Showing papers on "Point (geometry) published in 1978"

Computing Dirichlet Tessellations in the Plane

Abstract: A finite set of distinct points divides the plane into polygonal regions, each region containing one of the points and comprising that part of the plane nearer to its defining point than to any other. The resultant planar subdivision is called the Dirichlet tessellation; it is one of the most useful constructs associated with such a point configuration. The regions, which we call tiles, are also known as Voronoi or Thiessen polygons. We describe a recursive algorithm for computing the tessellation in a highly efficient way, and discuss the problems which arise in its implementation. Samples of graphical output demonstrate the application of the program on a modest scale; its efficiency allows its application to large sets of data, and detailed discussion of space and time considerations is given, based in part on theoretical predictions and in part on test runs on up to 10,000 points.

Locating an Obnoxious Facility on a Network

Abstract: We deal with the problem of locating a point on a network so as to maximize the sum of its weighted distances to the nodes. It is shown that there is at least one optimal point in a finite set of points which can easily be generated. An algorithm is given for locating an optimal point in this set. When the network is a tree, this set consists of the “dangling” nodes.

Transition elements to be used with quarter-point crack-tip elements

Abstract: A generalization of the (r−1/2) strain or stress singularity capability of the quadratic isoparametric element is presented. It is shown that, by variable placement of the side-nobe between quarter- and mid-point, the point of singularity sensed by the element can be controlled. By using eight-noded quadrilateral isoparametric elements with appropriately placed side-nodes as transition elements between the quarter-point crack-tip trinagular and remaining non-singular elements, stress intensity factors may be computed with higher accuracy.

Image Segmentation by Pixel Classification in (Gray Level, Edge Value) Space

Abstract: Image segmentation can be treated as a pixel classification problem. This classification may be done by measuring a set of features at each point and defining a decision surface in the feature space. This method is commonly used in multispectral images, but there is no obvious choice for the feature set in the case of monochromatic images. Ihis paper makes use of a two-dimensional feature set consisting of gray level and edge value. Ihe structure of this feature space is analyzed, and several plausible decision surfaces are suggested. These are compared experimentally on a set of FLIR test images.

Branch point structure of covering maps onto nonorientable surfaces

Abstract: Let /: M -> N be a degree n branched cover onto a compact, connected nonorientable surface with branch points yx, y2.ym in N, and let the multiplicities at points in f~\\y¡) be fti, fto • • • > Kv The branching array of/, designated by B, is the following array of numbers: fll'Ml2> • • -«Mi*, /*2i' to • • • » f*2*2 fini' Mm2> • • • ' /Vu We show that the numbers in the branching array must always satisfy the following conditions: (1)S{M»+IU1,2,... ,**}-«, (2) 2{ fy|< = 1, 2.m;j = 1, 2.*,} is even. Furthermore, if S is any array of numbers satisfying these conditions, and if N is not the projective plane, then there is a branched cover onto N with B as its branching array.

Simple Partitions of Space

Abstract: Consider an arrangement of n planes in general position in Euclidean 3-space, where by "general position" we mean that at most three of the planes pass through each point, no more than two of the planes pass through each line, there are no parallel planes, and no lines of intersection are parallel to planes of the arrangement. Into how many cells is space divided? This problem is studied from the heuristic point of view by G. P6lya in [4] and again in his film, "Let Us Teach Guessing." The solution,

Some results with relation to the control measure problem

Abstract: “If a sequentially point continuous submeasure (Maharam submeasure) defined on a measurable space admits a control measure, then a Fubini condition is fulfilled for measurable subsets of the product of the space with the unit interval (with usual Lebesgue measure). The main result is that this Fubini condition is also sufficient for the existence of control measure. Some related results are proved.”

