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A manner is presented with which complex curves including polylines, conics or free curves can be precisely represented, and corresponding algorithm is designed. The curve can be C〓 or C〓 continuous. So all type of curves and their composites can be represented in NURBS. A deep research is paid to skinning surface. Different forms of the formation of knots vector are applied to different section forms.

对由多段直线、二次曲线、自由曲线进行任意组合的这类复杂曲线，提出了一种用一条NURBS曲线进行精确表示的方法，并设计了相应的算法，曲线段连接处根据需要可为一阶连续或形成尖点，从而使所有类型的曲线及由它们任意组合所生成的复杂曲线统一用NURBS表示。

In order to overcome shortcomings that the circular arc and ellipse could not be accurately represented by CE-Bézier curves, this method used the continuity condition of CE-Bézier curves and C-Bézier curves to resolve the representation of circular arc and ellipse in CE-Bézier curve modeling.

该方法首先构造了一种具有优良形状可调性和更好逼近性的带3个形状参数α，β，γ的三次扩展Bézier曲线(CE-Bézier曲线)；并针对CE-Bézier曲线无法精确表示圆弧和椭圆弧等二次曲线的缺点，利用CE-Bézier曲线与C-Bézier曲线间的拼接技术，解决了CE-Bézier曲线造型中圆弧和椭圆弧的表示问题。

By means of the dual of Said-Ball basis, the Marsden identity is got in terms of Said-Ball basis, and a degree reduction algorithm for Said-Ball curves is presented through the transform from Bezier curves to Said-Ball curves.

利用Said-Ball基函数的对偶基，得到幂基函数在Said-Ball基下的Marsden恒等式，及从Bézier曲线到Said-Ball曲线的转换。并给出Said-Ball曲线的降阶赋值算法。

In order to transfer the experimental JR curves from laboratory to real cracked components, a mathematical expression representing a family of the JR curves was constructed for steel 18G2A by using the test data of JR curves for the SENB specimens.

同时，为了将实验得到的18G2A钢的JR曲线应用于实际裂纹构件，建立了JR曲线与约束参数A2之间的关系，给出了与约束参数A2相关的JR曲线族的表达式。

Some new formulae for the derivative bounds of parametric curves, such as the general polynomial curves and rational polynomial curves in CAGD, are presented.

对CAGD中常见的多项式曲线和有理多项式曲线的导矢的界提出了新的估计公式。

Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature. Finally, we will employ the Minkowskis support function to construct a new kind of non-circular smooth constant breadth curves in order to attack some open problems on the constant width curves for example, whether there is a non-circular polynomial curve of constant width, etc.

其次，对双曲平面上的曲线引入平均测地曲率的概念，并讨论双曲平面上凸曲线的嵌入性与它的平均测地曲率之间的关系，其目的是为了将双曲平面上曲线的性质与欧氏平面中曲线的性质作一些对比；最后，我们利用Minkowski支撑函数构造了一类新的非圆的光滑常宽曲线，其目的是想回答有关常宽曲线的一些未解决问题如是否存在非圆的多项式常宽曲线？

Results indicate that:(1) by using HANTS, the researchers could get the EVI/NDVI harmonic curves, the mean VIs and the amplitude of the harmonics which then were utilized in the identification of the cultivated land, and EVI appeared to be more precise, with the overall accuracies of 97.17% and 95.99% and Kappa coefficients of 0.7938 and 0.6518, respectively.(2) Multiple cropping index was extracted by counting the number of the curve's peak; and when the threshold of the peak value of the NDVI and EVI curves were set as 0.25 and 0.20, respectively, the fallow land could be well figured out.(3) From harmonic curves, some eigenvalues, such as time of the maximum growth rate, time of peak and the value of peak can be extracted, based on which the crop types can be primarily distinguished. And EVI still performed better than NDVI in this section.

结果显示：（1）利用傅立叶谐波变换得到的EVI和NDVI时间谱曲线的谐波余项及谐波振幅对耕地进行识别，从识别精度来看，EVI要优于NDVI，识别精度分别为97.17%和 95.99%，Kappa系数分别达到0.7938和0.6518；（2）通过计算时间序列曲线的波峰数能够提取耕地的复种指数，并且在EVI和NDVI曲线波峰阈值分别设为0.20和0.25时，休耕地能较为准确地被识别出来；（3）通过提取作物生长期内曲线的VI最大增长速率时间点以及峰值时间点等信息，作物种类能被初步识别，并且EVI较NDVI具有更强的识别能力。

Ythagorean hodograph curves enjoy a number of remarkable properties, such as, its offset curves have exact rational representations; the arc length function of a Pythagorean hodograph curve is simply a polynomial function of the curve parameter; and the lower degree Pythagorean hodograph curves have intuitive geometrical interpretation.

H曲线具有诸如有精确的有理 Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质。基于复分析方法，避免了实分析讨论中出现的复杂表示及繁琐计算，构造了满足给定 C1 Hermite插值条件且以C1拼接连续的三次 PH曲线偶。该曲线偶可灵活处理拐点，从而克服了一般三次 PH曲线因恒凸而无法处理拐点的缺陷。

In order to analyze rheological property and establish constitutive model of Q_2 loess, a series of uniaxial creep experiments on different water content are done .The creep test curves and stress-strain isochronism curves are drawed with the result of experiments and conclusions are reached from the curves. The creep performance of Q_2 loess is different under the different stress level. In the different time the stress-strain isochronism curve has obvious inflection point namely yield stress and the yield stress reduces along with the increase of water content, which can be described by exponential function.

为了分析黄土的流变特性和建立相应的本构模型，本文首先根据对不同含水量的Q_2黄土进行的一系列单轴应力条件的室内蠕变试验结果，分析总结了Q_2黄土蠕变特征和应力—应变等时曲线特征，得出Q_2黄土在不同的应力水平下蠕变变形表现形式不同；在不同的时刻应力—应变等时曲线存在有较明显的拐点，拐点所对应的应力即为屈服应力，屈服应力随着含水量的增大而呈指数形式降低；Q_2黄土可近似看成一种线性粘弹塑性体。

The technique of perturbations constraint when applied to degree reduction of Bézier curves gives fairly well results This paper discusses why these kind of technique have limitation when applied to B-spline curves, and the least squares approximation approach is presented for reducing the degree of B-spline curves Examples comparing the new method with existing ones are illustrate

将扰动约束技术应用于B啨zier曲线的降阶给出了理想的结果讨论了将这类方法应用于B样条曲线降阶时结果不理想的原因，提出了采用最佳平方逼近技术对B样条曲线做降阶运算的方法；并用实例对该方法和基于扰动约束的降阶方法进行了比

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