空间二仿射对应点列形成的双曲抛物面

空间两条直线交叉,且该两条直线是二仿射对应点列的底,其对应点的连线包络成的二次曲面称为双曲抛物面。借助于正投影图,讨论了双曲抛物面图示法的特点和截交线的变化规律。     

单叶双曲面在铝箔横切中的应用

在分析铝箔横切效果不佳原因的基础上,把单叶双曲面的几何特性应用于移动铝箔的横切机构之中,并确定了转刀刀刃的型线,从而得出一种移动铝箔横切的合理方法.     

两射影平面场的合同点列与线束

同素对应的两射影平面场存在两对对应合同点列，两对对应合同线束。且合同点列与线束之间具有特殊的位置关系。根据这一点，我们给出反映两射影平面场之间量的关系参数：射影比。     

基于空间仿射对应点列的双曲抛物面三维构建及分析

利用计算机3D软件构建基于空间仿射对应点列的双曲抛物面。对双曲抛物面进行不同方向的投射,可以准确得到双曲抛物面不同方位和角度的投影图。从这些投影图中,可以更直观、清楚的了解双曲抛物面的投影特点。使用多个不同位置的平面对双曲抛物面进行截切,并通过分析、观察截交线的变化趋势,得出几点规律性的结论。     

一种改进的基于圆环点的摄像机自标定方法

针对现有的基于圆环点的摄像机自标定算法抗噪性能差、计算过程复杂等问题,本丈提出了一种改进方法。根据射影几何中交比和调和共轭的性质,通过Harris角点计算出四条直径方向上的消失点。同时由拉盖尔定理求取圆环点的图像坐标,在圆环点与内参数的约束下求解所有内部参数。该方法的优点是圆环点求解简单,不需要检测椭圆和直径。实验结果表明,该算法精度高、鲁棒性强,且因无需知道圆的任何几何信息而有较好的实用性。     

双曲面麻花钻的参数节能优化

双曲面麻花钻的后刀面刃磨参数及前刀面螺旋沟槽结构参数在很大程度上决定了其切削性能.以平面表像法为工具,建立了螺旋沟槽发生线为任意直线的双曲面麻花钻的主刃和横刃的切削角度计算模型.基于单元刀具线性综合法建立了钻削功率与刃磨参数及螺旋沟槽结构参数之间的关系模型,提出了以钻削功率最小为目标,应用约束遗传算法优化刃磨参数及螺旋沟槽结构参数的方法.与标准麻花钻相比,优化钻头的钻削功率平均降低了16.0%,扭矩平均降低了15.9%,轴向力平均降低了42.3%.     

空间亲似变换在正投影中的应用

空间亲似变换是用来解决空间几何问题的一种方法。它可以扩大画法几何的解题范围。本文阐述了空间亲似变换在正投影中的建立,以及应用空间亲似变换来求解二次曲面上的截交线和两二次曲面相交后的相贯线。     

工程制图双语教学的探索与实践

分析了当前高校中工程制图双语教学的现状和特点,讨论了该校在工程制图双语教学课程中,在生源、教材、教学手段、辅导与考核、师资等各方面所作的工作。并以一节“平面与曲面立体截交线”的双语课为例,具体叙述了教学的实施情况和在教学中多种媒体相结合的互动式教学方法的实施情况,对如何提高双语教学的效率与质量方面作了有益的探索。     

大巷交岔点施工优化技术的应用与总结

矿井巷道的交岔点在煤矿施工中通常被称作“牛鼻子”工程,在矿井巷道掘进、支护和维护过程中一直是一个难题。本文以二十采区轨道巷与二水平西翼轨道大巷交岔点施工为例,提炼总结施工优化技术并及时服务指导现场。通过现场试验,在巷道交岔点掘进、支护和工程验收中取得了良好的效果。     

抽象空间二阶常微分方程两点边值问题解的存在唯一性

利用了半序理论和新的微分、积分不等式，在Ｂａｎａｃｈ空间中研究了二阶常微分方程两点边值问题解的存在唯一性，给出了逼近解的迭代序列和误差估计式。     

Extracting sectional contours from scanned point clouds via adaptive surface projection

This paper presents a new and fully automatic method to extract cross-sectional contour profiles of a physical object from the point cloud data scanned from its surface. Correctly extracting the sectional contours is of particular importance in the quality inspection of airfoil blades as the tolerances specified on a manufactured aero-engine blade are generally imposed at specific blade sections. The collected point cloud via 3D laser scanning is, however, distributed all over the blade surface rather than at the desired specific sections. In fact, no point in the point cloud is located exactly on the sectional planes. The desired sectional data have to be extracted from the nearby data points. If the underlying smooth surface geometry of the point cloud in the vicinity of a nearby data point can be approximated by a mathematical function, the approximated local surface formulation can be used to project the nearby point onto the desired sectional plane along a curvilinear trajectory. This is achieved in this work by fitting a local quadric surface to the neighbouring points of the point of interest. A systematic approach to establish a balanced set of neighbouring points is employed to avoid bias in fitting the local quadric surface as well as to guide the selection of points to be projected onto the sectional plane. The projected points are then used to construct the desired sectional contour profile. Implementation results have demonstrated the superior performance of the proposed fully automatic method in comparison with the existing methods.     