Set Theoretic, Measure Theoretic, Combinatorial, and Number Theoretic Problems Concerning Point Sets in Euclidean Space

Abstract: In this paper I will discuss a few problems which are on the • borderline of geometry, number theory, and set theory and which have occupied me for a long time. Perhaps they are more difficult than important, but I find them fascinating. It is a common paradox that problems on infinite sets are often very much simpler than problems on finite sets. This prompted Ulam and myself to state the following somewhat impudent and unfortunately somewhat inaccurate motto : \"The infinite we do right away, the finite takes some more time .\" (By the way, we \"stole\" this motto from the U .S. Navy-during World War II one of their mottos was \"The difficult we do right away, the impossible takes some more time\" .) To our motto (Ulam's and mine) I just want to add that the finite takes iri fact very much more time-perhaps more than ttie lifetime of the universe. In what follows I will give proofs only if the published proofs are hard to find, are excessively complicated, or are not quite accurate. In any case, I will give as

Digital filter design with short word-length coefficients

Abstract: This paper describes an algorithm for the design of digital filters with short word-length coefficients. Starting with a set of N optimized z -plane poles and zeros that meet specifications with some margin, the algorithm sequentially applies a limited search (up to 16 grid points) for the locally optimum grid point in the neighborhood of a particular z -plane singularity, followed by a global continuous reoptimization of the remaining N-1 singularities. As the number of available singularities decreases to zero, the algorithm terminates with a limited search in the neighborhood of the last singularity for the best grid point. The success depends crucially on the sequence in which the singularities are fixed at the locally optimum grid points in the z plane. The sequence itself is an integral part of the algorithm. The algorithm has been applied successfully to the design of high-order filters with stringent specifications, and the solutions obtained show 0- , 1- , or 2-bit improvement in the coefficient word length over the previously published results.

Bounds for the point spectrum for a Sturm-Liouville equation*

Abstract: This paper obtains, under certain general conditions on the coefficient q, a best-possible upper bound on the real parameter λ for the differential equationto have a non-trivial solution in the integrable-square space L2 (a, ∞).

Punctual control of a vibrating string: Numerical analysis

Abstract: In a paper by Melcher[6] the stabilization of a vibrating string has been studied from a theoretical point of view. The purposes of this paper are to study the same problem from both mathematical and numerical points of view and, furthermore, to look at stabilization and control problems. The main mathematical and numerical interests of this problem lie in the presence of a Dirac measure in the wave equation.

Multi-stage gear crank for a bicycle

Abstract: A multi-stage gear crank for a bicycle has chain detaching means facilitating disengagement of a driving chain from the teeth of sprockets, the detaching means being provided at teeth positioned in the vicinity of the upper and lower dead points of a larger diameter sprocket corresponding to the crank arms respectively, whereby the chain is adapted to be switched to a smaller diameter sprocket from the larger diameter sprocket at the upper dead point thereof.

Method and apparatus for machining spherical combustion chambers

Abstract: A spherically shaped combustion chamber is machined in the cylinder head of an internal combustion engine by revolving one or more cutting tools simultaneously about two axes; one axis being the central axis of the combustion chamber and the other axis being inclined thereto. The tools have a cutting point and a cutting edge extending from the cutting point. The tools are supported so that each cutting point passes through the axis of the combustion chamber, and, when each tool is located in its radially outermost position relative to the axis of the combustion chamber, the cutting edge of the tool cuts an annular surface around the periphery of the spherically shaped portion of the combustion chamber, which, at the bottom face of the cylinder head, corresponds in diameter to that of the cylinder bore.

Supporting frame for traffic cones on vehicles

Abstract: A supporting frame for use on motor vehicles for supporting highway traffic markers of the type having a flat square base and an elongated brightly colored cone extending vertically therefrom (commonly called traffic cones). The supporting frame is characterized by its ability to be installed on the vehicle in almost any position, e.g., horizontally or vertically. The frame comprises rectangular box-shaped framework having an interior shape fitting the periphery of the square bases of the traffic cones. The frame is open at one end for insertion and removal of traffic cones and has two open sides facilitating removal of said traffic cones. The supporting frame has a ring spaced from the base portion thereof and supported on supporting rods. The ring supports the cone portions of the traffic cones and also provides a point of attachment for the supporting frame to the structural member of the vehicle.

