几何化

An implicit Curve reconstruction method is proposed which represents the curve with all algebraic tensor-product B-spline,and minimizes the tension ofthe B-spline and the approximate geometric distance between the curve and the point set.

提出一种以代数张量积样条曲线作为几何表示形式，基于近似几何误差和薄板能量极小化的隐式重构模型。

Libermann.The early researcheson this kind of manifolds were closely related to Physics and Mechanics.But since1991,S.Kaneyuki published his result on the algebraic condition for the existence ofinvariant〓structures on a coset space,Lie theory has played the most impor-tant role in the study of this kind of manifolds.In particular,dipolarizations in a Liealgebra are closely related to the homogeneous〓manifolds.Dipolarizationsin semisimple Lie algebras and the homogeneous〓manifolds associated withthese dipolarizations have been studied by S.Kaneyuki,Z.X.Hou and S.Q.Deng.Inthe partⅡ of this thesis we study the dipolarizations in some quadratic Lie algebrasand the homogeneous parakahler manifolds associated with these dipolarizations.

Libermann给出的，早期的有关类流形的研究与物理和力学密切相关，自从1991年金行壮二发表了陪集空间上存在不变仿凯勒结构的代数化结果后，李群及李代数理论在这类流形的研究中起着主要作用，特别地，李代数的双极化与这类流形密切相关，半单李代数的双极化的相关几何，金行壮二，候自新和邓少强等人已作了研究，二次李代数是比半单李代数更广且带有非退化不变双线性型的李代数，本文主要研究了二次代数的双极化及相关几何。

The discrete random height variable of worn surface is described with continuous random variables by a mathematical method.

建立了磨损表面轮廓数值化基准、用连续随机变量来描述磨损表面轮廓线高度离散随机变量，对磨损表面高度分布作了数理统计分析，研究了载荷、滑动速度及镀层种类对磨损表面几何特性的影响，将数理统计分析结果与镀层的耐磨性作了比较分析，较为完整、深入地描述了磨损表面的几何特性。

The representation, estimation and computation of pointwise geometric constant are quantitative of pointwise geometric property and locally representation of geometric constant of space.

点态几何常数的表示、估计、计算是点态几何性质的量化，是空间几何常数的局部化。

Parametrization is a crucial problem in computer graphics,computer aided geometric design and digital geometric processing.

三角网格的参数化是对三角网格的几何和拓扑信息作进一步处理的基础，它在计算机图形学、计算机辅助几何设计和数字几何处理等领域有着广泛的应用。

In chapter 4, some vector mathematical definitions are first given to position tolerance zones; second, the principle of variation geometry is introduced, and the mathematical foundation of automatic generation of a approximate linear equation of tolerance design function by variation geometry is first proven; tangent method and two-point slope method based variation geometry are main studied.

第四章首先对一些位置公差带给出了矢量化的数学定义；然后介绍了变动几何的原理，首次论证了变动几何能产生近似线性公差设计函数的数学依据，并着重研究了基于变动几何的切线法和二点斜率法。

A new mathematical model is put forward numerically to simulate the wheel ovalization.. In the numerical simulation, the dynamic model of a half railway vehicle coupled with a tangent track is employed. Using the new numerical method investigates vehicle-track coupling system dynamic responses including lateral and vertical displacement of wheelsets and the vehicle, lateral and vertical vibration acceleration of the track at different phase angle of the two side wheels of the same wheelset, which are compared with that of the traditional model. The numerical results show that the discipline and frequency of dynamic responses are accordant, amplitude and phase of lateral dynamic responses are different. It is concluded the traditional track geometric irregularity excitation model does not simulate the effect of periodic wheels ovalization on vehicle-track coupling system dynamic behavior truly, the new model is more accurate and reasonable.

本文研究了车轮二阶周期性非圆化—椭圆化，建立了一个新的模拟车轮椭圆化的数学模型，结合车辆－轨道空间耦合动力学模型，计算了同一轮对左右车轮不同相位和车轮椭圆度下轮对和车体的横、垂向位移，钢轨横、垂向振动加速度，并与传统模型计算结果作了对比，分析表明两种模型的动力响应变化规律和频率一致，但横向动力响应幅值和相位均存在不同程度不可忽略的差异，因此传统的轨道几何不平顺激励模型不能真实模拟车轮的周期性椭圆化对车辆－轨道耦合动态行为的影响，而本文模型更能反映实际椭圆车轮与钢轨接触情形，计算方法准确而合理。

The results showed that:(1) some governing points, which were measured by submeter precision GPS, were utilized to correct the 1 m precision remote sensing image and it could satisfy the desired precision of geometrical correction, therefore, this method could be used as geometrical correction in the region where was short of the big scale relief map;(2) the density of the original data was the main factor to affect precision of the volume, and the precision of the calculated volume of earthwork could be improved to more than 90% when using the test points and feature points; the sparser the data density were, more significant could be improved; On the base that elevation of test points were measured by the submeter precision GPS, the error of the volume, which was produced by vectoring relief map to obtain DEM, could be calculated, and the calculation precision of the earthwork could be improved markedly.

结果表明：利用平面精度达亚米级的GPS测量控制点坐标对1米分辨率的遥感卫星影像进行几何校正，能够满足其几何校正的精度要求，可以解决缺乏大比例尺地形图地区的高分辨率遥感卫星影像的几何校正问题；通过对模型数据的分析，数据密度是影响体积精度的主要因素，利用检测点高程和特征点可以提高土方量计算的精度，使土方量计算的精度达到90％以上，数据密度越稀疏，精度提高越显著；采用高程精度达厘米级的RTK(Real Time Kinematic实时动态差分)测量检测点的高程，对用地形图扫描矢量化形成的DEM模型进行检测求出误差体积，可以大大提高土方量的计算精度。

Based on the framework of wheat morphology visualization, the 3D geometric modeling technologies of wheat organs were investigated, and the organ geometrical models were developed with characteristic architecture parameters. The model included three submodels: leaf geometry, stem geometry and wheat spike geometry submodels.

本研究以小麦作物为对象，在提出小麦形态可视化技术框架的基础上，首先研究了小麦不同器官的三维几何建模技术，构建了基于器官形态特征参数的几何模型，包括叶、茎秆和麦穗几何模型。

Methods of parametric modeling and analysis supplied by ADAMS/View were used to design and analyze front independent suspension of 6 × 6 off-road vehicle, and better results were received.

采用ADAMS／View提供的参数化建模及参数化分析方法，对6 6越野汽车前独立悬架进行了参数化设计，并对悬架主要的几何参数进行了分析，得出了较好的分析仿真结果。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