1 平移和旋转变换
1.1 平移变换
F = [ n x o x a x p x n y o y a x p y n z o z a x p z 0 0 0 1 ] F = \begin{bmatrix} n_x & o_x & a_x & p_x \\ n_y & o_y & a_x & p_y \\ n_z & o_z & a_x & p_z \\ 0 & 0 & 0 & 1 \end{bmatrix} F=⎣ ⎡nxnynz0oxoyoz0axaxax0pxpypz1⎦ ⎤
1.2 旋转变换
1.2.1 绕x轴变换
R o t ( x , θ ) = [ 1 0 0 0 c o s ( θ ) s i n ( θ ) 0 − s i n ( θ ) c o s ( θ ) ] Rot(x,\theta) = \begin{bmatrix} 1 & 0 & 0 \\ 0 & cos(\theta) & sin(\theta) \\ 0 & -sin(\theta) & cos(\theta) \end{bmatrix} Rot(x,θ)=⎣ ⎡1000cos(θ)−sin(θ)0sin(θ)cos(θ)⎦ ⎤
1.2.2 绕y轴变换
R o t ( y , θ ) = [ c o s ( θ ) 0 s i n ( θ ) 0 1 0 − s i n ( θ ) 0 c o s ( θ ) ] Rot(y,\theta) = \begin{bmatrix} cos(\theta) & 0 & sin(\theta) \\ 0 & 1 & 0 \\ -sin(\theta) & 0 & cos(\theta) \end{bmatrix} Rot(y,θ)=⎣ ⎡cos(θ)0−sin(θ)010sin(θ)0cos(θ)⎦ ⎤
1.2.3 绕z轴变换
R o t ( z , θ ) = [ c o s ( θ ) − s i n ( θ ) 0 s i n ( θ ) c o s ( θ ) 0 0 0 1 ] Rot(z,\theta) = \begin{bmatrix} cos(\theta) & -sin(\theta) & 0 \\ sin(\theta) & cos(\theta) & 0 \\ 0 & 0 & 1 \end{bmatrix} Rot(z,θ)=⎣ ⎡cos(θ)sin(θ)0−sin(θ)cos(θ)0001⎦ ⎤
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