Showing papers on "Point (geometry) published in 1982"

Model reduction via balanced state space representations

Abstract: A model reduction procedure, based on balanced state space representations, is studied in this paper. The reduced order model is examined from the point of view of stability, controllability, and observability. Both continuous time and discrete time systems are considered.

Computing Point Enclosures

Abstract: Given a set of n rectangles in the plane, the point enclosure query is the question to determine for any point p which rectangles of the set it is contained in. It is the "dual" of the well-known range query in computational geometry. It is shown that the point enclosure query in the plane can be answered in 0(log n + k) time, where k is the number of rectangles reported. The solution makes use of a new data structure, called the S-tree. The data structure can be generalized to obtain an efficient algorithm for the point enclosure problem in d-dimensional space d ≥ 2.

Continuum approximation to dense networks and its application to the analysis of urban road networks

Abstract: A continuum approximation is proposed for problems of flows in large and dense networks, where each point of the continuum is characterized by ‘capacity’ and/or ‘distance/cost’ which are convex sets in the tangent space. The problems of flows in continua corresponding to various problems of flows in networks are formulated in variational forms, of which mathematical properties are investigated and for which numerical algorithms are derived by means of the finite-element discretization technique. A practical procedure, based upon concepts from integral geometry, for constructing the continuum which approximates the original network is also proposed.

Arrangement of eliminating erroneous data in three-dimensional optical sensors

Abstract: An arrangement for eliminating erroneous data in three-dimensional optical sensors, in which a point on a surface is illuminated, and reflections from the point are received at a first location spaced from the source of illumination. The three-dimensional location of the point is computed as a function of the reflection that is received at the first location. The procedure of illuminating the point is repeated for obtaining reflections from the point at a second location which is spaced from the first location and the illuminating source. After computing the three-dimensional location of the point obtained from data dependent on the reflection at the second location, the computations relative to the first and second locations are compared. If the computations produce substantially identical results, the point is designated to be a true point on the surface. When, on the other hand, the results produced by the two computations differ substantially, then the point is designated to be a false point which does not lie on the surface.

Method for controlling an industrial robot

Abstract: Dimensions of a plurality of works of the same specification are subtantially identical among the works. Thus, a teach work point on the work to be worked by an industrial robot and a teach reference point to specify the teach work point are taught to memory means of the industrial robot. In an automatic mode, an actual reference point on the work of the same specification is detected by a sensor and an actual work point of the work is determined based on a difference between the detected actual reference point and the teach reference point and the resulting actual work point is conveyed to the industrial robot.

A critical index algorithm for nearest point problems on simplicial cones

Abstract: We consider the linear complementarity problem (q, M) in which M is a positive definite symmetric matrix of order n. This problem is equivalent to a nearest point problem [/'; b] in which F = {A4, ..., A~} is a basis for R", b is a given point in R'; and it is required to find the nearest point in the simplicial cone Pos(F) to b. We develop an algorithm for solving the linear complementarity problem (q,M) or the equivalent nearest point problem [Y;b]. Computational experience in comparison with an existing algorithm is presented.

Method and apparatus for providing a video display of concatenated lines and filled polygons

Abstract: A method and apparatus for compactly describing an image made up of concatenated lines or filled polygons. The drawing of lines for the image begins at an initial drawing point determined in a coordinate system defined by a unit screen and proceeds from point to point with the relative coordinates of each successive point specified as a positive or negative step in the horizontal and/or the vertical direction from the previous point. The step size parameters which separately define both the amount of a change in the horizontal direction and the amount of a change in the vertical direction are initially specified in fractional parts of the unit screen and remain constant in magnitude throughout the operation. The image is reflected about the horizontal axis and about the vertical axis simply by changing the sign of the step sizes. Turning on and off the drawing process is also facilitated.

