球面角

Compilation of the plane trigonometry and spherical trigonometry book, spherical trigonometry to solve some problems in, and first proposed the introduction of auxiliary angle method to solve the triangle .

编撰了有关平面三角学和球面三角学的著作，解决了球面三角学中的若干难题，并首先提出引进辅助角的方法解三角形。

Compilation of the plane trigonometry and spherical trigonometry book, spherical trigonometry to solve some problems in, and first proposed the method to solve the introduction of auxiliary angle triangles .

编撰了有关平面三角学和球面三角学的著作，解决了球面三角学中的若干难题，并首先提出引进辅助角的方法解三角形。

Prove that if this quantity is bounded above by that value of the Veronese surface then x is either a totally umbilical sphere or a conformal Veronese surface.

最后我们模仿3维的情况，引进一个保角不变量，并证明此保角不变量的上界若为Veronese曲面之值，则x不是全脐球面就是Veronese曲面的保角类。

We then introduce a conformal invariant quantity which is formulated in terms of the square of the length of the trace free part of the second fundamental form and the mean curvature, and prove that if this quantity is bounded above by that value of the Clifford torus then x is either a totally umbilical sphereor a conformal Clifford torus.

接著我们介绍一个由第二基本型式迹为零部份的张量长度平方与平均曲率形成的保角不变量，并证明此保角不变量的上界若为Clifford环面之值，则x不是全脐球面就是Clifford环面的保角类。

Cosine law of spherical triangles : in the spherical triangle , either side of the hot core corresponding to the cosine of angle equal to each other on both sides of the corresponding hot core product with the cosine angle on both sides of each angle of the sine and the corresponding spherical center piece of any side in the spherical triangle in ...

球面三角形余弦定律：在球面三角形中，任意一边所对应球心角的余弦等于其他两边各自对应球心角的余弦乘积加上这两边各自对应球心角的正弦及任意的那条边在球面三角形中。。。

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

In this chapter, three kinds of target recognition methods are performed, which are:①Target recognition method based on the description of polarization parameter plane. The echo polarization states of target are projected onto the polarization state plane described by the ellipticity ε and the tilt angle τ of the polarization ellipse, the change of parameter following ferquency becomes the chart. According to the changing trait of the chart, the multidimensional polarization feature space of target has been contructed. Furthermore, a series of polarization feature parameters used in designing the structure of target recognition device are extracted, and they are insensible to the posture of target.②Target recognition method based on the description of Poincare polarization sphere. The echo polarization states of target expressed by Stokes vector are projected onto the Poincare polarization sphere. The conception of polarization ferquency stability, which is used in describing the dynamic distribution characteristics of the target echo polarization states on Poincare polarization sphere, has been defined. A group of polarization feature parameters used in designing the structure of target recognition device are extracted, and they are insensible to the posture of target.③Target recognition method based on the description of frequency sensitivity. In accordance with the conception of the polarization state distance defined on Poincare polarization sphere, the frequency sensibility of the physical structure property of target has been investigated, the frequency distribution feature curves in PSD domain are obtained, and targets'features are extracted by means of the curve-fitting method with Least Square Criterion.

这章具体研究了基于三种极化散射特性描述的相应的目标识别方法：①基于极化参数平面描述的目标识别方法，将目标回波极化状态投影到以极化椭圆参数，即椭圆率角ε和倾角τ表征的极化状态平面上，参数随观测频率的变化就形成了图，根据图的变化特点构造了目标的多维极化特征空间，并提取了不敏感目标姿态变化的极化特征参数组来设计目标的识别器结构；②基于Poincare极化球面描述的目标识别方法，采用Stokes矢量表征目标回波的极化状态，并将其投影到描述极化状态的Poincare极化球面上，定义了极化频率稳定度的概念用以刻画目标回波极化状态在Poincare极化球面上的动态分布信息，提取了准方位不变性的目标极化特征，最后设计了目标的识别器结构；③基于频率敏感性描述的目标识别方法，通过在Poincare极化球面上所定义的极化状态距离的概念，研究的是复杂目标物理结构特性对探测信号频率的敏感程度问题，获得了在极化状态距离下的频率分布特性曲线，采用最小二乘估计曲线拟合方法，它既用于极化特征的降维，同时又直接将拟合参数作为目标的分类特征。

Spherical trigonometry is a part of spherical geometry, mainly in the processing, discovery and interpretation of polygons on the spherical surface contact angle and the edge and relevance.

球面三角学是球面几何学的一部分，主要在处理、发现和解释多边形在球面上的角与边的联系和关联。

Ah specifically, the angle of the sphere and the relationship side of spherical geometry, spherical trigonometry is a part, mainly in the processing, discovery and interpretation of polygons on the spherical surface contact angle and the edge and relevance.

具体一点啊研究球面上的角与边的关系球面三角学是球面几何学的一部分，主要在处理、发现和解释多边形在球面上的角与边的联系和关联。

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。