基本曲线

Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.

空间曲线是造型中最基本的几何元素之一，对其有效的表示是造型的基础，而特征参数化表示是其中一种包含语义信息的高层次表示，本文对空间自由曲线的特征参数化表示进行研究，建立了一种针织物线圈的特征参数化几何模型，采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系，并将该模型与能量极小化的方法相结合，得到了一种能较好地预测针织物缩水率的新模型，对随机选取的一些针织布缩水预测实验表明了算法的可行性。

The basic idea is as follows: with the help of the related results of differential geometry, the problem of interpolating curve on a parametric surface is converted to a similar one on its parametric plane.

基本思想是借助于微分几何的有关结论，曲面上曲线的插值问题被转化为其参数平面上类似的曲线插值问题。

To the question of fatigue invalidating of strain gages in dynamic test(normally the zero drift value being bigger than the permissible value),the equations for calculating the fatigue life of the strain gages are derived on the basis of the fracture mechanics theory.

针对应变片在长时间的动态测试中疲劳失效(一般是测量误差超过允许值)问题，本文从疲劳断裂力学的基本理论出发，导出了应变片疲劳寿命的计算公式；实验表明，实验曲线与理论曲线吻合，这证明我们推导的公式的正确性，为应变片的疲劳寿命的预测、许可载荷的确定、失效判据的确立提供了理论基础。

Properness of a parameterization is a basic property of rational parametric curves and it has been well studied when the coefficients of the parameterization are rational. However, such coefficients in engineering and CAGD are often represented with float numbers with errors.

有理参数曲线的恰当性是曲线的基本性质，虽然其在有理系数情况下已经有完备的结果，但在工程和CAGD应用中常常得到带误差浮点系数的有理表示形式。

The measuring data after pre-processing was fitted with NURBS curve with constructing the non-uniform node vector using the method of cumulating chord length and optimizing the rights of NURBS curve restrictively. The formula of surface skinning which can be realized by programming was proposed on the basis of the foundation formulas in existence, then NURBS curves was skinned to gain the corresponding NURBS surface.

对经过预处理后的测量点数据，通过采用累积弦长法构造非均匀节点矢量和对权因子的约束优化，进行测量点数据的NURBS 曲线拟合，在现有基本公式的基础上推导出了可以编程实现的曲面放样公式，对得到的NURBS 曲线进行放样处理，最终得到了测量点数据的NURBS 曲面。

The whole multi-Agent system runs based on the continuous communication among agents. The architecture of the cloverleaf is variable, the beeline, the round curve and the convolute curve is the basic elements for the plane curves,the longitudinal gradient reflects the change of the vertical section. We consider sufficiently these specific factors in building road Agent. The different parameters are set to describe the geometrical characteristic and traffic characteristic.

立交枢纽的线形多变，直线、圆曲线与缓和曲线为平面线形组成的三个基本要素，坡度反应纵断面的路线起伏，本文在建立路段智能体中充分考虑了这些立交枢纽的特有要素，为每个智能体设置了不同的几何特性及交通特性，并在决策单元中加入对车辆驶入、换道、超车、限速等的智能控制模型，使得车辆智能体能够在由路段智能体相互连接组成的立交枢纽上正常行驶。

Cutter blade in the face of the modeling, this paper presents a basic model of ideological confrontation flank milling reasoning and mathematical algorithm: First, the establishment of the cutter edge cross-section curve and the equation ruled surface and then through the algorithm to generate cutter rake face and the flank, Bezier curve-based algorithm to generate the surface of the spiral groove cutter in order to achieve the opposite blade face milling modeling.

在立铣刀的刃面的建模方面，本文提出了一种基本的建模思想对立铣刀的刀面进行数学推理和算法实现：首先建立立铣刀的刃口曲线及横截面的方程，然后通过直纹面生成算法建立立铣刀的前刀面和后刀面，通过基于Bezier曲线的曲面生成算法建立立铣刀的螺旋槽，从而实现了对立铣刀刃面的建模。

Test results show that the equivalent strain method exhibits a higher life assessment precision as compared to that by linear damage summation. The critical damage formula for equivalent strain can quite well predict the actual damage incurred and the equivalent strain-life curve with hardness modification fundamentally conforms with the pure fatigue strain-life curve.

试验结果表明，在预测寿命时等效应变法比线性累计损伤法具有更高的精度，等效应变的应力下临界损伤公式能够很好地预测实际损伤，考虑硬度修正的等效应变-寿命曲线和纯疲劳应变-寿命曲线基本一致。

Because Matlab uses complex matrix as its basic unit, we provided the matrix form of the Bezier curve and tensor product Bezier surface, and presented the ways to achieve them by using Matlab. On such a basis, we obtained the algorithm, made feasible programs and demonstrated them by concrete examples. Such a study aims at promoting the realization of CAGD toolbox by using Matlab.

由于Matlab的基本编程单元是复数矩阵，因此首先归纳出了一维Bezier曲线和二维张量积型Bezier曲面的矩阵表示形式，在此基础上形成算法，编写了可实现的程序，随后以具体实例的形式给予验证，最终得到了满足要求的曲线和曲面，以期能够推动Matlab的CAGD专业工具箱的产生。

Results The feeling threshold curve of mechanical middle ear model was similar to the hearing threshold curve of normal person.

结果模型感觉阈曲线和正常人听阈曲线对比，两者走势基本相同。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。