A recursive sweep-plane algorithm, determining all cells of a finite division of R d

Abstract: “Sweep-plane” algorithms seem to become more and more important for the solution of certain geometrical problems. We present an algorithm of this kind that enumerates the cells of all dimensions into whichR d is partitioned by a finite set of hyperplanesF 0 . A plane sweeping through space (remaining parallel to itself) finds new cells each time it includes an intersection of someF 0 (normally a point). An analysis of the intersection-properties allows the construction of an algorithm recursive with respect to the dimension of space. Full generality has been one of our main objectives.

Application of computational geometry to pattern recognition problems

Abstract: In this thesis it is shown that several pattern recognition problems can be solved efficiently by exploiting the geometrical structure of the problems. The problems considered are in the area of clustering and classification. These problems are: (i) computing the diameter of a finite planar set, (ii) computing the maximum and minimum distance between two finite planar sets of points, (iii) testing for point inclusion in a convex polyhedron in d-dimensional space, and (iv) exact and inexact reference set thinning for the nearest neighbor decision rule. Algorithms to solve the above problems are presented and analyzed for worst-case and average-case situations. These algorithms are implemented and experimentally compared with the existing algorithms. In solving the above problems, a geometrical construct, known as the Voronoi diagram is used extensively. However, there exists no practical algorithm to construct the Voronoi diagram in d dimensional spaces when d > 2. In this thesis an efficient algorithm to construct the Voronoi diagram in d-space is presented.

Vane pump motor

Abstract: PURPOSE:To improve the operating efficiency and to reduce the power consumption, by forming the chip of a vane such that the entire width will contact effectively with the cam face thereby reducing the heat production considerably. CONSTITUTION:A parallel line is provided from the side of a vane 3 at the angular point (j) side with the dimension of the length t20 from the long sliding side face of the vane 3 and the center of the curvature of the vane chip 3a obtained from a specific formula thus to obtain the cross point (k) between said parallel line and the circumference 3b of the vane 3 having the center of the housing 1. The radius of curvature (r) of the vane chip 3a is obtained from another specific formula, and the vane chip 3a formed by describing an arch with the radius (r) around the point (k) has such shape as designed by the radius of curvature (r) which may be the maximum in the range smaller than the radius of curvature of the cam face 1a. Consequently the entire width of the chip 3a will be used while contacting effectively with the cam face 1a thereby the generated heat can be reduced considerably resulting in the improvement of the operating efficiency and the reduction of the power consumption.

Image processing method and apparatus used for this

Abstract: PURPOSE:To control input and output of a layout scanner, by according the projection image of an original with the layout image of a layout paper, and by obtaining information on magnification and the position of an optional standard point of the original and the layout paper. CONSTITUTION:The intersecting point Q of a transparent plate 3 and the optical axis is situated on the origin as a standard point, and an optional point on an original 1 or an auxiliary piece 2 is selected as a standard point P, and the coordinates of its position are obtained. The original 1 is fixed to the plate 3, this is loaded on an original holder 5, and the image of the original 1 is projected on a projection plate 9. A layout paper 20 is placed on the plate 9, and projection magnification and a position of the paper 20 are adjusted so as to accord a layout image 21 formed on the paper 20 with the projected image of the original 1. The information of the point P and a given point S on the paper 20, the information of magnification, and the information of the positions of trimming frames are used for control of input to and output from a layout scanner.

Globally non-causal space-times

Abstract: It is shown that if a space-time has an isometry group whose Killing vector is time-like in a region V and if there exists one closed time-like curve somewhere in the space-time, then under suitable conditions on V (including the absence of horizons) there is a closed time-like curve through every point of the space-time.

Dynamics of liquid state chemical reactions: Modeling of R‐dependent correlation functions

Abstract: Methods for the simplified construction of those reagent configuration point r0‐dependent static and dynamic solvent correlation functions required to implement the molecular time scale generalized Langevin equation (MTGLE) approach to problems in liquid state chemical reaction dynamics [S. A. Adelman, J. Chem. Phys. 73, 3145 (1980)] are presented. These methods permit one to bypass straightforward but laborious construction of the correlation functions via molecular dynamics simulations of the solvent motion about the solute for many solute configurations r0. The methods are based on two approximations: (i) The matrix r0‐dependent friction kernel of the reagents β1(t;r0) is modeled via a matrix generalization of the conventional Gaussian approximation for scalar time correlation functions. This modeling permits one to reduce the problem of constructing β1(t;r0) to an equilibrium calculation which may be carried out by Monte Carlo as opposed to molecular dynamics techniques. (ii) The equilibrium r0‐depend...

