Showing papers on "Point (geometry) published in 1995"

Registering multiview range data to create 3D computer objects

Abstract: Concerns the problem of range image registration for the purpose of building surface models of 3D objects. The registration task involves finding the translation and rotation parameters which properly align overlapping views of the object so as to reconstruct from these partial surfaces, an integrated surface representation of the object. The registration task is expressed as an optimization problem. We define a function which measures the quality of the alignment between the partial surfaces contained in two range images as produced by a set of motion parameters. This function computes a sum of Euclidean distances from control points on one surfaces to corresponding points on the other. The strength of this approach is in the method used to determine point correspondences. It reverses the rangefinder calibration process, resulting in equations which can be used to directly compute the location of a point in a range image corresponding to an arbitrary point in 3D space. A stochastic optimization technique, very fast simulated reannealing (VFSR), is used to minimize the cost function. Dual-view registration experiments yielded excellent results in very reasonable time. A multiview registration experiment took a long time. A complete surface model was then constructed from the integration of multiple partial views. The effectiveness with which registration of range images can be accomplished makes this method attractive for many practical applications where surface models of 3D objects must be constructed. >

Closest-Point Problems in Computational Geometry

Abstract: A comprehensive overview is given of algorithms and data structures for proximity problems on point sets in ℝ D . In particular, the closest pair problem, the exact and approximate post-office problem, and the problem of constructing spanners are discussed in detail.

A new way to weigh Malnourished Euclidean graphs

Abstract: In this paper, we show that any Euclidean graph over a set V of n points in k-dimensional space that satisfies either the leapfrog property or the isolation property has small weight, i.e., has weight O(1) . wt(SMT), where SMT is a Steiner minimal tree of V. Both the leapfrog property as well as the isolation property constrain the way the edges of the graph are configured in space. Our main application is to prove that certain Euclidean graphs known as t-spanners can be constructed with optimal weight of O(1) + wt(SMT), an intriguing open problem that has attracted much attention recently. The main tool in obtaining the above weight bounds is a theorem that proves the existence of long edges in a Steiner minimal tree on a restricted set of points in k-dimensional space. We also generalize this theorem for Steiner minimal trees on arbitrary point sets. Since very little is known about high-dimensional Steiner minimal trees, these results are of independent interest.

Dynamic Euclidean minimum spanning trees and extrema of binary functions

Abstract: We maintain the minimum spanning tree of a point set in the plane subject to point insertions and deletions, in amortized timeO(n1/2 log2n) per update operation. We reduce the problem to maintaining bichromatic closest pairs, which we solve in timeO(ne) per update. Our algorithm uses a novel construction, theordered nearest neighbor path of a set of points. Our results generalize to higher dimensions, and to fully dynamic algorithms for maintaining minima of binary functions, including the diameter of a point set and the bichromatic farthest pair.

Method and apparatus for inspection and correction of wiring of electronic circuit and for manufacture thereof

Abstract: A method and apparatus for inspecting wirings of an electronic circuit substrate to detect a defect in the wiring and for enabling correction thereof. The inspection method and apparatus include electrostatically coupling at least one electrode to a wiring pattern, applying a time varying voltage between the electrode and wiring pattern at different locations so as to detect a current flow and determine a defect by a variation in the detected current flow at the different locations and a portion of the defect. A defect in the form of a disconnected or half-disconnected point of the wiring may be corrected by supplying a solution of a metal complex to the disconnected or half-disconnected point, heating the solution and end point areas of the disconnected or half-disconnected point by laser light and precipitating a metal thin film establishing a connection of the wiring.

Method and CAD system for designing wiring patterns using predetermined rules

Abstract: In a CAD system for designing wiring patterns, a wiring start point and a wiring end point are selected from a component placement drawing of a printed wiring board displayed on a display screen using a pointing device. The pointing device is used to designate a point through which the wiring will pass. When this designated point is neither in the horizontal nor vertical direction from the wiring start point, a pattern having two segments is drawn from the wiring start point to the designated point. One of the two segments is a vertical or horizontal segment. The other segment is an oblique segment at a predetermined angle to the horizontal. It can then be determined which of the two segments is to be drawn from the wiring start point. A pattern is similarly drawn from a last designated point to a new designated point.

Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’

Abstract: The purpose of this paper is to present some simple examples that are hyperbolic everywhere except at one point, but which do not admit SBR measures. Each example has a fixed point at which the larger eigenvalue is equal to one and the smaller eigenvalue is less than one.

3-d imaging system

Abstract: A 3-dimensional image is obtained from a 2-dimensional display by varying the apparent distance of the image from the viewer on a pixel by pixel basis. This is done by positioning an array of pixel-level optical elements in alignment with the pixels in the image. In a preferred format, each of the optical elements is generally elongate and has a focal length which varies along its length with the result that the point along its length at which light enters the optical element determines the apparent visual distance of the associated pixel from the viewer. In the case of a cathode-ray tube application, controlling the position of entry of the light is done by controlling the electron beam to move a minute distance vertically as it scans horizontally. In a television application, the vertical distance may be determined by a depth component incorporated in the broadcast signal received by a television set. Applications and embodiments relating to computer monitors, film and still printed imagery are also described.

System for controlling a vehicle relative to a judged shape of a travel road

Abstract: A vehicle position is determined and four reference coordinate points N1, N2, N3 and N4 are extracted at predetermined distances on a road output from a CD-ROM or an IC card, and an angle θ of turning of the vehicle from the coordinate point N2 to the coordinate point N3 is calculated according to an expression, θ=(θ1 +θ2) from an angle θ1 formed by a vector V12 between the points N1, N2 and a vector V23 between the points N2, N3 and an angle θ2 formed by the vector V23 between the points N2, N3 and a vector V34 between the points N3, N4. A steering angle permitting the vehicle to safely pass through a curve is calculated based on the turning angle θ and a vehicle speed V0, and a passable vehicle speed permitting the vehicle to safely pass through the curve is calculated based on a radius R=a/θ of curvature of the curve. Thus, the servicing of a conventional infrastructure requiring increased equipment and maintenance costs is not required, and it is possible to carry out a vehicle control based on a minimum amount of data storable in a CD-ROM or an IC card.

Vehicular navigation system

Abstract: A vehicular navigation system includes a central control unit which determines when a present position deviates from a searched route along which guidance is being provided from a starting point to a destination and determines whether or not the detected deviating present position is on a guidable road prior to re-searching the route and providing guidance based upon the re-searched route. A guidable road is a road upon which the navigation system contains sufficient map information and guide information for the navigation system to search a route and provide guidance. Additionally, system determines whether the vehicle has traveled a predetermined distance after re-search of the route prior to providing travel guidance based upon the re-searched route. Otherwise travel guidance continues to be provided based upon the previously searched route. A driver, after making a short deviation, may thus return to the previous route without travel guidance being interrupted by a re-searched route.

On P-simple points

Abstract: A simple point of an object is a point whose removal does not change the topology. However, the simultaneous deletion of simple points may change the topology. A popular way for overcoming this problem is to use a directional strategy. This method has good properties in two-dimensional discrete spaces but it does not work in three-dimensions. Through the notion of P-simple point we propose a general strategy for removing points in parallel without altering the topology of a 3D space. We also propose a characterization of P-simple points which may be implemented with a linear time complexity

One-dimensional Schrödinger operators with local point interactions.

Abstract: Both these methods have a disadvantage: Form methods can only be used to treat operators which are semi-bounded. This excludes a number of physically interesting situations like a homogeneous electric field V(x) = Ex. If, on the other hand, we want to introduce an infinite number of point interactions, the approadi via boundary conditions leads to infinite deficiency indices, thereby destroying one of the most useful features of the theory of ordinary differential expressions.