Point of contact.

Abstract: Compared with prior engagements, commanders today are exposed to a battlespace that is more dynamic and less predictable. With increasing frequency, commanders are confronted with an array of problems whose solution requires knowledge beyond their military training. In these novel situations, decision makers often rely on their past experiences incorporating a process best described in research as analogy-based reasoning and/or recognition primed decision making. While the relevancy of the experience is based on the individual, a key goal would be to capture and exchange relevant experiences between individual decision makers. The shocking events of 11 September 2001 may have been less shocking to anyone with experience serving in the Pacific theater of operations toward the end of World War II and experienced Kamikaze warfare. This paper describes work in progress at the USAF Research Laboratory Information Directorate to capture, develop, and provide an experience-based reasoning system to commanders during mixed-initiative planning. The objective of this work is to provide a rich database of experiences for the commander to compare to the current situation. The research described in this paper is aimed at developing a computational representation for episodic models, and reasoning on those models for retrieval and experience extraction.

Method of determining liquid flow in a conduit

Abstract: The instant invention provides a method for determining the streaming velocity of a streaming liquid by injecting a thermopulse into the liquid and measuring its transit time. The pulse is detected by its ascending flank at downstream points and by its ascending or descending flank at its point of injection. For short transit times, provision is made to eliminate the heat up time of the heating wire imparting the pulse from the transit time measurement. The liquid may stream continuously or discontinuously, and if the later, provision is made to delay measurement on initiation of flow until the flow pattern has stabilized. The time is determined by counting pulses from a pulse generator during the period the pulse is traveling between the point of injection and a detection point or between two detection points.

Electronic trip meter for an automotive vehicle

Abstract: An electronic trip meter for an automotive vehicle comprises an up-down counter, a memory circuit, an adder-subtractor, a display circuit, and other auxiliary circuits. The up-down counter produces a signal indicative of a remaining distance to a goal by subtracting an actually travelled distance from a preset distance between two points for displaying the remaining distance by the display circuit. When the vehicle reaches the goal, the adder-subtractor produces a signal indicative of the actually travelled distance in accordance with the output signals of the up-down counter and the memory circuit in which the preset distance is stored. The adder-subtractor output signal is then fed to the up-down counter for displaying the actual distance between the two points and to the memory circuit for correcting the preset distance whereby a remaining distance to the starting point in a return trip is easily and accurately obtained. The trip meter may be also utilized for a trip beyond the goal.

A systematic error in the measurement of frost point using a Meteorological Office Mk 3 hygrometer

Abstract: A series of laboratory and airborne experiments were undertaken to investigate a possible systematic error in the measurement of frost point using a Meteorological Office Mk 3 hygrometer. It was found that temperature gradients in the hygrometer thimble could cause the temperature sensor to read frost points too low by over 2 degC. The error was greater at low thimble temperatures. A table of corrections is presented for frost points in the range −40 to −85°C.

Set point sensing system for numerically controlled machine tools

Abstract: An automatic system for sensing and establishing the set point for numerically controlled machine tools. Before operating a numerical control (N/C) machine tool, such as a milling machine, it is necessary to precisely locate a basic reference point on the workpiece or work holding fixture. The disclosed system comprises a capacitive bridge sensing device positioned at the set or reference point. When a machine tool is positioned precisely at the set point, a null reading is observed on suitable readout means. When the tool is moved from null, a reading proportional to displacement is observed. The sensor basically consists of four individual capacitor plates arranged in a circle around a center point, in "X" and "Y" directions. The plates are excited by an audio oscillator and coupled into a bridge instrumentation oscillator. As a grounded machine tool is moved adjacent to these plates the capacitance between the individual plates and the grounded tool varies. In each of the "X" and "Y" directions the plus and minus capacitance are differentially measured using the amplifier to observe the phase difference in the bridge. The output of the differential amplifier is a sinewave whose phase is proportional to the grounded tool's displacement from center, which can be displayed on a digital readout device. An operator may then precisely locate the center position by manipulating the N/C machine and observing the readout.