Vector is a useless survival, or offshoot from quaternions.
向量是无用的幸存物或四元数的无价值的支流。
You pretty much know all the important stuff about quaternions now.
你现在几乎获得了所有关于四元数的重要信息。
Except for one thing: you don't have a good reason to use quaternions yet.
但除了一件事情，你还没有明白为何要使用四元数的原因。
The attitude kinematics and dynamics are both described by error quaternions.
姿态运动学和动力学用误差四元数描述。
Quaternions are used to describe the attitude of the rigid body system in this paper.
采用四元数法描述了刚体姿态系统。
The criterion of equality of two quaternions is that their scalar parts shall be equal.
两个四元数相等的准则是，它们的数量部分相等。
Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions.
四元数将三维中旋转的概念扩展到四维中的旋转。
Of course, you'll also need to be able to convert from "conventional" representations to quaternions.
当然，你可能也会用到四元数转换的“常规”表示法。
The matrices in CwMtx include vectors and square matrices, where vectors include space vectors and quaternions.
CwMtx中的矩阵包括向量和方阵，其中向量包括空间向量和四元数。
Quaternions do not suffer from gimbal lock, because they do not express rotations relative to three separate axes.
四元数就不会遭受万向节锁的痛苦，因为它不用三个分离的轴表示旋转。
Only the bone data needs to be stored for every frame of the animation. Usually, the bone data is represented by quaternions.
存储动画帧我们仅仅需要骨胳的数据。通常，骨胳数据由四元数表示。
The second argument that is commonly given for the use of quaternions is the possibility of smoothly interpolating between two orientations.
使用四元数的第二个理由，就是其可实现两个状态间的平滑插值。
However, it was later discovered that quaternions can also be used in computer graphics, as an alternative and compact way to represent rotations.
然而，人们发现四元数也可以应用在计算机图形学上，作为表现旋转的可选择方法之一。
Quaternions make it possible to extend the concept of rotation in three dimensions to four dimensions (see Resources for links to quaternion references).
四元数可能把三维旋转的概念推广到四维(请参阅参考资料，其中有四元数的参考资料的链接)。
With the help of the theory of quaternions the theorems of commutativity of composition for the finite rotation of rigid body are proved in the any order.
借助于四元数理论证明了任意顺序下刚体有限转动合成的可交换性定理。
The paper shows that the method of proving the commutative property of composition for the finite rotations by quaternions is simpler than that by vectors.
文中表明用四元数方法证明该定理比矢量法更为简单。
Compared to the Euler angles the main advantage of the quaternions expression of attitude motion is the avoidance of singular position in numeration procedure.
与欧拉角比较，姿态运动的四元数表达的主要优点是数值计算过程中不存在奇异位置。
Several weakly controled inequalities with relation to trace of quaternions matrices are proved, and relevant results in some references are generalized and improved.
证明了几个与四元数矩阵迹有关的弱控制不等式，推广、改进了有关文献的相应结果。
First, the probabilistic model of the rounding error in the computation of quaternions on a fixed point computer is established. Then, the probabilistic rounding error estimates are computed.
首先，对于定点计算机上四元数计算的舍入误差建立了概率模型，然后对舍入误差进行概率估计。
Indeed, quaternions support spherical linear interpolation (abbreviated as SLERP), which means that points travel along the surface of a sphere as they are moved from one orientation to the next.
的确，四元数支持球形线性插值(SLERP)，那意味着点沿着球体表面传播就像他们从一个方位移到另外一个一样。
Indeed, quaternions support spherical linear interpolation (abbreviated as SLERP), which means that points travel along the surface of a sphere as they are moved from one orientation to the next.
的确，四元数支持球形线性插值(SLERP)，那意味着点沿着球体表面传播就像他们从一个方位移到另外一个一样。
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