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In the particular ease where a and γ are equal to 1, the developable CE-Bézier surface is a developable Bézier surface. Finally, some applications in developable surfaces design are discussed, The modeling examples illustrate that the developable CE-Bézier surfaces provide two valuable ways for the design of developable surfaces.

由新方法生成的可展曲面不仅具有灵活的局部形状可调性和更强的描述能力，而且保留了CE-Bézier曲面的特性，特别是当α、γ都取值为1时，所生成的可展曲面即为CE-Bézier可展曲面。2种可展曲面设计方法的应用实例表明，该设计方法不仅简单、有效，而且易于控制曲面形状，从而为可展曲面的设计提供了一种新途径。

More specifically, Gauss studied the geometry of surfaces based on the first fundamental form (also called "line element") of surfaces and generalized Euclidean geometry to "curved geometry" on surfaces.

局部微分几何的一个里程碑是 Gauss关于曲面的理论，他建立了基于曲面第一基本形式的几何，并把欧几里得几何推广到曲面上"弯曲"的几何。

For the timelike surfaces with constant positive Gaussian curvature (K=1) in R〓, we construct the correspondence between R〓 and sl (2, R), and deduce the fundamental equations for a special choice of the velocity of motion of time-like surfaces in asymptotic coordinates under suitable conditions, meanwhile, we give the B〓cklund transformation and one soliton solution of the evolution equations, then in terms of a gauge transformation we obtain the explict expression of the motion of surfaces.

对于三维Minkowski空间R〓中具有正常高斯曲率（K=1）的类时曲面，取定特定速度，在以渐近线作为坐标曲线的情况下，曲面运动满足两个基本方程，即sinh-Gordon方程和θ随时间演化的方程（其中θ表示两条渐近线之间的夹角），同时给出两个基本方程的B〓cklund变换和单孤子解，并通过规范变换给出相应的正常高斯曲率曲面的显式表达式。

The surfaces of discrete form such as meshes, subdivision surfaces and point surfaces are becoming more and more important methods of geometric representation in the fields of computer graphics and geometric design.

离散曲面——网格曲面、细分曲面和点云曲面正逐渐成为计算机图形学和几何设计领域中的重要几何表示方法。

All quadrilateral mesh automatic generation for regular quadric surfaces based on Auto CAD AME;2. Represent Quadric Surfaces Using NURBS and Calculate the Control Vertecs and Weights;3. Through study,the property is found out that planes cutting edgewise quadric curve and quadric intersections from the quadric surfaces become the harmonic division.

文中采用了射影几何的方法，证明了画法几何中关于两个二次曲面相交的著名的复切定理和蒙日定理，通过研究得出了周切线平面和交线平面成调和分割的性质，同时还得出了处于复切的二次曲面必存在相公切的二次曲面的性

We generalize the concept of the set of variability defined in the unit diskby K.Strebel to general Riemann surfaces and prove that the set of variablity withrespect to the modulo homotopic class of a quasiconformal mapping between twoRiemann surfaces is a compact and connected subset.Consequently the num-ber of the extremal mappings in the modulo homotopic class of a quasiconformalmapping between two general Riemann surfaces is either one or infinity.

Strebel的定义在单位圆上的可变性集合的概念推广到一般Riemann曲面上去，并且证明了Riemann曲面之间的拟共形映射的模边同伦类所确定的可变性集合是一个连通的紧子集，从而得出一般Riemann曲面之间拟共形映射的模边同伦类中的极值映射要么唯一，要么有无穷多个。

Presents the design of longitudinal control for ASTOVL lift-fan aircraft, a multi-variable, strong-coupling, complicated nonlinear system to make the system nonlinear offset and decouple, and the method used for linear system in designing the system to gain expectant flying qualities and the combination of aerodynamic control surfaces with thrust vectors to delay the control surfaces getting into saturation, and the minimum N-norm generalized inverse theorem of weighted generalized inverse adopted to apportion the moments commands, which make the control surfaces gain appropriate deflection and the simulation results to verify the dynamic inverse control laws designed really make the system nonlinear offset and decouple; when one command is given, only this output will response, and others do not response; when all commands are given together, the responses will be just the linear superpose of the response of each command, therefore the operation of the pilot will be simplified greatly.

摘 要： ASTOVL升力风扇飞机是多变量、强耦合、复杂的非线性系统，采用非线性动态逆理论设计控制律以实现系统的非线性对消及解耦，然后，采用线性系统的设计方法对系统进行设计，以使系统获得期望的飞行品质。同时，考虑到ASTOVL升力风扇飞机是由气动舵面和推力矢量融合作用的，为了延缓各舵面进入饱和的时间，采用加权广义逆中的极小N-范数广义逆定理分配力矩指令，从而使各舵面达到适当的偏转角。并将所设计的控制律进行了仿真，结果验证了所设计的动态逆控制律使系统实现了非线性对消和解耦，单个指令作用时，只有该项响应，其余不受影响；所有指令作用时，其结果就等于单个指令作用时的线性叠加，这样使驾驶员的操纵大大简化而易于控制，从而大大降低了飞行事故率。

In chapter 4, the effects of orientation of rough surfaces on the lubrication behaviors of frictional pairs operating in the isothermal condition were studied and found that: the conclusion that the hydrodynamic load carrying capacity of transversely oriented surface is better than the isotropic surfaces is tenable only if the minimum clearance is relatively large, but the longitudinally oriented surfaces always decrease the load carrying capacity..

第四章在等温条件下，计算了粗糙表面的纹理方向对摩擦副润滑性能的影响，发现横向纹理表面具有比各向同性表面更大流体动力承载能力只有当最小间隙较大时才能显示出来，而纵向纹理表面总是使得流体承载能力下降。

Specifically, we apply the polar form in the conversion between triangular Bezier surfaces and rectangular Bezier surfaces. This problem helps us to understand the theory of polar form in a unified way. At the last half of this paper, we consider the problem of geometric continuity of parametric curves and parametric surfaces.

我们利用Polar形式实现了三角Bézier曲面和四边Bézier曲面之间的相互转化，同时通过应用，我们对Polar形式也有了一个统一、全面的认识；论文的后半部分考虑了参数曲线曲面间的几何连续性问题。

In relation to the feature extracting, the first step is to extract the "simple" surfaces such as planes, natural quadric surfaces and tori. Planes considered as degenerated quadric surfaces, the quadric surface feature extracting should be more important in RE.

而在点云的特征提取中，首先提取的是包括平面、自然二次曲面(包括球面、圆柱面、圆锥面)和圆环面的"简单"曲面，我们认为平面是一种退化了的二次曲面，因此研究二次曲面特征的提取是其中首要的课题。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了