An efficient algorithm for calculating the cutter location point based on projection method

Aiming at improving the efficiency of calculating the cutter location point with toroid cutter based on the projection method in NC machining for surface, a new algorithm is proposed to calculate the cutter location point directly by torus surface approximating the surface to be machined. According to the geometric information of the points on the surface, the geometrical conditions of the two tangential tori are figured out, and then the contact point is obtained by solving multivariate non-linear equations. Parameters of the tangent point on the surface to be machined are calculated in the next step. Finally, the cutter location point is calculated by a small adjustment. The proposed algorithm is applied to calculate the cutter location point with toroid cutter in surface machining and compared with the existing algorithm. The results show that the computing time of the proposed algorithm in this paper saved about 63–78%.     

On the formulation of closest‐point projection algorithms in elastoplasticity—part I: The variational structure

We present in this paper the characterization of the variational structure behind the discrete equations defining the closest‐point projection approximation in elastoplasticity. Rate‐independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite‐strain multiplicative plasticity. Primal variational principles in terms of the stresses and stress‐like hardening variables are presented first, followed by the formulation of dual principles incorporating explicitly the plastic multiplier. Augmented Lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate‐independent limit. The variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in Part II of this work. Copyright © 2001 John Wiley & Sons, Ltd.     

On the formulation of closest‐point projection algorithms in elastoplasticity—part II: Globally convergent schemes

This paper presents the formulation of numerical algorithms for the solution of the closest‐point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity. The main motivation behind this work is to avoid the poor global convergence properties of a straight application of a Newton scheme in the solution of these equations, the so‐called Newton‐CPPM. The mathematical structure behind the closest‐point projection equations identified in Part I of this work delineates clearly different strategies for the successful solution of these equations. In particular, primal and dual closest‐point projection algorithms are proposed, in non‐augmented and augmented Lagrangian versions for the imposition of the consistency condition. The primal algorithms involve a direct solution of the original closest‐point projection equations, whereas the dual schemes involve a two‐level structure by which the original system of equations is staggered, with the imposition of the consistency condition driving alone the iterative process. Newton schemes in combination with appropriate line search strategies are considered, resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes. These properties, together with the computational performance of the different schemes, are evaluated through representative numerical examples involving different models of finite‐strain plasticity. In particular, the avoidance of the large regions of no convergence in the trial state observed in the standard Newton‐CPPM is clearly illustrated. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessment of methods for computing the closest point projection,penetration, and gap functions in contact searching problems

In computational contact mechanics problems, local searching requires calculation of the closest point projection of a contactor point onto a given target segment. It is generally supposed that the contact boundary is locally described by a convex region. However, because this assumption is not valid for a general curved segment of a three‐dimensional quadratic serendipity element, an iterative numerical procedure may not converge to the nearest local minimum. To this end, several unconstrained optimization methods are tested: the Newton–Raphson method, the least square projection, the sphere and torus approximation method, the steepest descent method, the Broyden method, the Broyden–Fletcher–Goldfarb–Shanno method, and the simplex method. The effectiveness and robustness of these methods are tested by means of a proposed benchmark problem. It is concluded that the Newton–Raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods, whereas the torus approximation method can be recommended for contact searching algorithms, which employ the Lagrange method or the augmented Lagrangian method. Copyright © 2015 John Wiley & Sons, Ltd.     

Line source and point source diffraction by a reactive step

The diffraction of a line and a point source by a reactive step joined by two half planes where each half plane and step are characterized by different surface reactances have been studied. The problem is solved by using the Wiener–Hopf technique and the Fourier transform. The scattered field in the far zone is determined by the method of steepest descent. Graphical results for the line source are also presented. It is observed that if the source is shifted to a large distance the results of the line source differ from those of Buyukaksoy and Birbir [Int. J. Eng. Sci. 1997, 35, 311–319] by a multiplicative factor to the part of the scattered field containing the effects of incident and reflected waves. Subsequently, the point source diffraction is examined using the results obtained for a line source diffraction.     

代数双曲空间中拟Legendre基的应用

鉴于Legendre基等正交基在代数多项式空间中的广泛应用,论文在深入研究代数双曲空间的拟Legendre基性质的基础上,给出了其在反函数逼近和等距曲线逼近上的应用。利用多项式和双曲函数的混合多项式序列来逼近反函数,并通过实例证明给出方法的有效性;对基曲线的法矢曲线进行逼近,构造H-Bézier曲线的等距曲线的最佳逼近,这种方法直接求得逼近曲线的控制顶点,计算简单,截断误差小。     

AutoCAD环境下画法几何图解与三维绘图新方法的研讨

应用AutoCAD R14计算机绘图软件进行画法几何与工程制图图形的绘制与图解。如采用传统的画法几何的一些图解方法,则不便于在计算机显示屏幕上实现其图解步骤,并且存在投影民三维立体图不能同步绘制和显示的问题,以不能清楚显示空间几何元素的空间形状及其与三投影面投影关系的问题。为此,研究开发了一种新方法,它可以在读取已知二投影图（或视图）的同时补画出第三投影图（或视图）,并同步绘制出轴测图,且可以解决工程图解的一系列画法图解的问题。