Sample distribution device

Abstract: In this device for the successive transfer of samples from a number of sample vessels into partial-sample vessels with admixing of the reagents, the floor surface of the partial-sample vessel is in inclined alignment with respect to the plane, supply means being provided which supply a first quantity of a substance which takes part in the analysis to the inclined surface beneath the point where a subsequently added substance arrives.

On the computation of fixed points on the product space of unit simplices and an application to noncooperative N-person games

Abstract: In this paper an algorithm based on the principle of simplicial approximation is introduced to compute fixed points of upper semicontinuous point to set mappings from the product space S of unit simplices into itself. The algorithm is a modification of an algorithm, introduced in an earlier paper. The main feature is that it starts with an arbitrary chosen point in S and that the triangulation of S depends on the starting point. Moreover, the algorithm can terminate with a non-full-dimensional subsimplex, yielding a good approximation. An application is given for non cooperative n person games, where S is the strategy space. Some computational experiences are given.(This abstract was borrowed from another version of this item.)

Connection pin type axial force detector for railway diverging junction

Abstract: PURPOSE:To make it possible to determine a load generated at various parts of a switch lock unit during the switching of a point rail of a diverging junction and an impact load during the passage of rail vehicles by properly changing connection pins of the lock unif for a railway diverging junction. CONSTITUTION:A steel material with a proper strength is worked into a connection pin. The leg section thereof is divided into three detection sections... an upper level contact detection section 15, a medium level contact detection section 17 and a lower level contact detection section 16. Strain gauges 18 are applied into recesses provided between upper and medium level contact detection sections 15 and 17 and medium and lower level contact detection sections 17 and 16. After a conventional connection pin connecting a working rod 4 and a point rod 5 is pulled out, a connection pin type axial force detector body 14 is inserted and a split pin is inserted in a hole 21 to prevent the slipping of the detector body 14. The load can be detected easily with a strain gauge 18 after the top of a pin hole for connecting forked rod of the point rod 5 is brought into contact with the upper level contact detection section 15, the bottom of the pin hole with the lower level contact detector section 16 and a connection pin hole of the working rod 4 with the medium level contact detection section 17.

Setting system of sampling point for letter data compression

Abstract: PURPOSE:To obtain a reasonable setting method for sampling points by a method in which a sampling point is orderly set up by one-time tolerance com- parison by using as an appreciation value the area surrounding the approximation curve connecting the distance between sampling points set on a border with each sampling point and each border segment. CONSTITUTION:Any section in which the X-coordinate value of a series of borders are increased or decreased monotonically is set up as a block B, and the coordinate information of points P1 and P2 at both ends is used as coordinate information of existing sampling point. The distance L between the sampling points is calculated, the area S surrounded by the approximation curve C1 connecting each border segment between them with the sampling points P1 and P2 is calculated and S/L is used as approciation value xsi. When the maximum value xsimax and a predetermined value xsi' are in the relationship xsi'max>xsi', the point P3 at which DELTA becomes maximum is used a newly set sampling point. All newly set sampling points orderly calculated until xsimax<=xsi' are set on the borders as desired sampling point.

Implement supporting arrangement.

Abstract: An agricultural implement support comprising a chassis (10) a tow bar assembly (12, 16, 18, 26) at one end of the chassis, means (24, 30) whereby the inclination of the chassis with respect to a towing point of the two bar assembly is adjustable, a wheel assembly (36, 38, 40) and means (36, 56) whereby the position of an axle of the wheel assembly is adjustable with respect to the chassis.

