Showing papers on "Point (geometry) published in 1985"

A Framework for Computational Morphology

Abstract: This paper outlines a new methodology for describing the “internal structure” (or “skeleton”) of planar point sets. The methodology, which is based on parameterized measures of neighbourliness, gives rise to a spectrum of possible internal shapes. Applications to the analysis of both point set and network patterns are described.

Shading models for point and linear sources

Abstract: The degree of realism of the shaded image of a tree-dimensional scene depends on the successful simulation of shading effects. The shading model has two main ingredients, properties of the surface and properties of the illumination falling on it. Most previous work has concentrated on the former rather than the latter.This paper presents an improved version for generating scenes illuminated by point and linear light sources. The procedure can include intensity distributions for point light sources and output both umbrae and penumbrae for linear light sources, assuming thr environment is composed of convex polyhedra. This paper generalizes Crow's procedure for computing shadow volumes caused by the end points of the linear source results in an easy determination of the reions of penumbrae and umbrae on the face prior to shading calculation.This paper also discusses a method for displaying illuminance distribution on a shaded image aby using colored isolux contours.

Method and system for automatically attaching works onto vehicle bodies carried on a conveyor

Abstract: A method and system for automatically attaching works to respective vehicle bodies carried on a slat conveyor using a robot. The method comprises the steps of (a) providing a base on which the robot is mounted and which is movable within a movement range, at least one part of which is alongside of the conveyor; (b) providing work feeders for sequentially feeding plural kinds of the works which are different according to vehicle types (sedan, hardtop, etc.) of the vehicle bodies to predetermined positions; (c) identifying the vehicle type of one of the vehicle bodies to which the required work is to be attached at a first position; (d) determining a target position according to the identified vehicle type; (e) controlling the robot so as to grasp the required work from the work feeders at the target position; (f) positioning the robot to a stand-by position along the conveyor; (g) detecting sequentially a deviation of a relative position toward a direction of travel of the conveyor between a tracking point and reference point since the vehicle body has arrived at a second position downstream of the first position; and (h) moving the base to follow the conveyor so that the deviation becomes zero and simultaneously controlling the robot so as to attach the grasped work to the vehicle body.

Ray tracing generalized cylinders

Abstract: An algorithm is presented for ray tracing generalized cylinders, that is, objects defined by sweeping a two-dimensional contour along a three-dimensional trajectory. The contour can be any 'well-behaved' curve in the sense that it is continuous, and that the points where the tangent is horizontal or vertical can be determined, the trajectory can be any spline curve. First a definition is given of generalized cylinders in terms of the Frenet frame of the trajectory. Then the main problem in ray tracing these objects, the computation of the intersection points with a ray, is reduced to the problem of intersecting two two-dimensional curves. This problem is solved by a subdivision algorithm. The three-dimensional normal at the intersection point closest to the eye point, necessary to perform shading, is obtained by transforming the two-dimensional normal at the corresponding intersection point of the two two-dimensional curves. In this way it is possible to obtain highly realistic images for a very broad class of objects.

How to search history

Abstract: This paper considers the problem of granting a dynamic data structure the capability of remembering the situation it held at previous times. We present a new scheme for recording a history of h updates over an ordered set S of n objects, which allows fast neighbor computation at any time in the history. The novelty of the method is to allow the set S to be only partially ordered with respect to queries and the time measure to be multi-dimensional. The generality of the method makes it useful for a number of problems in 3-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3-dimensional complex, using linear space, or for finding which of n given points is closest to a query plane. Using a simpler, yet conceptually similar technique, we show that with O ( n 2 ) preprocessing, it is possible to determine in O (log 2 n ) time which of n given points in E 3 is closest to an arbitrary query point.

Collapse of two-dimensional linear polymers: a transfer matrix calculation of the exponent νt

Abstract: Using a transfer matrix technique and finite size scaling, the authors calculate the exponent nu t of two-dimensional polymers at the theta point. They find nu t=0.55+or-0.01 by two slightly different calculations on the square lattice. This value is compared with those which had been previously proposed in the literature.

The m-dimensional grid point space

Abstract: A wide variety of algorithms and methods in computer graphics and digital image processing is based on point grids Zm defined by regular orthogonal grids in m-dimensional real space Rm, and on the metrics that may be defined on Zm, for m ≥ 2. In this paper, half-norms ∥ · ∥l, metrics δl, and point products 〈·, ·〉l are introduced characterizing different m-dimensional metric grid point spaces, for 0 <- l < m. Furthermore, grid point ditizations in m-dimensional space are defined and grid intersection digitizations for hyperplanes are analyzed. It is shown that digital straight lines (according to grid intersection digitizations) are special digital curves which may be uniquely recognized by m −1 projections into the 2-dimensional point grid Z2.

The chain recurrent set, attractors, and explosions

Abstract: Charles Conley has shown that for a flow on a compact metric space, a point x is chain recurrent if and only if any attractor which contains the & ω-limit set of x also contains x. In this paper we show that the same statement holds for a continuous map of a compact metric space to itself, and additional equivalent conditions can be given. A stronger result is obtained if the space is locally connected.It follows, as a special case, that if a map of the circle to itself has no periodic points then every point is chain recurrent. Also, for any homeomorphism of the circle to itself, the chain recurrent set is either the set of periodic points or the entire circle. Finally, we use the equivalent conditions mentioned above to show that for any continuous map f of a compact space to itself, if the non-wandering set equals the chain recurrent set then f does not permit Ω-explosions. The converse holds on manifolds.

