四元数

Firstly, the key frames are created by the methods of inverse kinematics. Then, the internal key frames are computed by the interpolation of spline curve and spherical linear.

首先使用逆运动学方法求出关键状态，然后使用样条插值和四元数球状线性插值方法计算中间状态，完成跑步的过程。

The algebra of quaternions, the first noncommutative algebra was thus sudd ly born.

四元数的代数，第一非交换的代数，就这样在一夜之间诞生了。

Considering the influence of the layout of the attitude control, thruster forces are taken as the control input directly.

在对内动态分析的基础上，针对线性子系统设计了四元数PD反馈控制律。

A modified PID control law and an uncoupled variable structure control law all based on the error-quaternion are developed.

姿态控制系统研究：首先基于全局非奇异的误差四元数分别设计了改进的PID控制律和解耦变结构控制律。

Based on the unit quaternion decomposition of rotation matrix, this paper puts forward an algorithm to estimate motion parameters from the space position vectors of 3D feature points.

摘要本文基于旋转矩阵单位四元数分解定理，提出一种由3D特征点空间位置估计运动参数的算法。

The ellipse curre equation of circular image is derived based on the theory of spatial analytic geometry and rotation matrix s representation with unit quaternion then a mathematical model of the distortion error is established which relates the distortion error to the foca length of the used CCD camera,the radius as well as the position and the attitude of the inspected circle directly.

研究三维视觉检测中圆的中心经针孔摄像机成像后存在畸变误差的问题，首先基于空间解析几何理论和旋转矩阵的四元数表示法推导出像平面上投影椭圆的参数方程；然后根据参数方程建立圆中心成像畸变误差的数学模型；最后对影响畸变误差的主要因素进行分析。

If the norm is 1, you have a so-called unit quaternion (just as you would have a unit vector).

假如平均值为1，你就得到所谓的单位四元数。

I have avoided osg::Quat::slerp which interpolates between two quaternions as it is less accurate for our purposes.

我避免OSG的：：葛：：slerp这两个四元数插值，因为这是我们的目的不准确）。

We also give a method to compute the singular eigenvalues of some special quaternionic matrixes in this paper.

本文还给出了计算一些特殊四元数矩阵一个或多个奇异特征值的方法。

Quaternions are a compact, unintuitive way of representing rotations.

四元数是表现旋转的结实的、非直观的方法。

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。