Showing papers on "Point (geometry) published in 1988"

New methods for computing visibility graphs

Abstract: Let S be a set of n non-intersecting line segments in the plane The visibility graph GS of S is the graph that has the endpoints of the segments in S as nodes and in which two nodes are adjacent whenever they can “see” each other (ie, the open line segment joining them is disjoint from all segments or is contained in a segment) Two new methods are presented to construct GS Both methods are very simple to implement The first method is based on a new solution to the following problem: given a set of points, for each point sort the other points around it by angle It runs in time O(n2) The second method uses the fact that visibility graphs often are sparse and runs in time O(m log n) where m is the number of edges in GS Both methods use only Ogr;(n) storage

Exact robot navigation using cost functions: the case of distinct spherical boundaries in E/sup n/

Abstract: The utility of artificial potential functions is explored as a means of translating automatically a robot task description into a feedback control law to drive the robot actuators. A class of functions is sought which will guide a point robot amid any finite number of spherically bounded obstacles in Euclidean n-space toward an arbitrary destination point. By introducing a set of additional constraints, the subclass of navigation functions is defined. This class is dynamically sound in the sense that the actual mechanical system will inherit the essential aspects of the qualitative behavior of the gradient lines of the cost function. An existence proof is given by constructing a one parameter family of such functions; the parameter is used to guarantee the absence of local minima. >

Fast point spread function computation from aperture functions in high-resolution positron emission tomography

Abstract: The problem of extracting point spread functions from detector aperture functions in high-resolution PET is addressed. In the limit of very small size detectors relative to the ring dimensions, assumptions are made that lead to a fast and simple computation model yielding point spread functions with negligible errors due to the reconstruction algorithm. The methods allows one to assess accurately the intrinsic performance of a PET tomograph, and it appears to be adequate to relate the imaging capabilities in every point of the camera reconstruction field to the geometric and physical characteristics of the detection system. The method was developed as an investigation tool to help design the next generation of very-high-resolution PET tomographs. >

Tetrahedrizing Point Sets in Three Dimensions

Abstract: This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are coplanar. It also presents an algorithm that in O(nlog n) time constructs a tetrahedrization of a set of n points consisting of at most 3n–11 tetrahedra.

Markers for readout and delta-parameter measurements on a quasi-3-dimensional display of a spectrum

Abstract: An apparatus and method of using markers for identifying particular points on a quasi-3-dimensional display, such as a color spectrogram display or a waterfall display of multiple frequency spectra on an electronic spectrum analyzer, so that amplitude, time, and frequency values associated with a particular point can be conveniently read out, and so that differences in amplitude, time, and frequency between two points can be easily calculated and presented to the user. Two markers whose positions are ascertainable are generated on the quasi-3-dimensional display and are made subject to operator control. One of these markers is positioned by the operator on a particular point of interest and the values associated with that location are then displayed for readout with greater precision and convenience than would otherwise be possible. A second marker is placed at a second point of interest and the differences in the values of amplitude, time, and frequency between the two points are calculated and displayed.

Intersection of arbitrary surfaces

Abstract: Methods to solve intersections between two arbitrary surfaces must include, in most cases, iterative techniques both from one point to another of the intersection curve and for each point to adjust it into the curve. This is expensive in terms of computing time. A method is given to obtain points from the intersection curve, avoiding the adjustment of all the points to the intersection curve, each point being obtained from the previous point by means of simple operations. This method serves to intersect two given surfaces in implicit form and both derivables up to, at least, the second derivatives.

Symmetry calibration method for multi-configuration robots

Abstract: A symmetry calibration method for calibrating multi-configuration robots is disclosed. Specific points in the robot envelope are selected and the robot is moved to each point twice using different configurations. A linear measurement is made from an arbitrary fixed surface to a selected point on the robot at each envelope point. The origin for an axis is determined when the measurements for both configurations at the envelope point are substantially equal.

Does a point lie inside a polygon

Abstract: A superficially simple problem in computational geometry is that of determining whether a query point P lies in the interior of a polygon if it lies in the polygon's plane. Answering this question is often required when tracking particles in a Monte Carlo program; it is asked frequently and an efficient algorithm is crucial. Littlefield has recently rediscovered Shimrat's algorithm, while in separate works, Wooff, Preparata and Shamos and Mehlhorn, as well as Yamaguchi, give other algorithms. A practical algorithm answering this question when the polygon's plane is skewed in space is not immediately evident from most of these methods. Additionally, all but one fails when two sides extend to infinity (open polygons). In this paper the author review the above methods and present a new, efficient algorithm, valid for all convex polygons, open or closed, and topologically connected in n-dimensional space (n {ge} 2).