A Hierarchical Space Indexing Method

Abstract: Indexing methods are very important for rapid processing of a large amount of data. In this paper we discuss a spatial index, that is, a method for indexing a three dimensional space. We use a regular decomposition of the space, leading to a tree structure. The advantage of a space decomposition method over storing data in the form of a table is the quick access to a point in question by using a leaf node as an index. A set of basic algorithms is presented for generation and modification of objects. This set makes it easy to detect intersections of 3D objects, which is a useful property in such applications as interactive design of three dimensional shapes.

Boundary behavior of a non-parametric minimal surface in ℝ3 at a non-convex point

Abstract: Let Ω be a domain in iR which is locally convex at each point of its boundary except one, say (0,0), Ψ be a continuous function of 9Ω, and f be the unique generalized (variational) solution of the minimal surface equation with boundary values Φ. Assume that f e C°(Ώ\{(0,0)}). Then the radial limits of f at (0,0) from all directions in Ω exist and the restriction of f to Π η Η is a classical solution to the Dirichlet problem which continuously takes on all of its boundary values, where Η is a closed half space with (0,0) e 3H. 1980 AMS Subject Classification. Primary 35J65, 35B99.

Resolution and Noise Considerations in MRI Systems with Time-Varying Gradients

Abstract: The design and performance of spatial localization filters in an MR imaging system with time-varying gradients is presented. The system is based on recording measurements of the imaged volume-done in the presence of cosinusoidal gradients. A postprocessing scheme is shown which enables every point to be imaged from a single FID signal. Methods are shown which achieve a three-demensional localization with arbitrarily small sidelobes. Those localization filters are implemented without significant computational penalty. The signal-to-noise ratio (SNR) in the suggested imaging system is shown to be space-invariant (same SNR for each imaged point). We find a closed-form relation between the localization filter and the resulting noise. It is shown that the gain achieved by the localization filters highly exceeds the relatively small loss in SNR.

Analytic Geometry in Three Dimensions

Abstract: Analytic geometry in three dimensions makes essential use of coordinate systems. To introduce a coordinate system, we consider triples (a,b, c) of real numbers, and we call the set of all such triples of real numbers the three-dimensional number space. We denote this space by R’. Each individual triple is a point in R 3 . The three elements in each number triple are called its coordinates. We now show how three-dimensional number space may be represented on a geometric or Euclidean three-dimensional space.

Numerical computation of nonsimple turning points and cusps

Abstract: A method is developed for the numerical computation of a double turning point corresponding to a cusp catastrophe of a nonlinear operator equation depending on two parameters. An augmented system containing the original equation is introduced, for which the cusp point is an isolated solution. An efficient implementation of Newton's method in the finite-dimensional case is presented. Results are given for some chemical engineering problems and this direct method is compared with some other techniques to locate cusp points.

New algorithms for special cases of the hidden line elimination problem

Abstract: Hidden line elimination is a well-known problem in computer graphics and many practical solutions have been proposed. Only recently the problem has been studied from a theoretical point of view, taking asymptotic worst-case time- and spacebounds into account. Here we study three special cases of increasing difficulty and generality of the hidden line elimination problem. Applying some methods from computational geometry these problems can be solved with better worst-case bounds than those of the best known algorithms for the general problem.

Television video signal A/D converter apparatus

Abstract: A television video signal A/D converter apparatus in a liquid crystal television receiver has an A/D converter for A/D converting a television video signal. Upper and lower reference potentials for determining an operating voltage amplitude are supplied to the A/D converter from a reference potential generator. The upper and lower reference potentials are divided at a given ratio by a resistor so as to fix an average potential of the television video signal at a constant value using the potential at the dividing point as a bias potential, and thereafter the television video signal is supplied to the A/D converter.

Comparison of evaporation duct and path loss models

Abstract: This paper will evaluate the current meteorological measurement techniques used to infer the evaporation-ducting process. Included within this study is a comparison of relative performance, sensitivities to meteorological inputs, and ease of computation for three standard evaporation duct models and two electromagnetic wave propagation models. The evaporation duct models performed reasonably and equally well when considering statistically averaged meteorological inputs, but all were extremely sensitive to point-observed meteorological input parameters. The measurement techniques employed by naval and transiting commercial vessels are not of sufficient quality to infer adequately the evaporation-ducting process. The theory behind calculation of path loss values based upon current evaporation duct inputs is statistically sound. For studies of propagation phenomena or development of electromagnetic systems, both of the compared models perform reasonably well and are accurate predictors. However, the use of either model for estimation of a single propagation range based upon a point meteorological observation is severely limited by the accuracy of the data.

A point set everywhere dense in the plane

Abstract: Keywords: point sets everywhere dense in the plane Note: Professor Pach's number: [031] Reference DCG-ARTICLE-1985-001 Record created on 2008-11-14, modified on 2017-05-12

Thermal head for thermal recording

Abstract: PURPOSE:To perform a high density recording at a high speed by providing a protective cover having a projected part approaching a semiconductor element for driving heat generating bodies and a conductive heat transmission means between the projected part of the protective cover and the semiconductor for driving heat generating bodies. CONSTITUTION:A recording paper 9 is pressed on a thermal head 11 for thermal recording with a paper feed roller 10 and according to a picture signal, a heat generating body 13a is driven with a semiconductor element 15 for driving heat generating bodies and the recording paper 9 is fed in the direction of the arrow to perform a recording generating heat. A projected part 16b is provided at the point corresponding to a recessed relief part 16a of a protective cover 16 on the semiconductor element 15 for driving heat generating bodies while a heat transmission member 17b is provided between the projected part 16b of the protective cover 16 and the semiconductor element 15 for driving heat generating bodies. Thus, the protective cover 16 can be utilized as a radiating plate of the semiconductor elements 15 for driving heat generating bodies to reduce the temperature rise of the element 15.