ogre中四元数的问题

daijunhua

在camera以及其他的涉及位置和方位变换的地方都使用了四元数的乘，有点不明白，四元数乘以一个向量怎样说明一个方向呢？请高人指教！

Enigmaya

While walking by the Royal Canal in Dublin on a Monday in October 1843, Hamilton realized
that four numbers are needed to describe a rotation followed by a scaling. One number describes
the size of the scaling, one the number of degrees to be rotated, and the last two numbers
give the plane(*) in which the vector should be rotated.

After this insight, Hamilton found a closed multiplication for four-dimensional complex numbers of the form ix + jy + kz, where i2 = j2 = k2 = ijk = 􀀀1.

Hamilton dubbed his four-dimensional complex numbers quaternions.
The parallel to ordinary complex numbers stems from the imaginary parts.
A quaternion is usually written [s; v]; s 2 R; v 2 R3 . Here s is called the scalar part, and
v = (x; y; z) is the vector part.

===========
* The xy plane can be rotated to any plane in xyz space through the origin by giving the rotation angles about the x and y axes.

摘自：Quaternions, Interpolation and Animation 可以搜搜，详细讲四元数的。

PS： 不过这种涉及本质的问题，不太好有直观的认识。如矩阵为什么能表示旋转？显然不是直观上的乘法这么简单。所谓的“第二代数学模型”。

BNSummer

四元数的含义是围绕某一特定旋转轴旋转某一特定的角度，
将四元数表示的旋转作用于一个向量有其特殊的定义，
具体四元数也好，旋转矩阵也好，只是一个数学上的表示方法而已。
真正的目的还是对向量的分量进行操作。

daijunhua

谢谢楼上的解答！