Dealing with higher dimensions: the well-separated pair decomposition and its applications

Abstract: Many problems of great practical importance and theoretical interest can be posed as computations on finite point sets in fixed-dimensional Euclidean space. Often, these problems are expressed most naturally in terms of the set of all distinct pairs of points, along with the Euclidean distance between each such pair. Such problems include finding the nearest neighbor of each point and constructing a Euclidean minimum spanning tree. Though it is not purely geometric, computing the electrostatic interaction between point charges can also be posed in these terms, and has applications to particle simulation, a fundamental technique in computational physics. Because there are quadratically many distinct pairs, one would like to avoid enumerating these pairs explicitly. This dissertation develops a data structure, called the well-separated pair decomposition, that organizes the pairs of points into pairs of clusters, or well-separated pairs, in a way that preserves approximate distance. This structure has linear size and can be computed efficiently. Hence, it leads to substantial improvements over algorithms that enumerate all distinct pairs of points. The well-separated pair decomposition uses several ideas that have been exploited in previous algorithms. However, the development presented here has led to many simplifications and refinements to these approaches. Additionally, a more flexible treatment of tree construction has led to efficient parallel and dynamic algorithms that could not be developed using previous techniques. This dissertation presents sequential, parallel, and dynamic algorithms for computing the well-separated pair decomposition, along with applications to specific problems posed on point sets. Some empirical testing is also performed on a C implementation in order to estimate the geometric constants in the complexity.

The Finitistic Dimension Conjectures — A Tale of 3.5 Decades

Abstract: We review the history of several homological conjectures, both from a chronological and a methodological point of view.

Mean size-and-shapes and mean shapes: a geometric point of view

Abstract: Unlike the means of distributions on a euclidean space, it is not entirely clear how one should define the means of distributions on the size-and-shape or shape spaces of k labelled points in Rn1, since these spaces are all curved. In this paper, we discuss, from a shape-theoretic point of view, some questions which arise in practice while using procrustean methods to define mean size-and-shapes or shapes. We obtain sufficient conditions for such means to be unique and for the corresponding generalized procrustean algorithms to converge to them. These conditions involve the curvature of the size-and-shape or shape spaces and are much less restrictive than asking for the data to be concentrated.

New methods for computing a saddle-node bifurcation point for voltage stability analysis

Abstract: This paper proposes methods for calculating saddle-node bifurcation points of power system power flow equations. The first method calculates a saddle-node bifurcation point along a given ray in the parameter space of power flow equations. By exploiting the special structure of power flow equations, the method calculates a saddle-node bifurcation point along a given ray as a solution to a constrained optimization problem. The constrained optimization can be solved efficiently with standard optimization methods. The second method calculates a locally closest saddle-node bifurcation point with respect to the operating point. This method uses an iterative process of computing a saddle-node bifurcation point along a ray, and then updating the direction of the ray for calculating a closer saddle-node bifurcation point. The method is a quasi-Newton method that updates the direction of a ray based on the first-order derivatives and the approximations to the second-order derivatives of the distance between saddle-node bifurcation points and the operating point. The paper compares the proposed methods with other methods on two test examples. >

Constrained and unconstrained synthesis of array factor for circular arrays

Abstract: We consider arrays of N isotropic elements equally spaced on a circular ring. Our purpose is to determine the N element excitations which minimize the mean square distance between the corresponding array factor and a given radiation pattern. At first we examine the unconstrained synthesis problem, obtaining a closed form solution. Then we consider the case where each excitation is constrained to belong to a prescribed set of complex numbers. To solve this problem, we propose an iterative technique which produces a sequence of excitation vectors. Each point of the sequence is derived from the preceding one by modifying one of its N components within the corresponding constraint set, in such a way as to minimize the mean square distance. We show that if the constraint sets are closed and convex, then the sequence converges to the unique point of global minimum of the mean square distance for any starting point of the sequence. If the constraint sets are non-convex, the sequence admits a convergent subsequence, and the limit of the latter is a good approximation of the solution to the problem, in some cases of interest. Some examples illustrate the effectiveness of the method.

Apparatus for estimating motion vectors for feature points of a video signal

Abstract: An apparatus for determining a set of motion vectors for a set of feature points located on a contour of a moving object of a video signal comprises a contour displacement detection circuit for detecting a contour displacement range between a previous contour of the moving object contained in the previous frame and a current contour of the moving object contained in the current frame; and a feature point motion estimation circuit for comparing one of feature point blocks, having one of the feature points, with each of candidate blocks derived from a corresponding feature point search region adaptively regulated by the contour displacement range and for assigning a spatial displacements between one of the feature point block and a most similar candidate block thereto as a motion vector for a feature point corresponding to the one to thereby generating the set of motion vectors for the set of feature points.