Interpolating apparatus with a processing section for line segments parallel with a coordinate axis

Abstract: In an interpolator for a line segment parallel with either X axis or Y axis, when a first comparator detects the coincidence of the X coordinate of the starting point with that of the terminating point, a counter is supplied with the Y coordinate of the starting point as an initial value, and counts up until its count value reaches the Y coordinate value of the terminating point The successive count values from the counter are combined with the X coordinate of the starting point to produce a series of interpolating coordinates When a second comparator detects the coincidence of the Y coordinate of the starting point with that of the terminating point, a similar counting is performed with respect to the X coordinate, and the count values are combined with the Y coordinate of the starting point When both of the comparators fail to detect coincidence, a general purpose interpolator is started

Circular Separability of Planar Point Sets

Abstract: Two planar point sets S 1 and S 2 are circularly separable if there is a circle that encloses S 1 but excludes S 2 . In this note an O((| S 1 |+| S 2 |)log ((| S 1 |+| S 2 |)) algorithm is presented to determine the set S( S 1 , S 2 ) of points which are centers of circles that enclose S 1 but exclude S 2 . It is then shown that once S( S 1 , S 2 ) is known, all the smallest and the largest separating circles can be computed very easily.

Polygonizations of point sets in the plane

Abstract: We examine the different ways a set ofn points in the plane can be connected to form a simple polygon. Such a connection is called apolygonization of the points. For some point sets the number of polygonizations is exponential in the number of points. For this reason we restrict our attention to star-shaped polygons whose kernels have nonempty interiors; these are callednondegenerate star-shaped polygons. We develop an algorithm and data structure for determining the nondegenerate star-shaped polygonizations of a set ofn points in the plane. We do this by first constructing an arrangement of line segments from the point set. The regions in the arrangement correspond to the kernels of the nondegenerate star-shaped polygons whose vertices are the originaln points. To obtain the data structure representing this arrangement, we show how to modify data structures for arrangements of lines in the plane. This data structure can be computed inO(n4) time and space. By visiting the regions in this data structure in a carefully chosen order, we can compute the polygon associated with each region inO(n) time, yielding a total computation time ofO(n5) to compute a complete list ofO(n4) nondegenerate star-shaped polygonizations of the set ofn points.

On the constrained elastic ring

Abstract: The problem of a thin elastic ring contained within a smooth rigid cavity is considered for the case where the ring is subjected to a radial point load. The problem is approached as a moving intermediate boundary problem in the calculus of variation and a closed-form analytical solution is obtained. Numerical results are presented for several cases, revealing unstable behavior of the ring configuration.

Response of an infinite elastic transversely isotropic medium to a point force. An analytical solution in Hankel space

Abstract: SUMMARY The displacement field of an elastic transversely isotropic medium due to a harmonic force, located at one point of an infinite 3-D space, is given in this paper. The Kupradze method allows the number of unknown displacement functions to be reduced to only one potential scalar function and permits an analytical solution in Hankel space.

PROBE Spatial Data Modeling in an Image Database and Query Processing Application

Abstract: Abstracf-The PROBE research project has produced results in the areas of data modeling, spatial/temporal query processing, recursive query processing, and database system architecture for “nontraditional” application areas, many of which involve spatial data and data with complex structure. PROBE provides the point se? as a construct for modeling spatial data. This abstraction is compatible with notions of spatial data found in a wide variety of applications. PROBE is extensible and supports a generalization hierarchy, so it is possible to incorporate application-specific implementations of the point set abstraction. PROBE’s query processor supports point sets with the geometry filter, an optiniizer of spatial queries. Spatial queries are processed by decomposing them into 1) a set-at-a-time portion that is evaluated efficiently by the geometry filter and 2) a portion that involves detailed nianipulations of individual spatial objects by functions supplied with the application-specific representation. The output from the first step is an approximate answer, which is refined in the second step. The data model and the geometry filter are valid in all dimensions, and they are compatible with a wide variety of representations. PROBE’S spatial data model and geometry filter are described, and it is shown how these facilities can be used to support image database applications.

Pressure gauge with needle actuated alarm

Abstract: A pressure gauge has a turning button, a turning disc and a sliding block disposed thereon that, through a protruding wheel fixed on the needle shaft moves the sliding block to force a contact point of a conducting metal piece to contact with a contact point of the turning disc, can start an alarm in case the needle of the gauge comes to reach the designated pressure.

On the behaviour in the Euclidean or Lobachevsky plane of trajectories that cover trajectories of flows on closed surfaces. III

Abstract: Consider a flow on a surface of nonpositive Euler characteristic whose set of equilibrium points can be deformed, in , to a point (this, for example, is the case if there are only finitely many equilibrium points). For such a flow, it is proved that the semitrajectory of the covering flow on the universal cover (the Euclidean or Lobachevsky plane) of is either bounded or tends to infinity in a definite direction. For analytic flows (but not for -flows), this conclusion holds without any conditions on the equilibrium points. Bibliography: 21 titles.