic Wyckoff positions, are classified with respect to three properties: (1) the symmetry of a point configuration regarded by itself (the occurrence of limiting complexes), (2) the type of Dirichlet partitions that corresponds to the point configuration, (3) the type of sphere configurations (sphere packings, interpenetrating sphere packings, rodlike or polyhedral sphere configurations) referring to the point configuration. Detailed information on the Dirichlet polyhedra and on some properties of the space tilings is given in addition.

Guiding method of traveling object

Abstract: PURPOSE:To guide accurately a traveling object with a smooth locus, by calculating the target direction from a standard target position and a measured position which are previously stored and performing a steering control from the difference between the target and measured directions CONSTITUTION:A traveling object V like an automatic mower, etc is guided from a starting point A to a target point B along a prescribed rectilinear course Li The object V contains a microcomputer as well as three photodetectors which receive the light given from a laser light source set at a prescribed position Thus the present position Q and the traveling direction phi of the object V are successively measured The microcomputer calculates a target direction QT from the measured position Q and a standard target position P which is previously stored The steering control is carried out successively for wheels from the difference DELTAphi between the direction QT and the measured present direction Q so that the object V travels toward the target direction phiT Then the object V is guided toward the position P

31 Nonparametric methods in directional data analysis

Abstract: Publisher Summary This chapter describes the nonparametric methods in directional data analysis. In many natural and physical sciences, the observations are in the form of directions–directions either in plane or in three-dimensional (3D) space. A convenient sample frame for two-dimensional (2D) directions is the circumference of a unit circle centered at the origin with each point on the circumference representing a direction; or, equivalently, because magnitude has no relevance, a unit vector may represent each direction. Such data on 2D directions is called as “circular data.” Similarly, the surface of a unit sphere in three-dimensions can be used as the sample space for directions in space, with each point on the surface representing a 3D direction; or alternatively, a unit vector in three-dimensions may represent such a direction. Such data is known as the “spherical data.” The analysis of directional data gives rise to a host of novel statistical problems and does not fit into the usual methods of statistical analysis that one employs for observations on the real line or Euclidean space.

Grammatical Devices for Sharing Point

Abstract: Certain linguistic devices play a central role in facilitating the exchange of thoughts between the speaker and the listener in natural communication. These devices are designed to control the ebb and flow of knowledge, belief, narration, and assertion during both planned and unplanned discourse. The collection of such devices constitutes what I call the "point-sharing system." From the speaker's point of view, the function of point sharing is realized through point making, because each attempt by the speaker to share his thoughts with his listener involves the making of a "point." From the listener's point of view, the function of point sharing is realized through point using, because the listener takes the points that have been presented by the speaker and uses them to alter his own cognitive structures. When we wish to speak about both point making and point using, we can talk about the overall function of point sharing. In other papers, Elizabeth Bates and I have examined the development of point sharing in children (Bates and MacWhinney, 1979) and the theoretical place of functionalist grammar within modern-day psy-cholinguistics (Bates and MacWhinney, 1982a). We have also reported data on children's acquisition of point-sharing devices in English, Hungarian, and Italian (MacWhinney and Bates, 1978; MacWhinney and Price, 1980) and the use of these devices by adults in sentence comprehension (Bates and MacWhinney, 1982b; Bates et al., 1982). In the present chapter, I would like to focus attention on specific devices from the point-shaj ing system and the ways in which these devices convey instructions to a listener that guide him in elaborating his cognitive representations. The analysis of these devices is guided by the functionalist approach to semantics—an approach that is summarized in Bolinger's (1972) observation that "when we say two things that are different we mean two different things by them." According to the functionalist perspective, differences in word order, article use, ellipsis, and so on are not arbitrary formal facts. Rather, they reflect fundamental differences in the kinds of points the speaker is trying to make. This chapter shows how both children and adults use different devices from the point-sharing system to convey different instructions to a listener.