以下不加证明地给出在世界坐标系中,以坐标点(0,0,0)为原点的旋转矩阵
包含平移的线性变换称作仿射变换,3D中的仿射变换不能用 3 x 3 矩阵表达,必须使用4 x 4矩阵
1.绕X坐标轴旋转
|1 0 0 0|
|0 cos(a) sin(a) 0|
|0 -sin(a) cos(a) 0|
|0 0 0 1|
2.绕Y坐标轴旋转
|cos(a) 0 -sin(a) 0|
|0 1 sin(a) 0|
|sin(a) 0 cos(a) 0|
|0 0 0 1|
3.绕Z坐标轴旋转
|cos(a) sin(a) 0 0|
|-sin(a) cos(a) 1 0|
|0 0 1 0|
|0 0 0 1|
4.绕任意向量n(x,y,z)旋转a角度
|x*x(1-cos(a)+cos(a) xy(1-cos(a))+zsin(a) xz(1-cos(a))-ysin(a) 0|
|xy(1-cos(a))-zsin(a) y*y(1-cos(a))+cos(a) yz(1-cos(a))+xsin(a) 0|
|xz(1-cos(a))+ysin(a) yz(1-cos(a))-xsin(a) z*z(1-cos(a))+cos(a) 0|
|0 0 0 1|