Reference planes for the assessment of surface roughness in three dimensions

Abstract: The objective of this paper is to carry out a comprehensive study of reference planes for surface roughness assessment in 3-D. From a standardisation point of view, reference planes for assessing nominally flat and curved surfaces are recommended through theoretical analysis of algorithms and verification of experimental results.

Image processing system and method for generating data representing a number of points in a three-dimensional space from a plurality of two-dimensional images of the space

Abstract: An image processing method is disclosed for generating 3-D graphical model data representing the appearance of a number of points in a 3-D region from two or more 2-D images of the region, the method comprising the steps of a) calculating, for each point, at least one variance value representing the variation, between different ones of the 2-D images in the region of the position on the 2-D images at which the point would appear if it were visible in the images; b) calculating, for each point and using a predetermined rule, a merit value from the variance values, the merit value representing the probability that, if the point lay on a visible surface in the 3-D region, the calculated variance values would be obtained; and c) assigning appearance data to each point in accordance with the merit values and the appearances of the positions on the 2-D images where the point would appear if it were visible thereon. The model is to be rendered to produce images for graphics applications.

Machine readable binary codes

Abstract: A machine readable binary code comprises a two-dimensional matrix of data cells (6) having a plurality of sides. A unique sub-array of data cells (1, 2, 3, 4) is positioned at the point of intersection of each pair of adjacent sides to define and uniquely identify each corner of the matrix.

The study of 3D-from-2D using elimination

Abstract: The paper unifies most of the current literature on 3D geometric invariants from point correspondences across multiple 2D views by using the tool of elimination from algebraic geometry. The technique allows one to predict results by counting parameters and reduces many complicated results obtained in the past (reconstructuon from two and three views, epipolar geometry from seven points, trilinearity of three views, the use of a priori 3D information such as bilateral symmetry, shading and color constancy, and more) into a few lines of reasoning each. The tool of Grobner base computation is used in the elimination process. In the process we obtain several results on N view geometry, and obtain a general result on invariant functions of 4 views and its corresponding quadlinear tensor: 4 views admit minimal sets of 16 invariant functions (of quadlinear forms) with 81 distinct coefficients that can be solved linearly from 6 corresponding points across 4 views. This result has non trivial implications to the understanding of N view geometry. We show a new result on single view invariants based on 6 points and show that certain relationships are impossible. One of the appealing features of the elimination approach is that it is simple to apply and does not require any understanding of the underlying 3D from 2D geometry and algebra. >

A Computer-Aided Design Technique for Semi-Automated Infinite Point Coupler Curve Synthesis of Four-Bar Linkages

Abstract: At the present time, there are no satisfactory computer-aided solution schemes for solving the infinite point coupler curve synthesis problem (i.e., the problem of synthesizing a four-bar linkage whose coupler curve best approximates a fully specified closed trajectory). In order to develop a programmable solution process for this class of problems, it is necessary to devise a way of storing a catalog of coupler curves in a computer database. In addition, comparison procedures must be developed for detecting geometric similarities between curves; these procedures must be capable of observing similarities in the shapes of curves which may be scaled or oriented differently. In this paper, a data representation scheme based on uniform periodic B-splines is proposed as a viable means of storing coupler curves in a database. Automated procedures for fitting B-splines to coupler cures or other closed curves are also developed. The paper also presents a set of algorithms for comparing the shapes ofcurves based on the control polygons of their B-spline approximations. These algorithms are implemented in a computer program that is an effective tool for semi-automated computer-aided solution of the infinite point coupler curve synthesis problem. Example problems solved using this program are discussed, along with some suggestions for further work on this topic

Helical micro-drill point design and grinding

Abstract: A new drill point geometry, termed the helical drill point, specifically intended for micro-drills, is developed in order to alleviate the disadvantages of existing planar micro-drill points. A mathematical model for this new drill point has been established. It is shown that this model is more general than existing drill point models. The commonly used conical, cylindrical and planar drill point models are only special cases of the helical model. For uniquely determining the grinding parameters of the new drill point as well as guiding the grinder design, the characteristics, the controllability and the sensitivity of the grinding parameters have been analyzed. Finally the geometric characteristics of this new drill point are investigated.