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The definition, operation, properties, geometric meaning of quaternion and its three expressions are discussed. It is also demonstrated how to use quaternion to transform points.

本文详细叙述了四元数的这一功能，讨论了四元数的定义、运算、性质、几何意义和它的3种表达形式，给出了使用四元数处理点的各种几何变换的一般结论。

It can reflect the separability better than the criterion based on within-class and among-class distance,and has better geometric meaning.

这种判据优点是计算简单；不足是当类间距离较小、类内距离较大时，此判据仍有可能取得较大的值，而此时的

The new scheme can more intuitionally express geometric meaning of fold shape,possesses the effect of seeing its form knowing its name.

新方案可较直观地表示出褶皱形态的几何意义，具有见其名而知其形的效果。

The Article based on structural reliability theory and connected to the optimization model based on geometric meaning of reliability index, the study on the anti-slide stability of gravity dams is carried out RAGA.

文章以可靠度理论为基础，以基于可靠指标几何涵义的而建立的优化模型为联系，以基于实数编码的加速遗传算法为手段进行重力坝的抗滑稳定分析。

According to the geometric meaning of RTS, this paper proposes a technique of testing RTS of boundary point by the optimal value of BCC model, this testing method is concise and explicit.

本文根据规模收益的几何含义，仅仅从BCC模型的最优值出发，给出技术有效单元的规模收益判别方法，该方法简单准确。

Aiming at three-dimensional construction of point object,lease square-method is usually used in traditional method.But because it don't consider geometric meaning that the over-determined equation set is represent for,the precision of point object measured is low.

针对空间点目标的三维重构，传统的方法是采用最小二乘法进行的，但是由于最小二乘法没有考虑所建立的超定方程组所代表的几何意义，所以计算出的点坐标精度不高。

The reason why quaternion is used in flight simulation of fighter aircraft and the geometric meaning of quaternion are described,according to axis system used in flight simulation of fighter aircraft in China,three problems are introduced as follows:(1) quaternion kinematic equations,(2) relationship of quaternion and coordinate transformation matrix,(3) Euler angles in terms of quaternion.

阐述了在战斗机的飞行仿真中采用四元数的原因和四元数的几何意义，并按照中国战斗机飞行仿真中采用的坐标系，介绍了三个问题：四元数运动学方程；四元数与坐标变换矩阵的关系；用四元数表示的欧拉角。

To improve the accuracy of the coordinates of points,a model is described which consider the equation geometric meaning,making use of mid-point of crossover line to get 3D points coordinate.

三维坐标点计算方面，考虑方程组的几何意义，采用异面直线公垂线中点逼近三维空间点的方法，提高了点坐标的计算精度。

Three dimensional rotation represented by quaternion has two advantages over that by matrix: first, the geometric meaning is definitude; second, computation is easy.

用四元数表达三维的旋转与使用矩阵相比具有两个优点：第一，几何意义明确；第二，计算简单。

Aimed at the structural equation models with two latent variables and two blocks of indicators, the iterative process of PLS algorithm was analyzed and the algorithm geometric meaning has been demonstrated in this paper.

首先给出了含两个潜变量结构方程模型的路径图、模型设定方法以及迭代步骤、几何意义，然后将其推广到含多个潜变量结构方程模型的情况。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。