Wind tunnel balance calibrator

Abstract: A check calibration device for a sting-held strain-gauge wind tunnel balance to permit pre-test or inter-test checking of the calibration of the balance in a short time is provided. The device comprises a housing adapted to be secured rigidly to the sting. A plurality of actuators are secured to the housing. Each actuator is positioned to act to generate a force in a predetermined direction at a predetermined location on the body of the balance when the balance and housing are in position secured to the sting. The device further comprises means to vary the load force applied by each actuator. Means are also provided to determine the load force applied by each actuator at a particular point in time and to measure the behavior of the balance in response to that load force at that point in time. Such a device provides a relatively fast means to confirm the accuracy of the constants in the equations chosen to represent the actual behavior of the balance, thereby avoiding the necessity of having to recalibrate the balance unless such constants are shown to be inaccurate for the balance.

Picture processing system

Abstract: PURPOSE:To enable recognizing and discriminating an object of less than one pic ture element by restoring the shape and spectrum characteristics before digitizing as far as possible considering aperture characteristics of a sensor. CONSTITUTION:An aperture correction enlarging 6 is made on a known training observation picture 5', and an aperture correction enlarged training picture 7 is obtained. The shape of an object to be discriminated is indicated from the training enlarged picture 7 in the aperture correction enlarged picture space, and the shape characteristics and spectrum characteristics are extracted. Extracted shape characteristics and spectrum characteristics are analyzed, and the point of classification of the object from the object picture is prepared 8. On the other hand, an objective actual picture 9 is an unknown picture and various bodies other than the object are included. Accordingly, the other shapes are restored by making aperture correction enlarging 10. When classification is made on the third object enlarged picture based on the point prepared in preparation 8 of the point of classification, even if the spectrum characteristics of the object and other shape resemble, only the object can be classified 12 without error, and the correct discrimination of the object becomes possible.

Orientation of orthogonal coordinate systems used for registration of cephalometric landmarks

Abstract: Accurate orientation of orthogonal coordinate systems facilitates repeated registration of cephalometric landmarks, addition of new data at a later date and the evaluation of superimposional methods in longitudinal analysis. The precision of a template designed to mark radiographs with four fiducial points was examined. It was found that the envelopes of error surrounding each point were circular, of similar magnitude and closely approached the previously established standard error of the measuring instrument employed. It was concluded that for most practical purposes the precision offered by the template was well matched to that of the coordinatograph used for registering cephalometric data and to the ability of the operator to align the instrument.

Input system of symbol command

Abstract: PURPOSE:To improve the performance for input operation of a command, by fetching both a character train and a coordinate data at one time from a supplied symbol command to combine the character train with the coordinate data and accordingly applying an integrated command executing indication. CONSTITUTION:The coordinate point train which is supplied from a coordinate input device 1 in the form of a symbol command is analyzed through a symbol command analyzing part 2, then coded. At the same time, the specific coordinate data on the coordinate point train which are supplied to registers 3 and 4 are fetched at one time. Then an integrated command executing indication is applied by combining the character train and the coordinate data. Thus both the working contents of the command and the coordinate data signified by the above- mentioned working contents can be supplied by just an input operation of the symbol command. As a result, the input performance is improve for a command.

Measuring method and device for shape of planary pattern

Abstract: PURPOSE:To enable simplification of processing and to enable to perform a highspeed processing, by a method wherein an image sensor or a pattern is made to turn centering around a point in the pattern, and the normalized function of amplitude function of a tangent at each coordinate point on a profile is Fourie-transformed at high speed. CONSTITUTION:Either a CCD image sensor of a linear array or a plane pattern is intermittently turned in one-way direction at a pitch angle of 2pi/n to the other centering around a point O in a profile of a plane pattern and starting from one point on the frofile. A declination function of a tangent of each of n-pieces of coordinate point (ri, thetai) on the profile from the tangent at the starting point is decided, and a normalized function phii*=phii-thetai of the amplitude function is Fourie-transformed at high speed to decide the shape of the plane pattern from the factor. This eliminates the need for the rearrangement of a coordinate point and an interpolating processing for sampling which are required in the case of the conventional X Y soanning, and permits the simplification and acceleration of the processing speeed.