参数曲线

According to the matrix presentation of NURBS curve, ordinary interpolating algorithm on cubic NURBS curve is shown.

根据NURBS曲线的矩阵表示，对常用的三次NURBS曲线进行插值计算，可以了解边界条件和型值点的参数化对插值曲线的影响。

Based on vector expression of parametric equation of a third－order Bezier curve, Bezier curve interpolation algorithm is proposed in order to imitate tabulation curve.

为了描述列表曲线，本文从三次Bezier曲线参数方程的矢量表达式出发，推导出CNC系统三次Bezier曲线插补法。

In this paper, based on the vector analysis and the warping torsion theory of curved thin-walled girders, a set of governing differential equations for the non-uniform torsion of thinwalled spatial helicoid girders is developed.

本文应用矢量运算及薄壁曲线梁翘曲扭转理论，建立了空间螺旋形的薄壁曲线梁基本微分方程，用初参数法解出翘曲扭转微分方程，为进一步进行薄壁螺旋曲线梁的空间结构分析提供理论基础。

In order to control the flow separation by reducing the diffusion factor and enlarging the diameter of inner circle, the meridian plane profile of the return channel was redesigned, which is achieved by substituting arbitrary curve for the circle with no change of the axial length of the stage. Bezier curve with eight parameters was chose to describe the shape of meridian plane profile, and the optimization of the meridian plane profile was implemented combining back-propagation neural network with genetic algorithm.

改进的主要思路是减小弯道前半部分通道的扩压度，并同时加大弯道出口内侧的转弯半径，主要做法是在不增加整级轴向尺寸的前提下，用任意曲线取代传统弯道的同心圆环结构，给定弯道回流器子午型线的外侧型线，采用Bezier曲线对内侧型线的2段曲线进行参数化描述，利用遗传算法和反向传播(back-propagation，BP)神经网络相结合的方法对内侧型线进行优化，得到新的弯道回流器子午型线。

The study methods: Based on digital printing and offset printing technology principle, the basic parameters having effect on the ink-jet printing output quality were analyzed. And the mathematics models between the ink quantity and the solid density, and the relation between the gamma and printing contrast were established. The relation among the output dot area coverage, the original dot area coverage and the dot-gain percent was analyzed. And the mathematics models of printing characteristics curves and dot-gain curves were established. The factors influencing the dot-gain were analyzed, and then the dot-gain compensation function was acquired. All the models were verified by the method of regression analysis. And the precisions of the models were obtained by the correlation coefficient and multiple correlation coefficients.

研究方法：根据数码印刷以及胶版印刷的工艺原理，分析了影响喷墨印刷输出质量的基本参数，建立墨量与样张实地密度、γ与相对反差的数学模型；分析输出网点面积率、标定网点面积率以及网点扩大率三者之间的关系，建立网点扩大曲线和印刷阶调复制曲线的数学模型，并对网点扩大的影响因素进行了分析，导出了网点扩大补偿函数；运用回归分析方法分析模型，并用相关系数和复相关系数检验回归模型的显著性；使用灰平衡方程，结合回归法得出灰平衡控制曲线。

The gray balance curves were obtained by the gray balance function and regression analysis. The main works: The parameters in the mathematic models were ascertained, as well as all the regression functions. The models included the relation between the ink quantity and the solid density, the relation between the gamma and printing contrast, the printing reproduction curves, the dot-gain curves and the dot-gain compensation curves. The fitting accuracies of the regression models were checked out by the correlation coefficient or multiple correlation coefficients. The effect that the ink had on the solid density and the gamma on the printing contrast were analyzed. And the methods of choosing the ink and gamma were gained.

主要工作：确定了墨量与样张实地密度、γ与相对反差、阶调复制曲线、网点扩大曲线以及网点扩大补偿曲线各自数学模型中的参数，得到了回归表达式；得到了各个回归表达式的相关系数或复相关系数，检验了回归模型的拟合程度；分析了墨量对实地密度的影响以及γ对相对反差的影响，并提出了墨量和γ的选取方法；得到了喷墨印刷质量控制的灰平衡控制、网点扩大以及扩大补偿规律。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Besides, they can not nefleat the neal property out anditory function. Based on the mechanism of real auditory system, a mathematical model is established in which a forward feed back pash is introduced and the static gain curve is derived from input-output curve, therefore the model has dynamic property.

我们根据听觉的生理学机制，建立前馈自适应模型，从输入输出特性曲线上引出静态增益曲线，再在静态增益曲线上引入动态过程，由此建立的数学模型，利用心理学试验数据得到模型参数。

In order to realize the transition from quartic Wang-Ball to Said-Ball curve, and the transition from quartic Said-Ball to B6zier curve, two new classes of curves with shape parameters are defined.

为了实现从四次Wang-Ball到Said-Ball曲线的过渡，以及从四次Said-Ball到B6zier曲线的过渡，定义了2种带形状参数的曲线。

The relationship between the transformation of weights on rational Bézier curve and parameterization of the curve with the shape unchanged is discussed.

研究了在曲线形状保持不变的条件下，有理n次Bézier曲线的权因子改变与曲线参数化的关系。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。