Instantaneous Point, Line, and Plane Motions Using a Clifford Algebra

The motions of points, lines, and planes, embedded in a rigid body are expressed in a unified algebraic framework using a Clifford algebra. A Clifford algebra based displacement operator is addressed and its higher derivatives from which the coordinate-independent characteristic numbers with simple geometric meaning are defined. Because of the coordinate independent feature, no tedious coordinate transformation typically found in the conventional instantaneous invariants methods is needed.

Mathematical Definitions of Point, Line and Area Symbols in Cartography

The line cartographic symbol located on the boundary and the point cartographic symbol located by single point are the main body and stress of the map. The cartographic symbols are divided into point, line and area symbol in cartography and traditional educational books, but up to now there is only qualitative description about the three kinds of symbols, there are not the mathematical definitions of point, line and area symbols. This paper tries to solve the problem. The authors propose the mathematical definition about point, line and area cartographic symbol according to the theory of topology and expound their dependence relation.

Plane Elasticity and Dislocation of One-Dimensional Hexagonal Quasicrystals with Point Group 6

Plane elasticity theory of one-dimensional hexagonal quasicrystals with point group 6 is proposed and established. As an application of this theory, one typical example of dislocation problem in the quasicrystals is investigated and its exact analytic solution is presented. The result obtained indicates that the stress components of (elastic) fields of a straight dislocation in the quasicrystals still first order singularity, which is the same as the (general crystals,) but are related with the Burgers vector of phason fields, which is different from the general (crystals.)

NEAR CRACK LINE ELASTIC－PLASTIC ANALYSIS FOR A CRACK LOADED BY ANTIPLANE POINT FORCES

In this paper, the improved near crack line analysis method proposed in Refs. [1]and [2] is used to investigate a mode Ⅲ crack loaded by antiplane point forces in aninfinite plate in an elastic-perfectly plastic solid. The solutions of this paper aresufficiently precise near the crack line region because. the assumptions of the smallscale yielding theory have not been used and no other assumptions have been taken.

Evolution of emergent C-points,L-lines,and C-lines in free space

Polarization singularities,which emerge from the incoherent superposition of two vector electric fields with the same frequency,and their evolution in free space are studied analytically and illustrated by numerical examples.It is shown that there exist C-points,L-lines,in particular,C-lines in incoherently superimposed two-dimensional wavefields.Usually,the C-lines are unstable and disappear during the free-space propagation.The motion,pair creation-annihilation process of the emergent C-points,as well as the distortion of the L-lines may take place,and the degree of polarization of the emergent C-points varies upon propagation and may be less than 1.

Loop Closure Detection of Visual SLAM Based on Point and Line Features

For traditional loop closure detection algorithm,only using the vectorization of point features to build visual dictionary is likely to cause perceptual ambiguity.In addition,when scene lacks texture information,the number of point features extracted from it will be small and cannot describe the image effectively.Therefore,this paper proposes a loop closure detection algorithm which combines point and line features.To better recognize scenes with hybrid features,the building process of traditional dictionary tree is improved in the paper.The features with different flag bits were clustered separately to construct a mixed dictionary tree and word vectors that can represent the hybrid features,which can better describe structure and texture information of scene.To ensure that the similarity score between images is more reasonable,different similarity coefficients were set in different scenes,and the candidate frame with the highest similarity score was selected as the candidate closed loop.Experiments show that the point line comprehensive feature was superior to the single feature in the structured scene and the strong texture scene,the recall rate of the proposed algorithm was higher than the state of the art methods when the accuracy is 100%,and the algorithm can be applied to more diverse environments.

Teaching method for reading views by analyzing lines and planes

This paper deals with the teaching method in reading engineering drawing. It introduces the basic theory and fundamental ideas as well as the approach of reading views by analyzing lines and planes. It gives out the steps for completing the third view based on the other two views. As it is easy and quick for students to read and understand views by this method, it is welcome by students in teaching practice.

m-degree Center-connecting Line of Finite Points Set and Its Properties

In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.

NEAR CRACK LINE ELASTIC-PLASTIC ANALYSIS FOR A FINITE PLATE LOADED BY TWO PAIRS OF ANTIPLANE POINT FORCES

In this paper, the improved near crack line analysis method proposed in Refs. [1] and [2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly plastic solid. And the analytical solutions are obtained, that is elastic-plastic stress fields near the crack line and the law that the length of the plastic zone along the crack line is varied with an external loads tr,ld the bearing capacity of a finite plate with a center crack. The results of this paper are sufficiently precise near the crack line, because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.

Sub-pixel extraction of laser stripeand itsapplication in laser plane calibration

For calibrating the laser plane to implement 3D shape measurement, an algorithm for extracting the laser stripe with sub-pixel accuracy is proposed. The proposed algorithm mainly consists of two stages： two-side edge detection and center line extraction. First, the two-side edge of laser stripe is detected using the principal component angle-based progressive probabilistic Hough transform and its width is calculated through the distance between these two edges. Secondly, the center line of laser strip is extracted with 2D Taylor expansion at a sub-pixel level and the laser plane is calibrated with the 3D reconstructed coordinates from the extracted 2D sub-pixel ones. Experimental results demonstrate that the proposed method can not only extract the laser stripe at a high speed, nearly average 78 ms/frame, but also calibrate the coplanar laser stripes at a low error, limited to 0.3 mm. The proposed algorithm can satisfy the system requirement of two-side edge detection and center line extraction, and rapid speed, high precision, as well as strong anti-jamming.

