Quaternion 计算3D物体旋转角度

 在3D程序中，通常用quaternion来计算3D物体的旋转角度，与Matrix相比，quaternion更加高效，占用的储存空间更小，此外也更便于插值。在数学上，quaternion表示复数w+xi+yj+zk，其中i,j,k都是虚数单位。

 

可以把quaternion看做一个标量和一个3D向量的组合。实部w表示标量，虚部表示向量标记为V，或三个单独的分量（x,y,z）。所以quaternion可以记为[w,V]或[ w,x,y,z]。对quaternion最大的误解在于认为w表示旋转角度，V表示旋转轴，正确的理解应该是w与旋转角度有关，v与旋转轴有关。

 

unity3d里的Quaternion自带了一些方便的改变形式：

 

AngleAxis	Creates a rotation which rotates angle degrees around axis.
FromToRotation	Creates a rotation which rotates from fromDirection to toDirection.
LookRotation	Creates a rotation that looks along forward with the the head upwards along upwards
Slerp	Spherically interpolates from towards to by t.
Lerp	Interpolates from towards to by t and normalizes the result afterwards.
Inverse	Returns the Inverse of rotation.
Angle	Returns the angle in degrees between two rotations a and b.
Euler	Returns a rotation that rotates x degrees around the x axis. y degrees around the y axis. z degrees around the z axis.

本文来自：http://www.meebe.net/blog/article/unity3d/u3d_quater.html