Showing papers on "Point (geometry) published in 1980"

A Maxmin Location Problem

Abstract: The problem considered is to locate a point in a given convex polyhedron which maximizes the minimum Euclidean distance from a given set of points. The paper describes several possible application areas and shows the existence of a finite set of candidates for the optimal solution. A combinatorial algorithm is presented for the problem in three dimensions, and it is compared with existing nonconvex programming algorithms.

Conformal Geometry and the Cyclides of Dupin

Abstract: A Riemannian manifold (M, g) is said to be conformally flat if every point has a neighborhood conformai to an open set in Euclidean space. Over the past thirty years, many papers have appeared attacking, with varying degrees of success, the problem of classifying the conformally flat spaces which occur as hypersurfaces in Euclidean space. Most of these start from the following pointwise result of Schouten.

Line recognition method

Abstract: In a pattern recognition apparatus for recognizing a pattern including a line pattern consisting of a plurality of line segments, there is proposed a line recognition method which comprises steps of: recognizing the coordinates of end points of each of segments constituting a line pattern; employing the coordinates of an end point of a first line segment as base point coordinates; deciding whether the distance between the base point and an end point of a second line segment is less than a certain value or not; employing as a suitable point the end point of the second line segment with said distance being less than the certain value; and selecting a connectable second line segment and connecting said suitable point to the base point of the first line segment.

A note on extremally disconnected spaces

Abstract: A topological space X is said to be locally S-closed if each point of X has an open neighborhood which is an S-closed subspace of X. In this note it is shown that every locally S-closed weakly Hausdorff (or almost-regular) space is extremally disconnected.

Non-Compact Extremal Integral Representations: Some Probabilistic Aspects

Abstract: The verification of the topological assumption in classical Choquet theory often is difficult. We review some results concerning this problem from a probabilistic point of view. The abstract results are mainly due to G. Edgar and G.E.F. Thomas whereas the probabilistic applications are derived from a result on the convex set of solutions of a generalized moment problem.

A nondevelopable Čech-complete space with a point-countable base

Abstract: An example is presented which is a p-space, in fact a Cech-complete space, which has a point-countable base and is not developable. This answers questions raised by Burke in 1970 and by Burke and Tall in 1972.

Measuring device for center position of hole

Abstract: PURPOSE:To enable an easy and accurate detection of a center position of a hole, by a method wherein a center position of a hole shown in a processing drawing or the like is operated from outputs of two light-detecting elements. CONSTITUTION:Through the movement of an image 22 in the direction X, two light-detecting elements 5 located on points P2 and P3 are set into ON for a duration of only a time during which it moves between a distance M from a point P4 to a point P5 and a distance N from a point P6 to a point P7. Because the points P2 and P3 are fixed on a screen 4, a distance L is fixed, and thus, if the distances M and N during which the light-detecting element 5 is set into ON are found, a point P1, which is the center of the image 22, can be found through the computation. Or, as noted from the drawing, the light-detecting element 5 can be positioned at two points P2 and P3 in order to find the distances M and N, and the two units are enough for the light-detecting element 5.

Character recognition system

Abstract: PURPOSE:To decrease the number of processing steps, by picking up the profile information of characters and performing character recognition. CONSTITUTION:The light from the document 1 is converted into binary video information with the sensor 2 and quantizing circuit 3, and stored in the memory 4. Every time when one line of the memory 4 is scanned, the changing point from white to black and present scanning line position is picked up and the profile address pick up circuit 5, and the position of changing point and present scanning line position is written in the profile address memory 6. The start point and end point 7-1-7-4 compare the changing point location at scanning line before one scanning and that at present scanning line, and if the both are discontinuous, the changing point location at scanning line before one scanning is taken as end point and that at present scanning line is taken as start point, and they are written in the memories 9-1-9-4. Character recognition is made based on the profile information of the memories 9-1-9-4 and white part characteristic pair memories 10-1- 10-2.

An algorithm for finding the position of a point relative to a fixed polygonal boundary

Abstract: This article describes a method that determines the position of a point relative to a fixed boundary. Its advantage over the other existing algorithms described below is that in most cases it is necessary that only part of the algorithm be executed to determine the position of the point. A possible inconvenience of using this algorithm is that the contour boundary has to be entered as data. For problems where the boundary often changes the algorithm is not suitable in its present form. The applications envisaged here are to cases where the position of a very large number of points have to be determined relative to one fixed polygonal boundary whose shape is known in advance, for example, blanking out of contours in automatic contouring, or selecting drill holes which lie in the particular part of a mineral deposit.

Grid evolution in time asymptotic problems

Abstract: A technique for generating systems of coordinates for solving time asymptotic problems is described which provides a simple way of moving the mesh points in physical space and reduces the error in the solution relative to that obtained using a fixed mesh. First order partial differential equations are formulated for the grid point velocity in transient problems. Local flow information and boundary motion are used to determine the interior grid point motion.

From a learner's point of view.

Abstract: IT is sometimes possible for a looker-on to intervene without excessive presumption in the disputes of experts. In the matter of education, all who are more or less educated must watch the controversies of teachers with acute interest and even some anxiety. We have ourselves been taught; our children, perhaps, are being taught at the present day. In any case the question of effective and useful teaching is one which admittedly concerns the whole nation. It is a matter of common knowledge that the unrest in India and the agitation of the suffragists, to take two only of the burning questions of the day, can be traced to educational causes. Perhaps there is no dispute in which the ordinary citizen need feel less hesitation in intervening than an educational dispute.

Extraction device of normal direction in case of tracking contour line of input character graphic form of character recognition unit

Abstract: PURPOSE:To make it possible to operate at a high speed by selecting out of the encoded information which has been stored in the memory in advance based on the moving state of the aimed point, and deciding it, without calculating the normal direction of the contour line between the aimed points from the co-ordinates of each aimed point. CONSTITUTION:The tracking circuit consists of the two-dimension memories 1, 2, the address controller 3, and the tracking controller 4, and not only tracks the contour line of the input character graphic form, moving the aimed point at every address of the two-dimension memory, but also outputs the direction code signal whose contents are the moving direction to the next aimed point at every aimed point. The memory 8 is accessed whenever the aimed point moves, and when it is accessed by the input address code signal which contains the own output code signal at the time of previous access due to the previous movement of the aimed point, and the direction code signal at the time of movement to the next aimed point, the latch circuit maintains the output code signal once at every access by setting the two-dimensional address area which provides the output code signal having the projected signal contents corresponding to the contents of the aforesaid signal.