GENERAL FORM OF MATCHING EQUATION OF ELASTIC-PLASTIC FIELD NEAR CRACK LINE FOR MODE I CRACK UNDER PLANE STRESS CONDITION

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

Dynamic Response Analysis of the Equivalent Water Depth Truncated Point of the Catenary Mooring Line

The real-time computer-controlled actuators are used to connect the truncated parts of moorings and risers in the active hybrid model testing system. This must be able to work in model-scale real time, based on feedback input from the floater motions. Thus, mooring line dynamics and damping effects are artificially simulated in real time, based on a computer-based model of the problem. In consideration of the nonlinear characteristics of the sea platform catenary mooring line, the equations of the mooring line motion are formulated by using the lumped-mass method and the dynamic response of several points on the mooring line is investigated by the time and frequency domain analysis method. The dynamic response of the representative point on the mooring line is analyzed under the condition of two different corresponding upper endpoint movements namely sine wave excitation and random wave excitation. The corresponding laws of the dynamic response between the equivalent water depth truncated points at different locations and the upper endpoint are obtained, which can provide technical support for further study of the active hybrid model test.

Near Crack Line Elastic-Plastic Analysis for an Infinite Plate Loaded by a Pair of Point Shear Forces

The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the elastic-plastic fields near crack line and law that the length of the plastic zone along the crack line is varied with external loads. The results are sufficiently precise near the crack line and are not confined by small scale yielding conditions.

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.

ELASTIC-PLASTIC ANALYTICAL SOLUTIONS FOR AN ECCENTRIC CRACK LOADED BY TWO PAIRS OF ANTI-PLANE POINT FORCES

The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti_plane point forces at the crack surface in an elastic_perfectly plastic solid. The analytical solutions of the elastic_plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding. The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.

Research and Application for the Regularity of Distribution about Curvature Radius and Curvature Center of the Linkage Point Track in a Link Mechanism

It is illustrated that there exists an inflection circle on the linkage rigid body by the principle of relative motion. Confirmed methods of the inflection circle, curvature radius and curvature center of the point track on the linkage rigid body are given in the case of the different contact type of move instantaneous center line and static instantaneous center line. The regularity of distribution of curvature radius and curvature center of the point track is researched. The identification methods called determination parameters and auxiliary vertical line of the diameter and direction of the inflection circle in the four bar mechanism are pointed out. A design method of the crane hoisting mechanism is discussed in the end of this paper.

Research on Distance Judgement Method from Point to Line to Generate a Line

Regarding the problem that the traditional straight-line generating has a low accuracy, we study straightline generating with the distance of point to line. We explore generating a line to approximate the ideal line and the issue is to pick out the pixel point of approximating the ideal line. The paper plays a significant scientific role in elucidating linear optimization norm and it lays a foundation for showing a straight line. The algorithm is valuable for computer graphics.

基于Point-to-Plane ICP的点云与影像数据自动配准

针对三维激光点云与二维影像数据的融合问题,采用了一种基于Point-to-Plane ICP的配准方法;该方法仅采用一块普通的平面黑白棋盘格作为标定板,能同时完成单目相机的标定与三维激光扫描仪和相机的联合标定,进而实现三维点云数据与二维影像数据的配准;与以往基于控制点或者边缘对应的配准方法不同,该方法使用RANSAC算法自动提取场景中的标定平面,通过优化点到平面的距离来求取两组数据的变换。实验结果表明,该配准方法减少了人工的干预,并获得了很高的精度。

A New Method for Locating Calculation of Arbitrary Spatial Straight Line or Plane in NC Machining

In the manufacturing process, we often encounter so me location machining of space arbitrary straight lines and planes that are not on ly unparalleled but also not vertical with the machine tool spindle or the cutti ng tool. In the past, we can do the location machining through the methods of dr awing line and making level in the ordinary machine tool. In the numerical contr ol machining of the CNC machine tool and manufacturing center, however, the spac e location and angle of the arbitrary straight lines and planes must be precisel y calculated in advance. So that precisely locating can be guaranteed in machini ng. Therefore, how to work out the space location angle of the arbitrary straigh t lines and planes to be machined both conveniently and precisely, turns out to be the must-be-solved chief problem in the numerical control machining. In thi s paper, through the deeply research of this problem, a new kind of calculating formula that calculates and defines the space location angle of the arbitrary st raight lines and planes by using the methods of analytic calculating. The formul a has been applied in the practical manufacturing calculation. It is proved that the new space angle calculating methods of arbitrary straight lines and planes is convenient in calculating and precise in locating. And it provides us a n ew, brief and precise calculating method in the numerical control machining of t he numerical control machine tool and manufacturing center.

The detailed characteristics of positive corona current pulses in the line-to-plane electrodes

The corona current pulses generated by corona discharge are the sources of the radio interference from transmission lines and the detailed characteristics of the corona current pulses from conductor should be investigated in order to reveal their generation mechanism.In this paper,the line-to-plane electrodes are designed to measure and analyze the characteristics of corona current pulses from positive corona discharges.The influences of inter-electrode gap and line diameters on the detail characteristics of corona current pulses,such as pulse amplitude,rise time,duration time and repetition frequency,are carefully analyzed.The obtained results show that the pulse amplitude and the repetition frequency increase with the diameter of line electrode when the electric fields on the surface of line electrodes are same.With the increase of inter-electrode gap,the pulse amplitude and the repetition frequency first decrease and then turn to be stable,while the rise time first increases and finally turns to be stable.The distributions of electric field and space charges under the line electrodes are calculated,and the influences of inter-electrode gap and line electrode diameter on the experimental results are qualitatively explained.